%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG185+1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 04:58:34 AM UTC 2025
% Result : Theorem 0.18s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG185+1 : TPTP v9.0.0. Released v2.7.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n011.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 10:48:41 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.39 % SZS status Theorem
% 0.18/0.39 % SZS output start Proof
% 0.18/0.39 tff(e11_type, type, (
% 0.18/0.39 e11: $i)).
% 0.18/0.39 tff(j_type, type, (
% 0.18/0.39 j: $i > $i)).
% 0.18/0.39 tff(e21_type, type, (
% 0.18/0.39 e21: $i)).
% 0.18/0.39 tff(e24_type, type, (
% 0.18/0.39 e24: $i)).
% 0.18/0.39 tff(e23_type, type, (
% 0.18/0.39 e23: $i)).
% 0.18/0.39 tff(h_type, type, (
% 0.18/0.39 h: $i > $i)).
% 0.18/0.39 tff(e12_type, type, (
% 0.18/0.39 e12: $i)).
% 0.18/0.39 tff(e14_type, type, (
% 0.18/0.39 e14: $i)).
% 0.18/0.39 tff(e13_type, type, (
% 0.18/0.39 e13: $i)).
% 0.18/0.39 tff(e10_type, type, (
% 0.18/0.39 e10: $i)).
% 0.18/0.39 tff(e22_type, type, (
% 0.18/0.39 e22: $i)).
% 0.18/0.39 tff(e20_type, type, (
% 0.18/0.39 e20: $i)).
% 0.18/0.39 tff(op1_type, type, (
% 0.18/0.39 op1: ( $i * $i ) > $i)).
% 0.18/0.39 tff(op2_type, type, (
% 0.18/0.39 op2: ( $i * $i ) > $i)).
% 0.18/0.39 tff(1,plain,
% 0.18/0.39 ((h(j(e23)) = e23) <=> (h(j(e23)) = e23)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(2,plain,
% 0.18/0.39 ((~(((((((((((((((h(e10) = e20) | (h(e10) = e21)) | (h(e10) = e22)) | (h(e10) = e23)) | (h(e10) = e24)) & (((((h(e11) = e20) | (h(e11) = e21)) | (h(e11) = e22)) | (h(e11) = e23)) | (h(e11) = e24))) & (((((h(e12) = e20) | (h(e12) = e21)) | (h(e12) = e22)) | (h(e12) = e23)) | (h(e12) = e24))) & (((((h(e13) = e20) | (h(e13) = e21)) | (h(e13) = e22)) | (h(e13) = e23)) | (h(e13) = e24))) & (((((h(e14) = e20) | (h(e14) = e21)) | (h(e14) = e22)) | (h(e14) = e23)) | (h(e14) = e24))) & (((((j(e20) = e10) | (j(e20) = e11)) | (j(e20) = e12)) | (j(e20) = e13)) | (j(e20) = e14))) & (((((j(e21) = e10) | (j(e21) = e11)) | (j(e21) = e12)) | (j(e21) = e13)) | (j(e21) = e14))) & (((((j(e22) = e10) | (j(e22) = e11)) | (j(e22) = e12)) | (j(e22) = e13)) | (j(e22) = e14))) & (((((j(e23) = e10) | (j(e23) = e11)) | (j(e23) = e12)) | (j(e23) = e13)) | (j(e23) = e14))) & (((((j(e24) = e10) | (j(e24) = e11)) | (j(e24) = e12)) | (j(e24) = e13)) | (j(e24) = e14))) => (~((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((h(op1(e10, e10)) = op2(h(e10), h(e10))) & (h(op1(e10, e11)) = op2(h(e10), h(e11)))) & (h(op1(e10, e12)) = op2(h(e10), h(e12)))) & (h(op1(e10, e13)) = op2(h(e10), h(e13)))) & (h(op1(e10, e14)) = op2(h(e10), h(e14)))) & (h(op1(e11, e10)) = op2(h(e11), h(e10)))) & (h(op1(e11, e11)) = op2(h(e11), h(e11)))) & (h(op1(e11, e12)) = op2(h(e11), h(e12)))) & (h(op1(e11, e13)) = op2(h(e11), h(e13)))) & (h(op1(e11, e14)) = op2(h(e11), h(e14)))) & (h(op1(e12, e10)) = op2(h(e12), h(e10)))) & (h(op1(e12, e11)) = op2(h(e12), h(e11)))) & (h(op1(e12, e12)) = op2(h(e12), h(e12)))) & (h(op1(e12, e13)) = op2(h(e12), h(e13)))) & (h(op1(e12, e14)) = op2(h(e12), h(e14)))) & (h(op1(e13, e10)) = op2(h(e13), h(e10)))) & (h(op1(e13, e11)) = op2(h(e13), h(e11)))) & (h(op1(e13, e12)) = op2(h(e13), h(e12)))) & (h(op1(e13, e13)) = op2(h(e13), h(e13)))) & (h(op1(e13, e14)) = op2(h(e13), h(e14)))) & (h(op1(e14, e10)) = op2(h(e14), h(e10)))) & (h(op1(e14, e11)) = op2(h(e14), h(e11)))) & (h(op1(e14, e12)) = op2(h(e14), h(e12)))) & (h(op1(e14, e13)) = op2(h(e14), h(e13)))) & (h(op1(e14, e14)) = op2(h(e14), h(e14)))) & (j(op2(e20, e20)) = op1(j(e20), j(e20)))) & (j(op2(e20, e21)) = op1(j(e20), j(e21)))) & (j(op2(e20, e22)) = op1(j(e20), j(e22)))) & (j(op2(e20, e23)) = op1(j(e20), j(e23)))) & (j(op2(e20, e24)) = op1(j(e20), j(e24)))) & (j(op2(e21, e20)) = op1(j(e21), j(e20)))) & (j(op2(e21, e21)) = op1(j(e21), j(e21)))) & (j(op2(e21, e22)) = op1(j(e21), j(e22)))) & (j(op2(e21, e23)) = op1(j(e21), j(e23)))) & (j(op2(e21, e24)) = op1(j(e21), j(e24)))) & (j(op2(e22, e20)) = op1(j(e22), j(e20)))) & (j(op2(e22, e21)) = op1(j(e22), j(e21)))) & (j(op2(e22, e22)) = op1(j(e22), j(e22)))) & (j(op2(e22, e23)) = op1(j(e22), j(e23)))) & (j(op2(e22, e24)) = op1(j(e22), j(e24)))) & (j(op2(e23, e20)) = op1(j(e23), j(e20)))) & (j(op2(e23, e21)) = op1(j(e23), j(e21)))) & (j(op2(e23, e22)) = op1(j(e23), j(e22)))) & (j(op2(e23, e23)) = op1(j(e23), j(e23)))) & (j(op2(e23, e24)) = op1(j(e23), j(e24)))) & (j(op2(e24, e20)) = op1(j(e24), j(e20)))) & (j(op2(e24, e21)) = op1(j(e24), j(e21)))) & (j(op2(e24, e22)) = op1(j(e24), j(e22)))) & (j(op2(e24, e23)) = op1(j(e24), j(e23)))) & (j(op2(e24, e24)) = op1(j(e24), j(e24)))) & (h(j(e20)) = e20)) & (h(j(e21)) = e21)) & (h(j(e22)) = e22)) & (h(j(e23)) = e23)) & (h(j(e24)) = e24)) & (j(h(e10)) = e10)) & (j(h(e11)) = e11)) & (j(h(e12)) = e12)) & (j(h(e13)) = e13)) & (j(h(e14)) = e14))))) <=> (~((~(((h(e10) = e20) | (h(e10) = e21) | (h(e10) = e22) | (h(e10) = e23) | (h(e10) = e24)) & ((h(e11) = e20) | (h(e11) = e21) | (h(e11) = e22) | (h(e11) = e23) | (h(e11) = e24)) & ((h(e12) = e20) | (h(e12) = e21) | (h(e12) = e22) | (h(e12) = e23) | (h(e12) = e24)) & ((h(e13) = e20) | (h(e13) = e21) | (h(e13) = e22) | (h(e13) = e23) | (h(e13) = e24)) & ((h(e14) = e20) | (h(e14) = e21) | (h(e14) = e22) | (h(e14) = e23) | (h(e14) = e24)) & ((j(e20) = e10) | (j(e20) = e11) | (j(e20) = e12) | (j(e20) = e13) | (j(e20) = e14)) & ((j(e21) = e10) | (j(e21) = e11) | (j(e21) = e12) | (j(e21) = e13) | (j(e21) = e14)) & ((j(e22) = e10) | (j(e22) = e11) | (j(e22) = e12) | (j(e22) = e13) | (j(e22) = e14)) & ((j(e23) = e10) | (j(e23) = e11) | (j(e23) = e12) | (j(e23) = e13) | (j(e23) = e14)) & ((j(e24) = e10) | (j(e24) = e11) | (j(e24) = e12) | (j(e24) = e13) | (j(e24) = e14)))) | (~((h(op1(e10, e10)) = op2(h(e10), h(e10))) & (h(op1(e10, e11)) = op2(h(e10), h(e11))) & (h(op1(e10, e12)) = op2(h(e10), h(e12))) & (h(op1(e10, e13)) = op2(h(e10), h(e13))) & (h(op1(e10, e14)) = op2(h(e10), h(e14))) & (h(op1(e11, e10)) = op2(h(e11), h(e10))) & (h(op1(e11, e11)) = op2(h(e11), h(e11))) & (h(op1(e11, e12)) = op2(h(e11), h(e12))) & (h(op1(e11, e13)) = op2(h(e11), h(e13))) & (h(op1(e11, e14)) = op2(h(e11), h(e14))) & (h(op1(e12, e10)) = op2(h(e12), h(e10))) & (h(op1(e12, e11)) = op2(h(e12), h(e11))) & (h(op1(e12, e12)) = op2(h(e12), h(e12))) & (h(op1(e12, e13)) = op2(h(e12), h(e13))) & (h(op1(e12, e14)) = op2(h(e12), h(e14))) & (h(op1(e13, e10)) = op2(h(e13), h(e10))) & (h(op1(e13, e11)) = op2(h(e13), h(e11))) & (h(op1(e13, e12)) = op2(h(e13), h(e12))) & (h(op1(e13, e13)) = op2(h(e13), h(e13))) & (h(op1(e13, e14)) = op2(h(e13), h(e14))) & (h(op1(e14, e10)) = op2(h(e14), h(e10))) & (h(op1(e14, e11)) = op2(h(e14), h(e11))) & (h(op1(e14, e12)) = op2(h(e14), h(e12))) & (h(op1(e14, e13)) = op2(h(e14), h(e13))) & (h(op1(e14, e14)) = op2(h(e14), h(e14))) & (j(op2(e20, e20)) = op1(j(e20), j(e20))) & (j(op2(e20, e21)) = op1(j(e20), j(e21))) & (j(op2(e20, e22)) = op1(j(e20), j(e22))) & (j(op2(e20, e23)) = op1(j(e20), j(e23))) & (j(op2(e20, e24)) = op1(j(e20), j(e24))) & (j(op2(e21, e20)) = op1(j(e21), j(e20))) & (j(op2(e21, e21)) = op1(j(e21), j(e21))) & (j(op2(e21, e22)) = op1(j(e21), j(e22))) & (j(op2(e21, e23)) = op1(j(e21), j(e23))) & (j(op2(e21, e24)) = op1(j(e21), j(e24))) & (j(op2(e22, e20)) = op1(j(e22), j(e20))) & (j(op2(e22, e21)) = op1(j(e22), j(e21))) & (j(op2(e22, e22)) = op1(j(e22), j(e22))) & (j(op2(e22, e23)) = op1(j(e22), j(e23))) & (j(op2(e22, e24)) = op1(j(e22), j(e24))) & (j(op2(e23, e20)) = op1(j(e23), j(e20))) & (j(op2(e23, e21)) = op1(j(e23), j(e21))) & (j(op2(e23, e22)) = op1(j(e23), j(e22))) & (j(op2(e23, e23)) = op1(j(e23), j(e23))) & (j(op2(e23, e24)) = op1(j(e23), j(e24))) & (j(op2(e24, e20)) = op1(j(e24), j(e20))) & (j(op2(e24, e21)) = op1(j(e24), j(e21))) & (j(op2(e24, e22)) = op1(j(e24), j(e22))) & (j(op2(e24, e23)) = op1(j(e24), j(e23))) & (j(op2(e24, e24)) = op1(j(e24), j(e24))) & (h(j(e20)) = e20) & (h(j(e21)) = e21) & (h(j(e22)) = e22) & (h(j(e23)) = e23) & (h(j(e24)) = e24) & (j(h(e10)) = e10) & (j(h(e11)) = e11) & (j(h(e12)) = e12) & (j(h(e13)) = e13) & (j(h(e14)) = e14)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(3,axiom,(~(((((((((((((((h(e10) = e20) | (h(e10) = e21)) | (h(e10) = e22)) | (h(e10) = e23)) | (h(e10) = e24)) & (((((h(e11) = e20) | (h(e11) = e21)) | (h(e11) = e22)) | (h(e11) = e23)) | (h(e11) = e24))) & (((((h(e12) = e20) | (h(e12) = e21)) | (h(e12) = e22)) | (h(e12) = e23)) | (h(e12) = e24))) & (((((h(e13) = e20) | (h(e13) = e21)) | (h(e13) = e22)) | (h(e13) = e23)) | (h(e13) = e24))) & (((((h(e14) = e20) | (h(e14) = e21)) | (h(e14) = e22)) | (h(e14) = e23)) | (h(e14) = e24))) & (((((j(e20) = e10) | (j(e20) = e11)) | (j(e20) = e12)) | (j(e20) = e13)) | (j(e20) = e14))) & (((((j(e21) = e10) | (j(e21) = e11)) | (j(e21) = e12)) | (j(e21) = e13)) | (j(e21) = e14))) & (((((j(e22) = e10) | (j(e22) = e11)) | (j(e22) = e12)) | (j(e22) = e13)) | (j(e22) = e14))) & (((((j(e23) = e10) | (j(e23) = e11)) | (j(e23) = e12)) | (j(e23) = e13)) | (j(e23) = e14))) & (((((j(e24) = e10) | (j(e24) = e11)) | (j(e24) = e12)) | (j(e24) = e13)) | (j(e24) = e14))) => (~((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((h(op1(e10, e10)) = op2(h(e10), h(e10))) & (h(op1(e10, e11)) = op2(h(e10), h(e11)))) & (h(op1(e10, e12)) = op2(h(e10), h(e12)))) & (h(op1(e10, e13)) = op2(h(e10), h(e13)))) & (h(op1(e10, e14)) = op2(h(e10), h(e14)))) & (h(op1(e11, e10)) = op2(h(e11), h(e10)))) & (h(op1(e11, e11)) = op2(h(e11), h(e11)))) & (h(op1(e11, e12)) = op2(h(e11), h(e12)))) & (h(op1(e11, e13)) = op2(h(e11), h(e13)))) & (h(op1(e11, e14)) = op2(h(e11), h(e14)))) & (h(op1(e12, e10)) = op2(h(e12), h(e10)))) & (h(op1(e12, e11)) = op2(h(e12), h(e11)))) & (h(op1(e12, e12)) = op2(h(e12), h(e12)))) & (h(op1(e12, e13)) = op2(h(e12), h(e13)))) & (h(op1(e12, e14)) = op2(h(e12), h(e14)))) & (h(op1(e13, e10)) = op2(h(e13), h(e10)))) & (h(op1(e13, e11)) = op2(h(e13), h(e11)))) & (h(op1(e13, e12)) = op2(h(e13), h(e12)))) & (h(op1(e13, e13)) = op2(h(e13), h(e13)))) & (h(op1(e13, e14)) = op2(h(e13), h(e14)))) & (h(op1(e14, e10)) = op2(h(e14), h(e10)))) & (h(op1(e14, e11)) = op2(h(e14), h(e11)))) & (h(op1(e14, e12)) = op2(h(e14), h(e12)))) & (h(op1(e14, e13)) = op2(h(e14), h(e13)))) & (h(op1(e14, e14)) = op2(h(e14), h(e14)))) & (j(op2(e20, e20)) = op1(j(e20), j(e20)))) & (j(op2(e20, e21)) = op1(j(e20), j(e21)))) & (j(op2(e20, e22)) = op1(j(e20), j(e22)))) & (j(op2(e20, e23)) = op1(j(e20), j(e23)))) & (j(op2(e20, e24)) = op1(j(e20), j(e24)))) & (j(op2(e21, e20)) = op1(j(e21), j(e20)))) & (j(op2(e21, e21)) = op1(j(e21), j(e21)))) & (j(op2(e21, e22)) = op1(j(e21), j(e22)))) & (j(op2(e21, e23)) = op1(j(e21), j(e23)))) & (j(op2(e21, e24)) = op1(j(e21), j(e24)))) & (j(op2(e22, e20)) = op1(j(e22), j(e20)))) & (j(op2(e22, e21)) = op1(j(e22), j(e21)))) & (j(op2(e22, e22)) = op1(j(e22), j(e22)))) & (j(op2(e22, e23)) = op1(j(e22), j(e23)))) & (j(op2(e22, e24)) = op1(j(e22), j(e24)))) & (j(op2(e23, e20)) = op1(j(e23), j(e20)))) & (j(op2(e23, e21)) = op1(j(e23), j(e21)))) & (j(op2(e23, e22)) = op1(j(e23), j(e22)))) & (j(op2(e23, e23)) = op1(j(e23), j(e23)))) & (j(op2(e23, e24)) = op1(j(e23), j(e24)))) & (j(op2(e24, e20)) = op1(j(e24), j(e20)))) & (j(op2(e24, e21)) = op1(j(e24), j(e21)))) & (j(op2(e24, e22)) = op1(j(e24), j(e22)))) & (j(op2(e24, e23)) = op1(j(e24), j(e23)))) & (j(op2(e24, e24)) = op1(j(e24), j(e24)))) & (h(j(e20)) = e20)) & (h(j(e21)) = e21)) & (h(j(e22)) = e22)) & (h(j(e23)) = e23)) & (h(j(e24)) = e24)) & (j(h(e10)) = e10)) & (j(h(e11)) = e11)) & (j(h(e12)) = e12)) & (j(h(e13)) = e13)) & (j(h(e14)) = e14))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.18/0.40 tff(4,plain,
% 0.18/0.40 (~((~(((h(e10) = e20) | (h(e10) = e21) | (h(e10) = e22) | (h(e10) = e23) | (h(e10) = e24)) & ((h(e11) = e20) | (h(e11) = e21) | (h(e11) = e22) | (h(e11) = e23) | (h(e11) = e24)) & ((h(e12) = e20) | (h(e12) = e21) | (h(e12) = e22) | (h(e12) = e23) | (h(e12) = e24)) & ((h(e13) = e20) | (h(e13) = e21) | (h(e13) = e22) | (h(e13) = e23) | (h(e13) = e24)) & ((h(e14) = e20) | (h(e14) = e21) | (h(e14) = e22) | (h(e14) = e23) | (h(e14) = e24)) & ((j(e20) = e10) | (j(e20) = e11) | (j(e20) = e12) | (j(e20) = e13) | (j(e20) = e14)) & ((j(e21) = e10) | (j(e21) = e11) | (j(e21) = e12) | (j(e21) = e13) | (j(e21) = e14)) & ((j(e22) = e10) | (j(e22) = e11) | (j(e22) = e12) | (j(e22) = e13) | (j(e22) = e14)) & ((j(e23) = e10) | (j(e23) = e11) | (j(e23) = e12) | (j(e23) = e13) | (j(e23) = e14)) & ((j(e24) = e10) | (j(e24) = e11) | (j(e24) = e12) | (j(e24) = e13) | (j(e24) = e14)))) | (~((h(op1(e10, e10)) = op2(h(e10), h(e10))) & (h(op1(e10, e11)) = op2(h(e10), h(e11))) & (h(op1(e10, e12)) = op2(h(e10), h(e12))) & (h(op1(e10, e13)) = op2(h(e10), h(e13))) & (h(op1(e10, e14)) = op2(h(e10), h(e14))) & (h(op1(e11, e10)) = op2(h(e11), h(e10))) & (h(op1(e11, e11)) = op2(h(e11), h(e11))) & (h(op1(e11, e12)) = op2(h(e11), h(e12))) & (h(op1(e11, e13)) = op2(h(e11), h(e13))) & (h(op1(e11, e14)) = op2(h(e11), h(e14))) & (h(op1(e12, e10)) = op2(h(e12), h(e10))) & (h(op1(e12, e11)) = op2(h(e12), h(e11))) & (h(op1(e12, e12)) = op2(h(e12), h(e12))) & (h(op1(e12, e13)) = op2(h(e12), h(e13))) & (h(op1(e12, e14)) = op2(h(e12), h(e14))) & (h(op1(e13, e10)) = op2(h(e13), h(e10))) & (h(op1(e13, e11)) = op2(h(e13), h(e11))) & (h(op1(e13, e12)) = op2(h(e13), h(e12))) & (h(op1(e13, e13)) = op2(h(e13), h(e13))) & (h(op1(e13, e14)) = op2(h(e13), h(e14))) & (h(op1(e14, e10)) = op2(h(e14), h(e10))) & (h(op1(e14, e11)) = op2(h(e14), h(e11))) & (h(op1(e14, e12)) = op2(h(e14), h(e12))) & (h(op1(e14, e13)) = op2(h(e14), h(e13))) & (h(op1(e14, e14)) = op2(h(e14), h(e14))) & (j(op2(e20, e20)) = op1(j(e20), j(e20))) & (j(op2(e20, e21)) = op1(j(e20), j(e21))) & (j(op2(e20, e22)) = op1(j(e20), j(e22))) & (j(op2(e20, e23)) = op1(j(e20), j(e23))) & (j(op2(e20, e24)) = op1(j(e20), j(e24))) & (j(op2(e21, e20)) = op1(j(e21), j(e20))) & (j(op2(e21, e21)) = op1(j(e21), j(e21))) & (j(op2(e21, e22)) = op1(j(e21), j(e22))) & (j(op2(e21, e23)) = op1(j(e21), j(e23))) & (j(op2(e21, e24)) = op1(j(e21), j(e24))) & (j(op2(e22, e20)) = op1(j(e22), j(e20))) & (j(op2(e22, e21)) = op1(j(e22), j(e21))) & (j(op2(e22, e22)) = op1(j(e22), j(e22))) & (j(op2(e22, e23)) = op1(j(e22), j(e23))) & (j(op2(e22, e24)) = op1(j(e22), j(e24))) & (j(op2(e23, e20)) = op1(j(e23), j(e20))) & (j(op2(e23, e21)) = op1(j(e23), j(e21))) & (j(op2(e23, e22)) = op1(j(e23), j(e22))) & (j(op2(e23, e23)) = op1(j(e23), j(e23))) & (j(op2(e23, e24)) = op1(j(e23), j(e24))) & (j(op2(e24, e20)) = op1(j(e24), j(e20))) & (j(op2(e24, e21)) = op1(j(e24), j(e21))) & (j(op2(e24, e22)) = op1(j(e24), j(e22))) & (j(op2(e24, e23)) = op1(j(e24), j(e23))) & (j(op2(e24, e24)) = op1(j(e24), j(e24))) & (h(j(e20)) = e20) & (h(j(e21)) = e21) & (h(j(e22)) = e22) & (h(j(e23)) = e23) & (h(j(e24)) = e24) & (j(h(e10)) = e10) & (j(h(e11)) = e11) & (j(h(e12)) = e12) & (j(h(e13)) = e13) & (j(h(e14)) = e14))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.18/0.41 tff(5,plain,
% 0.18/0.41 ((h(op1(e10, e10)) = op2(h(e10), h(e10))) & (h(op1(e10, e11)) = op2(h(e10), h(e11))) & (h(op1(e10, e12)) = op2(h(e10), h(e12))) & (h(op1(e10, e13)) = op2(h(e10), h(e13))) & (h(op1(e10, e14)) = op2(h(e10), h(e14))) & (h(op1(e11, e10)) = op2(h(e11), h(e10))) & (h(op1(e11, e11)) = op2(h(e11), h(e11))) & (h(op1(e11, e12)) = op2(h(e11), h(e12))) & (h(op1(e11, e13)) = op2(h(e11), h(e13))) & (h(op1(e11, e14)) = op2(h(e11), h(e14))) & (h(op1(e12, e10)) = op2(h(e12), h(e10))) & (h(op1(e12, e11)) = op2(h(e12), h(e11))) & (h(op1(e12, e12)) = op2(h(e12), h(e12))) & (h(op1(e12, e13)) = op2(h(e12), h(e13))) & (h(op1(e12, e14)) = op2(h(e12), h(e14))) & (h(op1(e13, e10)) = op2(h(e13), h(e10))) & (h(op1(e13, e11)) = op2(h(e13), h(e11))) & (h(op1(e13, e12)) = op2(h(e13), h(e12))) & (h(op1(e13, e13)) = op2(h(e13), h(e13))) & (h(op1(e13, e14)) = op2(h(e13), h(e14))) & (h(op1(e14, e10)) = op2(h(e14), h(e10))) & (h(op1(e14, e11)) = op2(h(e14), h(e11))) & (h(op1(e14, e12)) = op2(h(e14), h(e12))) & (h(op1(e14, e13)) = op2(h(e14), h(e13))) & (h(op1(e14, e14)) = op2(h(e14), h(e14))) & (j(op2(e20, e20)) = op1(j(e20), j(e20))) & (j(op2(e20, e21)) = op1(j(e20), j(e21))) & (j(op2(e20, e22)) = op1(j(e20), j(e22))) & (j(op2(e20, e23)) = op1(j(e20), j(e23))) & (j(op2(e20, e24)) = op1(j(e20), j(e24))) & (j(op2(e21, e20)) = op1(j(e21), j(e20))) & (j(op2(e21, e21)) = op1(j(e21), j(e21))) & (j(op2(e21, e22)) = op1(j(e21), j(e22))) & (j(op2(e21, e23)) = op1(j(e21), j(e23))) & (j(op2(e21, e24)) = op1(j(e21), j(e24))) & (j(op2(e22, e20)) = op1(j(e22), j(e20))) & (j(op2(e22, e21)) = op1(j(e22), j(e21))) & (j(op2(e22, e22)) = op1(j(e22), j(e22))) & (j(op2(e22, e23)) = op1(j(e22), j(e23))) & (j(op2(e22, e24)) = op1(j(e22), j(e24))) & (j(op2(e23, e20)) = op1(j(e23), j(e20))) & (j(op2(e23, e21)) = op1(j(e23), j(e21))) & (j(op2(e23, e22)) = op1(j(e23), j(e22))) & (j(op2(e23, e23)) = op1(j(e23), j(e23))) & (j(op2(e23, e24)) = op1(j(e23), j(e24))) & (j(op2(e24, e20)) = op1(j(e24), j(e20))) & (j(op2(e24, e21)) = op1(j(e24), j(e21))) & (j(op2(e24, e22)) = op1(j(e24), j(e22))) & (j(op2(e24, e23)) = op1(j(e24), j(e23))) & (j(op2(e24, e24)) = op1(j(e24), j(e24))) & (h(j(e20)) = e20) & (h(j(e21)) = e21) & (h(j(e22)) = e22) & (h(j(e23)) = e23) & (h(j(e24)) = e24) & (j(h(e10)) = e10) & (j(h(e11)) = e11) & (j(h(e12)) = e12) & (j(h(e13)) = e13) & (j(h(e14)) = e14)),
% 0.18/0.41 inference(or_elim,[status(thm)],[4])).
% 0.18/0.41 tff(6,plain,
% 0.18/0.41 (h(j(e23)) = e23),
% 0.18/0.41 inference(and_elim,[status(thm)],[5])).
% 0.18/0.41 tff(7,plain,
% 0.18/0.41 (h(j(e23)) = e23),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.18/0.41 tff(8,assumption,(~(j(e24) = e11)), introduced(assumption)).
% 0.18/0.41 tff(9,assumption,(~(j(e20) = e12)), introduced(assumption)).
% 0.18/0.41 tff(10,assumption,(j(e21) = e12), introduced(assumption)).
% 0.18/0.41 tff(11,plain,
% 0.18/0.41 ((op1(e14, e12) = e11) <=> (op1(e14, e12) = e11)),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(12,axiom,(((((((((((((((((((((((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)) & (op1(e11, e10) = e14)) & (op1(e11, e11) = e11)) & (op1(e11, e12) = e13)) & (op1(e11, e13) = e12)) & (op1(e11, e14) = e10)) & (op1(e12, e10) = e11)) & (op1(e12, e11) = e10)) & (op1(e12, e12) = e12)) & (op1(e12, e13) = e14)) & (op1(e12, e14) = e13)) & (op1(e13, e10) = e12)) & (op1(e13, e11) = e14)) & (op1(e13, e12) = e10)) & (op1(e13, e13) = e13)) & (op1(e13, e14) = e11)) & (op1(e14, e10) = e13)) & (op1(e14, e11) = e12)) & (op1(e14, e12) = e11)) & (op1(e14, e13) = e10)) & (op1(e14, e14) = e14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax4')).
% 0.18/0.41 tff(13,plain,
% 0.18/0.41 ((((((((((((((((((((((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)) & (op1(e11, e10) = e14)) & (op1(e11, e11) = e11)) & (op1(e11, e12) = e13)) & (op1(e11, e13) = e12)) & (op1(e11, e14) = e10)) & (op1(e12, e10) = e11)) & (op1(e12, e11) = e10)) & (op1(e12, e12) = e12)) & (op1(e12, e13) = e14)) & (op1(e12, e14) = e13)) & (op1(e13, e10) = e12)) & (op1(e13, e11) = e14)) & (op1(e13, e12) = e10)) & (op1(e13, e13) = e13)) & (op1(e13, e14) = e11)) & (op1(e14, e10) = e13)) & (op1(e14, e11) = e12)) & (op1(e14, e12) = e11)) & (op1(e14, e13) = e10)),
% 0.18/0.41 inference(and_elim,[status(thm)],[12])).
% 0.18/0.41 tff(14,plain,
% 0.18/0.41 (((((((((((((((((((((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)) & (op1(e11, e10) = e14)) & (op1(e11, e11) = e11)) & (op1(e11, e12) = e13)) & (op1(e11, e13) = e12)) & (op1(e11, e14) = e10)) & (op1(e12, e10) = e11)) & (op1(e12, e11) = e10)) & (op1(e12, e12) = e12)) & (op1(e12, e13) = e14)) & (op1(e12, e14) = e13)) & (op1(e13, e10) = e12)) & (op1(e13, e11) = e14)) & (op1(e13, e12) = e10)) & (op1(e13, e13) = e13)) & (op1(e13, e14) = e11)) & (op1(e14, e10) = e13)) & (op1(e14, e11) = e12)) & (op1(e14, e12) = e11)),
% 0.18/0.41 inference(and_elim,[status(thm)],[13])).
% 0.18/0.41 tff(15,plain,
% 0.18/0.41 (op1(e14, e12) = e11),
% 0.18/0.41 inference(and_elim,[status(thm)],[14])).
% 0.18/0.41 tff(16,plain,
% 0.18/0.41 (op1(e14, e12) = e11),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.18/0.41 tff(17,plain,
% 0.18/0.41 (e12 = j(e21)),
% 0.18/0.41 inference(symmetry,[status(thm)],[10])).
% 0.18/0.41 tff(18,plain,
% 0.18/0.41 ((op1(e13, e14) = e11) <=> (op1(e13, e14) = e11)),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(19,plain,
% 0.18/0.41 ((((((((((((((((((((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)) & (op1(e11, e10) = e14)) & (op1(e11, e11) = e11)) & (op1(e11, e12) = e13)) & (op1(e11, e13) = e12)) & (op1(e11, e14) = e10)) & (op1(e12, e10) = e11)) & (op1(e12, e11) = e10)) & (op1(e12, e12) = e12)) & (op1(e12, e13) = e14)) & (op1(e12, e14) = e13)) & (op1(e13, e10) = e12)) & (op1(e13, e11) = e14)) & (op1(e13, e12) = e10)) & (op1(e13, e13) = e13)) & (op1(e13, e14) = e11)) & (op1(e14, e10) = e13)) & (op1(e14, e11) = e12)),
% 0.18/0.41 inference(and_elim,[status(thm)],[14])).
% 0.18/0.41 tff(20,plain,
% 0.18/0.41 (((((((((((((((((((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)) & (op1(e11, e10) = e14)) & (op1(e11, e11) = e11)) & (op1(e11, e12) = e13)) & (op1(e11, e13) = e12)) & (op1(e11, e14) = e10)) & (op1(e12, e10) = e11)) & (op1(e12, e11) = e10)) & (op1(e12, e12) = e12)) & (op1(e12, e13) = e14)) & (op1(e12, e14) = e13)) & (op1(e13, e10) = e12)) & (op1(e13, e11) = e14)) & (op1(e13, e12) = e10)) & (op1(e13, e13) = e13)) & (op1(e13, e14) = e11)) & (op1(e14, e10) = e13)),
% 0.18/0.42 inference(and_elim,[status(thm)],[19])).
% 0.18/0.42 tff(21,plain,
% 0.18/0.42 ((((((((((((((((((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)) & (op1(e11, e10) = e14)) & (op1(e11, e11) = e11)) & (op1(e11, e12) = e13)) & (op1(e11, e13) = e12)) & (op1(e11, e14) = e10)) & (op1(e12, e10) = e11)) & (op1(e12, e11) = e10)) & (op1(e12, e12) = e12)) & (op1(e12, e13) = e14)) & (op1(e12, e14) = e13)) & (op1(e13, e10) = e12)) & (op1(e13, e11) = e14)) & (op1(e13, e12) = e10)) & (op1(e13, e13) = e13)) & (op1(e13, e14) = e11)),
% 0.18/0.42 inference(and_elim,[status(thm)],[20])).
% 0.18/0.42 tff(22,plain,
% 0.18/0.42 (op1(e13, e14) = e11),
% 0.18/0.42 inference(and_elim,[status(thm)],[21])).
% 0.18/0.42 tff(23,plain,
% 0.18/0.42 (op1(e13, e14) = e11),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.18/0.42 tff(24,plain,
% 0.18/0.42 ((op2(e21, e20) = e22) <=> (op2(e21, e20) = e22)),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(25,axiom,(((((((((((((((((((((((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)) & (op2(e21, e20) = e22)) & (op2(e21, e21) = e21)) & (op2(e21, e22) = e23)) & (op2(e21, e23) = e24)) & (op2(e21, e24) = e20)) & (op2(e22, e20) = e21)) & (op2(e22, e21) = e24)) & (op2(e22, e22) = e22)) & (op2(e22, e23) = e20)) & (op2(e22, e24) = e23)) & (op2(e23, e20) = e24)) & (op2(e23, e21) = e20)) & (op2(e23, e22) = e21)) & (op2(e23, e23) = e23)) & (op2(e23, e24) = e22)) & (op2(e24, e20) = e23)) & (op2(e24, e21) = e22)) & (op2(e24, e22) = e20)) & (op2(e24, e23) = e21)) & (op2(e24, e24) = e24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax5')).
% 0.18/0.42 tff(26,plain,
% 0.18/0.42 ((((((((((((((((((((((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)) & (op2(e21, e20) = e22)) & (op2(e21, e21) = e21)) & (op2(e21, e22) = e23)) & (op2(e21, e23) = e24)) & (op2(e21, e24) = e20)) & (op2(e22, e20) = e21)) & (op2(e22, e21) = e24)) & (op2(e22, e22) = e22)) & (op2(e22, e23) = e20)) & (op2(e22, e24) = e23)) & (op2(e23, e20) = e24)) & (op2(e23, e21) = e20)) & (op2(e23, e22) = e21)) & (op2(e23, e23) = e23)) & (op2(e23, e24) = e22)) & (op2(e24, e20) = e23)) & (op2(e24, e21) = e22)) & (op2(e24, e22) = e20)) & (op2(e24, e23) = e21)),
% 0.18/0.42 inference(and_elim,[status(thm)],[25])).
% 0.18/0.42 tff(27,plain,
% 0.18/0.42 (((((((((((((((((((((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)) & (op2(e21, e20) = e22)) & (op2(e21, e21) = e21)) & (op2(e21, e22) = e23)) & (op2(e21, e23) = e24)) & (op2(e21, e24) = e20)) & (op2(e22, e20) = e21)) & (op2(e22, e21) = e24)) & (op2(e22, e22) = e22)) & (op2(e22, e23) = e20)) & (op2(e22, e24) = e23)) & (op2(e23, e20) = e24)) & (op2(e23, e21) = e20)) & (op2(e23, e22) = e21)) & (op2(e23, e23) = e23)) & (op2(e23, e24) = e22)) & (op2(e24, e20) = e23)) & (op2(e24, e21) = e22)) & (op2(e24, e22) = e20)),
% 0.18/0.42 inference(and_elim,[status(thm)],[26])).
% 0.18/0.42 tff(28,plain,
% 0.18/0.42 ((((((((((((((((((((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)) & (op2(e21, e20) = e22)) & (op2(e21, e21) = e21)) & (op2(e21, e22) = e23)) & (op2(e21, e23) = e24)) & (op2(e21, e24) = e20)) & (op2(e22, e20) = e21)) & (op2(e22, e21) = e24)) & (op2(e22, e22) = e22)) & (op2(e22, e23) = e20)) & (op2(e22, e24) = e23)) & (op2(e23, e20) = e24)) & (op2(e23, e21) = e20)) & (op2(e23, e22) = e21)) & (op2(e23, e23) = e23)) & (op2(e23, e24) = e22)) & (op2(e24, e20) = e23)) & (op2(e24, e21) = e22)),
% 0.18/0.42 inference(and_elim,[status(thm)],[27])).
% 0.18/0.42 tff(29,plain,
% 0.18/0.42 (((((((((((((((((((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)) & (op2(e21, e20) = e22)) & (op2(e21, e21) = e21)) & (op2(e21, e22) = e23)) & (op2(e21, e23) = e24)) & (op2(e21, e24) = e20)) & (op2(e22, e20) = e21)) & (op2(e22, e21) = e24)) & (op2(e22, e22) = e22)) & (op2(e22, e23) = e20)) & (op2(e22, e24) = e23)) & (op2(e23, e20) = e24)) & (op2(e23, e21) = e20)) & (op2(e23, e22) = e21)) & (op2(e23, e23) = e23)) & (op2(e23, e24) = e22)) & (op2(e24, e20) = e23)),
% 0.18/0.43 inference(and_elim,[status(thm)],[28])).
% 0.18/0.43 tff(30,plain,
% 0.18/0.43 ((((((((((((((((((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)) & (op2(e21, e20) = e22)) & (op2(e21, e21) = e21)) & (op2(e21, e22) = e23)) & (op2(e21, e23) = e24)) & (op2(e21, e24) = e20)) & (op2(e22, e20) = e21)) & (op2(e22, e21) = e24)) & (op2(e22, e22) = e22)) & (op2(e22, e23) = e20)) & (op2(e22, e24) = e23)) & (op2(e23, e20) = e24)) & (op2(e23, e21) = e20)) & (op2(e23, e22) = e21)) & (op2(e23, e23) = e23)) & (op2(e23, e24) = e22)),
% 0.18/0.43 inference(and_elim,[status(thm)],[29])).
% 0.18/0.43 tff(31,plain,
% 0.18/0.43 (((((((((((((((((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)) & (op2(e21, e20) = e22)) & (op2(e21, e21) = e21)) & (op2(e21, e22) = e23)) & (op2(e21, e23) = e24)) & (op2(e21, e24) = e20)) & (op2(e22, e20) = e21)) & (op2(e22, e21) = e24)) & (op2(e22, e22) = e22)) & (op2(e22, e23) = e20)) & (op2(e22, e24) = e23)) & (op2(e23, e20) = e24)) & (op2(e23, e21) = e20)) & (op2(e23, e22) = e21)) & (op2(e23, e23) = e23)),
% 0.18/0.43 inference(and_elim,[status(thm)],[30])).
% 0.18/0.43 tff(32,plain,
% 0.18/0.43 ((((((((((((((((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)) & (op2(e21, e20) = e22)) & (op2(e21, e21) = e21)) & (op2(e21, e22) = e23)) & (op2(e21, e23) = e24)) & (op2(e21, e24) = e20)) & (op2(e22, e20) = e21)) & (op2(e22, e21) = e24)) & (op2(e22, e22) = e22)) & (op2(e22, e23) = e20)) & (op2(e22, e24) = e23)) & (op2(e23, e20) = e24)) & (op2(e23, e21) = e20)) & (op2(e23, e22) = e21)),
% 0.18/0.43 inference(and_elim,[status(thm)],[31])).
% 0.18/0.43 tff(33,plain,
% 0.18/0.43 (((((((((((((((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)) & (op2(e21, e20) = e22)) & (op2(e21, e21) = e21)) & (op2(e21, e22) = e23)) & (op2(e21, e23) = e24)) & (op2(e21, e24) = e20)) & (op2(e22, e20) = e21)) & (op2(e22, e21) = e24)) & (op2(e22, e22) = e22)) & (op2(e22, e23) = e20)) & (op2(e22, e24) = e23)) & (op2(e23, e20) = e24)) & (op2(e23, e21) = e20)),
% 0.18/0.43 inference(and_elim,[status(thm)],[32])).
% 0.18/0.43 tff(34,plain,
% 0.18/0.43 ((((((((((((((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)) & (op2(e21, e20) = e22)) & (op2(e21, e21) = e21)) & (op2(e21, e22) = e23)) & (op2(e21, e23) = e24)) & (op2(e21, e24) = e20)) & (op2(e22, e20) = e21)) & (op2(e22, e21) = e24)) & (op2(e22, e22) = e22)) & (op2(e22, e23) = e20)) & (op2(e22, e24) = e23)) & (op2(e23, e20) = e24)),
% 0.18/0.43 inference(and_elim,[status(thm)],[33])).
% 0.18/0.43 tff(35,plain,
% 0.18/0.43 (((((((((((((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)) & (op2(e21, e20) = e22)) & (op2(e21, e21) = e21)) & (op2(e21, e22) = e23)) & (op2(e21, e23) = e24)) & (op2(e21, e24) = e20)) & (op2(e22, e20) = e21)) & (op2(e22, e21) = e24)) & (op2(e22, e22) = e22)) & (op2(e22, e23) = e20)) & (op2(e22, e24) = e23)),
% 0.18/0.43 inference(and_elim,[status(thm)],[34])).
% 0.18/0.43 tff(36,plain,
% 0.18/0.43 ((((((((((((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)) & (op2(e21, e20) = e22)) & (op2(e21, e21) = e21)) & (op2(e21, e22) = e23)) & (op2(e21, e23) = e24)) & (op2(e21, e24) = e20)) & (op2(e22, e20) = e21)) & (op2(e22, e21) = e24)) & (op2(e22, e22) = e22)) & (op2(e22, e23) = e20)),
% 0.18/0.43 inference(and_elim,[status(thm)],[35])).
% 0.18/0.43 tff(37,plain,
% 0.18/0.43 (((((((((((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)) & (op2(e21, e20) = e22)) & (op2(e21, e21) = e21)) & (op2(e21, e22) = e23)) & (op2(e21, e23) = e24)) & (op2(e21, e24) = e20)) & (op2(e22, e20) = e21)) & (op2(e22, e21) = e24)) & (op2(e22, e22) = e22)),
% 0.18/0.43 inference(and_elim,[status(thm)],[36])).
% 0.18/0.43 tff(38,plain,
% 0.18/0.43 ((((((((((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)) & (op2(e21, e20) = e22)) & (op2(e21, e21) = e21)) & (op2(e21, e22) = e23)) & (op2(e21, e23) = e24)) & (op2(e21, e24) = e20)) & (op2(e22, e20) = e21)) & (op2(e22, e21) = e24)),
% 0.18/0.43 inference(and_elim,[status(thm)],[37])).
% 0.18/0.43 tff(39,plain,
% 0.18/0.43 (((((((((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)) & (op2(e21, e20) = e22)) & (op2(e21, e21) = e21)) & (op2(e21, e22) = e23)) & (op2(e21, e23) = e24)) & (op2(e21, e24) = e20)) & (op2(e22, e20) = e21)),
% 0.18/0.43 inference(and_elim,[status(thm)],[38])).
% 0.18/0.43 tff(40,plain,
% 0.18/0.43 ((((((((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)) & (op2(e21, e20) = e22)) & (op2(e21, e21) = e21)) & (op2(e21, e22) = e23)) & (op2(e21, e23) = e24)) & (op2(e21, e24) = e20)),
% 0.18/0.43 inference(and_elim,[status(thm)],[39])).
% 0.18/0.43 tff(41,plain,
% 0.18/0.43 (((((((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)) & (op2(e21, e20) = e22)) & (op2(e21, e21) = e21)) & (op2(e21, e22) = e23)) & (op2(e21, e23) = e24)),
% 0.18/0.43 inference(and_elim,[status(thm)],[40])).
% 0.18/0.43 tff(42,plain,
% 0.18/0.43 ((((((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)) & (op2(e21, e20) = e22)) & (op2(e21, e21) = e21)) & (op2(e21, e22) = e23)),
% 0.18/0.43 inference(and_elim,[status(thm)],[41])).
% 0.18/0.43 tff(43,plain,
% 0.18/0.43 (((((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)) & (op2(e21, e20) = e22)) & (op2(e21, e21) = e21)),
% 0.18/0.43 inference(and_elim,[status(thm)],[42])).
% 0.18/0.43 tff(44,plain,
% 0.18/0.43 ((((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)) & (op2(e21, e20) = e22)),
% 0.18/0.43 inference(and_elim,[status(thm)],[43])).
% 0.18/0.43 tff(45,plain,
% 0.18/0.43 (op2(e21, e20) = e22),
% 0.18/0.43 inference(and_elim,[status(thm)],[44])).
% 0.18/0.43 tff(46,plain,
% 0.18/0.43 (op2(e21, e20) = e22),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[45, 24])).
% 0.18/0.43 tff(47,plain,
% 0.18/0.43 (j(op2(e21, e20)) = j(e22)),
% 0.18/0.43 inference(monotonicity,[status(thm)],[46])).
% 0.18/0.43 tff(48,plain,
% 0.18/0.43 ((j(op2(e21, e20)) = op1(j(e21), j(e20))) <=> (j(op2(e21, e20)) = op1(j(e21), j(e20)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(49,plain,
% 0.18/0.43 (j(op2(e21, e20)) = op1(j(e21), j(e20))),
% 0.18/0.43 inference(and_elim,[status(thm)],[5])).
% 0.18/0.43 tff(50,plain,
% 0.18/0.43 (j(op2(e21, e20)) = op1(j(e21), j(e20))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.18/0.43 tff(51,plain,
% 0.18/0.43 (op1(j(e21), j(e20)) = j(op2(e21, e20))),
% 0.18/0.43 inference(symmetry,[status(thm)],[50])).
% 0.18/0.43 tff(52,assumption,(j(e20) = e13), introduced(assumption)).
% 0.18/0.43 tff(53,plain,
% 0.18/0.43 (e13 = j(e20)),
% 0.18/0.43 inference(symmetry,[status(thm)],[52])).
% 0.18/0.43 tff(54,plain,
% 0.18/0.43 (op1(e12, e13) = op1(j(e21), j(e20))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[17, 53])).
% 0.18/0.43 tff(55,plain,
% 0.18/0.43 ((op1(e12, e13) = e14) <=> (op1(e12, e13) = e14)),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(56,plain,
% 0.18/0.43 (((((((((((((((((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)) & (op1(e11, e10) = e14)) & (op1(e11, e11) = e11)) & (op1(e11, e12) = e13)) & (op1(e11, e13) = e12)) & (op1(e11, e14) = e10)) & (op1(e12, e10) = e11)) & (op1(e12, e11) = e10)) & (op1(e12, e12) = e12)) & (op1(e12, e13) = e14)) & (op1(e12, e14) = e13)) & (op1(e13, e10) = e12)) & (op1(e13, e11) = e14)) & (op1(e13, e12) = e10)) & (op1(e13, e13) = e13)),
% 0.18/0.43 inference(and_elim,[status(thm)],[21])).
% 0.18/0.43 tff(57,plain,
% 0.18/0.43 ((((((((((((((((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)) & (op1(e11, e10) = e14)) & (op1(e11, e11) = e11)) & (op1(e11, e12) = e13)) & (op1(e11, e13) = e12)) & (op1(e11, e14) = e10)) & (op1(e12, e10) = e11)) & (op1(e12, e11) = e10)) & (op1(e12, e12) = e12)) & (op1(e12, e13) = e14)) & (op1(e12, e14) = e13)) & (op1(e13, e10) = e12)) & (op1(e13, e11) = e14)) & (op1(e13, e12) = e10)),
% 0.18/0.44 inference(and_elim,[status(thm)],[56])).
% 0.18/0.44 tff(58,plain,
% 0.18/0.44 (((((((((((((((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)) & (op1(e11, e10) = e14)) & (op1(e11, e11) = e11)) & (op1(e11, e12) = e13)) & (op1(e11, e13) = e12)) & (op1(e11, e14) = e10)) & (op1(e12, e10) = e11)) & (op1(e12, e11) = e10)) & (op1(e12, e12) = e12)) & (op1(e12, e13) = e14)) & (op1(e12, e14) = e13)) & (op1(e13, e10) = e12)) & (op1(e13, e11) = e14)),
% 0.18/0.44 inference(and_elim,[status(thm)],[57])).
% 0.18/0.44 tff(59,plain,
% 0.18/0.44 ((((((((((((((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)) & (op1(e11, e10) = e14)) & (op1(e11, e11) = e11)) & (op1(e11, e12) = e13)) & (op1(e11, e13) = e12)) & (op1(e11, e14) = e10)) & (op1(e12, e10) = e11)) & (op1(e12, e11) = e10)) & (op1(e12, e12) = e12)) & (op1(e12, e13) = e14)) & (op1(e12, e14) = e13)) & (op1(e13, e10) = e12)),
% 0.18/0.44 inference(and_elim,[status(thm)],[58])).
% 0.18/0.44 tff(60,plain,
% 0.18/0.44 (((((((((((((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)) & (op1(e11, e10) = e14)) & (op1(e11, e11) = e11)) & (op1(e11, e12) = e13)) & (op1(e11, e13) = e12)) & (op1(e11, e14) = e10)) & (op1(e12, e10) = e11)) & (op1(e12, e11) = e10)) & (op1(e12, e12) = e12)) & (op1(e12, e13) = e14)) & (op1(e12, e14) = e13)),
% 0.18/0.44 inference(and_elim,[status(thm)],[59])).
% 0.18/0.44 tff(61,plain,
% 0.18/0.44 ((((((((((((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)) & (op1(e11, e10) = e14)) & (op1(e11, e11) = e11)) & (op1(e11, e12) = e13)) & (op1(e11, e13) = e12)) & (op1(e11, e14) = e10)) & (op1(e12, e10) = e11)) & (op1(e12, e11) = e10)) & (op1(e12, e12) = e12)) & (op1(e12, e13) = e14)),
% 0.18/0.44 inference(and_elim,[status(thm)],[60])).
% 0.18/0.44 tff(62,plain,
% 0.18/0.44 (op1(e12, e13) = e14),
% 0.18/0.44 inference(and_elim,[status(thm)],[61])).
% 0.18/0.44 tff(63,plain,
% 0.18/0.44 (op1(e12, e13) = e14),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.18/0.44 tff(64,plain,
% 0.18/0.44 (e14 = op1(e12, e13)),
% 0.18/0.44 inference(symmetry,[status(thm)],[63])).
% 0.18/0.44 tff(65,plain,
% 0.18/0.44 (e14 = j(e22)),
% 0.18/0.44 inference(transitivity,[status(thm)],[64, 54, 51, 47])).
% 0.18/0.44 tff(66,plain,
% 0.18/0.44 (op1(e13, e14) = op1(j(e20), j(e22))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[53, 65])).
% 0.18/0.44 tff(67,plain,
% 0.18/0.44 (op1(j(e20), j(e22)) = op1(e13, e14)),
% 0.18/0.44 inference(symmetry,[status(thm)],[66])).
% 0.18/0.44 tff(68,plain,
% 0.18/0.44 ((j(op2(e20, e22)) = op1(j(e20), j(e22))) <=> (j(op2(e20, e22)) = op1(j(e20), j(e22)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(69,plain,
% 0.18/0.44 (j(op2(e20, e22)) = op1(j(e20), j(e22))),
% 0.18/0.44 inference(and_elim,[status(thm)],[5])).
% 0.18/0.44 tff(70,plain,
% 0.18/0.44 (j(op2(e20, e22)) = op1(j(e20), j(e22))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.18/0.44 tff(71,plain,
% 0.18/0.44 ((op2(e20, e22) = e24) <=> (op2(e20, e22) = e24)),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(72,plain,
% 0.18/0.44 (((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)) & (op2(e20, e24) = e21)),
% 0.18/0.44 inference(and_elim,[status(thm)],[44])).
% 0.18/0.44 tff(73,plain,
% 0.18/0.44 ((((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)) & (op2(e20, e23) = e22)),
% 0.18/0.44 inference(and_elim,[status(thm)],[72])).
% 0.18/0.44 tff(74,plain,
% 0.18/0.44 (((op2(e20, e20) = e20) & (op2(e20, e21) = e23)) & (op2(e20, e22) = e24)),
% 0.18/0.44 inference(and_elim,[status(thm)],[73])).
% 0.18/0.44 tff(75,plain,
% 0.18/0.44 (op2(e20, e22) = e24),
% 0.18/0.44 inference(and_elim,[status(thm)],[74])).
% 0.18/0.44 tff(76,plain,
% 0.18/0.44 (op2(e20, e22) = e24),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.18/0.44 tff(77,plain,
% 0.18/0.44 (e24 = op2(e20, e22)),
% 0.18/0.44 inference(symmetry,[status(thm)],[76])).
% 0.18/0.44 tff(78,plain,
% 0.18/0.44 (j(e24) = j(op2(e20, e22))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[77])).
% 0.18/0.44 tff(79,plain,
% 0.18/0.44 (j(e24) = e11),
% 0.18/0.44 inference(transitivity,[status(thm)],[78, 70, 67, 23])).
% 0.18/0.44 tff(80,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[8, 79])).
% 0.18/0.44 tff(81,plain,((~(j(e20) = e13)) | (j(e24) = e11) | (~(j(e21) = e12))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.44 tff(82,plain,
% 0.18/0.44 (~(j(e20) = e13)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[81, 10, 8])).
% 0.18/0.44 tff(83,assumption,(~(h(e10) = e22)), introduced(assumption)).
% 0.18/0.44 tff(84,plain,
% 0.18/0.44 ((h(j(e22)) = e22) <=> (h(j(e22)) = e22)),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(85,plain,
% 0.18/0.44 (h(j(e22)) = e22),
% 0.18/0.44 inference(and_elim,[status(thm)],[5])).
% 0.18/0.44 tff(86,plain,
% 0.18/0.44 (h(j(e22)) = e22),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.18/0.44 tff(87,plain,
% 0.18/0.44 ((op1(e12, e11) = e10) <=> (op1(e12, e11) = e10)),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(88,plain,
% 0.18/0.44 (((((((((((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)) & (op1(e11, e10) = e14)) & (op1(e11, e11) = e11)) & (op1(e11, e12) = e13)) & (op1(e11, e13) = e12)) & (op1(e11, e14) = e10)) & (op1(e12, e10) = e11)) & (op1(e12, e11) = e10)) & (op1(e12, e12) = e12)),
% 0.18/0.44 inference(and_elim,[status(thm)],[61])).
% 0.18/0.44 tff(89,plain,
% 0.18/0.44 ((((((((((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)) & (op1(e11, e10) = e14)) & (op1(e11, e11) = e11)) & (op1(e11, e12) = e13)) & (op1(e11, e13) = e12)) & (op1(e11, e14) = e10)) & (op1(e12, e10) = e11)) & (op1(e12, e11) = e10)),
% 0.18/0.44 inference(and_elim,[status(thm)],[88])).
% 0.18/0.44 tff(90,plain,
% 0.18/0.44 (op1(e12, e11) = e10),
% 0.18/0.44 inference(and_elim,[status(thm)],[89])).
% 0.18/0.44 tff(91,plain,
% 0.18/0.44 (op1(e12, e11) = e10),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[90, 87])).
% 0.18/0.44 tff(92,assumption,(j(e20) = e11), introduced(assumption)).
% 0.18/0.44 tff(93,plain,
% 0.18/0.44 (e11 = j(e20)),
% 0.18/0.44 inference(symmetry,[status(thm)],[92])).
% 0.18/0.44 tff(94,plain,
% 0.18/0.44 (op1(e12, e11) = op1(j(e21), j(e20))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[17, 93])).
% 0.18/0.44 tff(95,plain,
% 0.18/0.44 (op1(j(e21), j(e20)) = op1(e12, e11)),
% 0.18/0.44 inference(symmetry,[status(thm)],[94])).
% 0.18/0.44 tff(96,plain,
% 0.18/0.44 (j(e22) = j(op2(e21, e20))),
% 0.18/0.44 inference(symmetry,[status(thm)],[47])).
% 0.18/0.44 tff(97,plain,
% 0.18/0.44 (j(e22) = e10),
% 0.18/0.44 inference(transitivity,[status(thm)],[96, 50, 95, 91])).
% 0.18/0.44 tff(98,plain,
% 0.18/0.44 (h(j(e22)) = h(e10)),
% 0.18/0.44 inference(monotonicity,[status(thm)],[97])).
% 0.18/0.44 tff(99,plain,
% 0.18/0.44 (h(e10) = h(j(e22))),
% 0.18/0.44 inference(symmetry,[status(thm)],[98])).
% 0.18/0.44 tff(100,plain,
% 0.18/0.44 (h(e10) = e22),
% 0.18/0.44 inference(transitivity,[status(thm)],[99, 86])).
% 0.18/0.44 tff(101,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[83, 100])).
% 0.18/0.44 tff(102,plain,((~(j(e20) = e11)) | (h(e10) = e22) | (~(j(e21) = e12))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.44 tff(103,plain,
% 0.18/0.44 (~(j(e20) = e11)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[102, 10, 83])).
% 0.18/0.44 tff(104,assumption,(~(j(e20) = e13)), introduced(assumption)).
% 0.18/0.44 tff(105,assumption,(~(j(e20) = e11)), introduced(assumption)).
% 0.18/0.44 tff(106,assumption,(~(j(e23) = e14)), introduced(assumption)).
% 0.18/0.44 tff(107,assumption,(j(e20) = e14), introduced(assumption)).
% 0.18/0.44 tff(108,plain,
% 0.18/0.44 (e14 = j(e20)),
% 0.18/0.44 inference(symmetry,[status(thm)],[107])).
% 0.18/0.44 tff(109,plain,
% 0.18/0.44 (op1(e12, e14) = op1(j(e21), j(e20))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[17, 108])).
% 0.18/0.44 tff(110,plain,
% 0.18/0.44 ((op1(e12, e14) = e13) <=> (op1(e12, e14) = e13)),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(111,plain,
% 0.18/0.44 (op1(e12, e14) = e13),
% 0.18/0.44 inference(and_elim,[status(thm)],[60])).
% 0.18/0.44 tff(112,plain,
% 0.18/0.44 (op1(e12, e14) = e13),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.18/0.44 tff(113,plain,
% 0.18/0.44 (e13 = op1(e12, e14)),
% 0.18/0.44 inference(symmetry,[status(thm)],[112])).
% 0.18/0.44 tff(114,plain,
% 0.18/0.44 (e13 = j(e22)),
% 0.18/0.44 inference(transitivity,[status(thm)],[113, 109, 51, 47])).
% 0.18/0.44 tff(115,plain,
% 0.18/0.44 (op1(e12, e13) = op1(j(e21), j(e22))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[17, 114])).
% 0.18/0.44 tff(116,plain,
% 0.18/0.44 (op1(j(e21), j(e22)) = op1(e12, e13)),
% 0.18/0.44 inference(symmetry,[status(thm)],[115])).
% 0.18/0.44 tff(117,plain,
% 0.18/0.44 ((j(op2(e21, e22)) = op1(j(e21), j(e22))) <=> (j(op2(e21, e22)) = op1(j(e21), j(e22)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(118,plain,
% 0.18/0.45 (j(op2(e21, e22)) = op1(j(e21), j(e22))),
% 0.18/0.45 inference(and_elim,[status(thm)],[5])).
% 0.18/0.45 tff(119,plain,
% 0.18/0.45 (j(op2(e21, e22)) = op1(j(e21), j(e22))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.18/0.45 tff(120,plain,
% 0.18/0.45 ((op2(e21, e22) = e23) <=> (op2(e21, e22) = e23)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(121,plain,
% 0.18/0.45 (op2(e21, e22) = e23),
% 0.18/0.45 inference(and_elim,[status(thm)],[42])).
% 0.18/0.45 tff(122,plain,
% 0.18/0.45 (op2(e21, e22) = e23),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.18/0.45 tff(123,plain,
% 0.18/0.45 (j(op2(e21, e22)) = j(e23)),
% 0.18/0.45 inference(monotonicity,[status(thm)],[122])).
% 0.18/0.45 tff(124,plain,
% 0.18/0.45 (j(e23) = j(op2(e21, e22))),
% 0.18/0.45 inference(symmetry,[status(thm)],[123])).
% 0.18/0.45 tff(125,plain,
% 0.18/0.45 (j(e23) = e14),
% 0.18/0.45 inference(transitivity,[status(thm)],[124, 119, 116, 63])).
% 0.18/0.45 tff(126,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[106, 125])).
% 0.18/0.45 tff(127,plain,((~(j(e20) = e14)) | (j(e23) = e14) | (~(j(e21) = e12))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(128,plain,
% 0.18/0.45 (~(j(e20) = e14)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[127, 106, 10])).
% 0.18/0.45 tff(129,plain,
% 0.18/0.45 ((op1(e10, e12) = e14) <=> (op1(e10, e12) = e14)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(130,plain,
% 0.18/0.45 (((((((((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)) & (op1(e11, e10) = e14)) & (op1(e11, e11) = e11)) & (op1(e11, e12) = e13)) & (op1(e11, e13) = e12)) & (op1(e11, e14) = e10)) & (op1(e12, e10) = e11)),
% 0.18/0.45 inference(and_elim,[status(thm)],[89])).
% 0.18/0.45 tff(131,plain,
% 0.18/0.45 ((((((((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)) & (op1(e11, e10) = e14)) & (op1(e11, e11) = e11)) & (op1(e11, e12) = e13)) & (op1(e11, e13) = e12)) & (op1(e11, e14) = e10)),
% 0.18/0.45 inference(and_elim,[status(thm)],[130])).
% 0.18/0.45 tff(132,plain,
% 0.18/0.45 (((((((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)) & (op1(e11, e10) = e14)) & (op1(e11, e11) = e11)) & (op1(e11, e12) = e13)) & (op1(e11, e13) = e12)),
% 0.18/0.45 inference(and_elim,[status(thm)],[131])).
% 0.18/0.45 tff(133,plain,
% 0.18/0.45 ((((((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)) & (op1(e11, e10) = e14)) & (op1(e11, e11) = e11)) & (op1(e11, e12) = e13)),
% 0.18/0.45 inference(and_elim,[status(thm)],[132])).
% 0.18/0.45 tff(134,plain,
% 0.18/0.45 (((((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)) & (op1(e11, e10) = e14)) & (op1(e11, e11) = e11)),
% 0.18/0.45 inference(and_elim,[status(thm)],[133])).
% 0.18/0.45 tff(135,plain,
% 0.18/0.45 ((((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)) & (op1(e11, e10) = e14)),
% 0.18/0.45 inference(and_elim,[status(thm)],[134])).
% 0.18/0.45 tff(136,plain,
% 0.18/0.45 (((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)) & (op1(e10, e14) = e12)),
% 0.18/0.45 inference(and_elim,[status(thm)],[135])).
% 0.18/0.45 tff(137,plain,
% 0.18/0.45 ((((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)) & (op1(e10, e13) = e11)),
% 0.18/0.45 inference(and_elim,[status(thm)],[136])).
% 0.18/0.45 tff(138,plain,
% 0.18/0.45 (((op1(e10, e10) = e10) & (op1(e10, e11) = e13)) & (op1(e10, e12) = e14)),
% 0.18/0.45 inference(and_elim,[status(thm)],[137])).
% 0.18/0.45 tff(139,plain,
% 0.18/0.45 (op1(e10, e12) = e14),
% 0.18/0.45 inference(and_elim,[status(thm)],[138])).
% 0.18/0.45 tff(140,plain,
% 0.18/0.45 (op1(e10, e12) = e14),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[139, 129])).
% 0.18/0.45 tff(141,assumption,(j(e20) = e10), introduced(assumption)).
% 0.18/0.45 tff(142,plain,
% 0.18/0.45 (e10 = j(e20)),
% 0.18/0.45 inference(symmetry,[status(thm)],[141])).
% 0.18/0.45 tff(143,plain,
% 0.18/0.45 (op1(e10, e12) = op1(j(e20), j(e21))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[142, 17])).
% 0.18/0.45 tff(144,plain,
% 0.18/0.45 (op1(j(e20), j(e21)) = op1(e10, e12)),
% 0.18/0.45 inference(symmetry,[status(thm)],[143])).
% 0.18/0.45 tff(145,plain,
% 0.18/0.45 ((j(op2(e20, e21)) = op1(j(e20), j(e21))) <=> (j(op2(e20, e21)) = op1(j(e20), j(e21)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(146,plain,
% 0.18/0.45 (j(op2(e20, e21)) = op1(j(e20), j(e21))),
% 0.18/0.45 inference(and_elim,[status(thm)],[5])).
% 0.18/0.45 tff(147,plain,
% 0.18/0.45 (j(op2(e20, e21)) = op1(j(e20), j(e21))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.18/0.45 tff(148,plain,
% 0.18/0.45 ((op2(e20, e21) = e23) <=> (op2(e20, e21) = e23)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(149,plain,
% 0.18/0.45 ((op2(e20, e20) = e20) & (op2(e20, e21) = e23)),
% 0.18/0.45 inference(and_elim,[status(thm)],[74])).
% 0.18/0.45 tff(150,plain,
% 0.18/0.45 (op2(e20, e21) = e23),
% 0.18/0.45 inference(and_elim,[status(thm)],[149])).
% 0.18/0.45 tff(151,plain,
% 0.18/0.45 (op2(e20, e21) = e23),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[150, 148])).
% 0.18/0.45 tff(152,plain,
% 0.18/0.45 (e23 = op2(e20, e21)),
% 0.18/0.45 inference(symmetry,[status(thm)],[151])).
% 0.18/0.45 tff(153,plain,
% 0.18/0.45 (j(e23) = j(op2(e20, e21))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[152])).
% 0.18/0.45 tff(154,plain,
% 0.18/0.45 (j(e23) = e14),
% 0.18/0.45 inference(transitivity,[status(thm)],[153, 147, 144, 140])).
% 0.18/0.45 tff(155,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[106, 154])).
% 0.18/0.45 tff(156,plain,((~(j(e20) = e10)) | (j(e23) = e14) | (~(j(e21) = e12))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(157,plain,
% 0.18/0.45 (~(j(e20) = e10)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[156, 106, 10])).
% 0.18/0.45 tff(158,plain,
% 0.18/0.45 (((j(e20) = e10) | (j(e20) = e11) | (j(e20) = e12) | (j(e20) = e13) | (j(e20) = e14)) <=> ((j(e20) = e10) | (j(e20) = e11) | (j(e20) = e12) | (j(e20) = e13) | (j(e20) = e14))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(159,plain,
% 0.18/0.45 (((h(e10) = e20) | (h(e10) = e21) | (h(e10) = e22) | (h(e10) = e23) | (h(e10) = e24)) & ((h(e11) = e20) | (h(e11) = e21) | (h(e11) = e22) | (h(e11) = e23) | (h(e11) = e24)) & ((h(e12) = e20) | (h(e12) = e21) | (h(e12) = e22) | (h(e12) = e23) | (h(e12) = e24)) & ((h(e13) = e20) | (h(e13) = e21) | (h(e13) = e22) | (h(e13) = e23) | (h(e13) = e24)) & ((h(e14) = e20) | (h(e14) = e21) | (h(e14) = e22) | (h(e14) = e23) | (h(e14) = e24)) & ((j(e20) = e10) | (j(e20) = e11) | (j(e20) = e12) | (j(e20) = e13) | (j(e20) = e14)) & ((j(e21) = e10) | (j(e21) = e11) | (j(e21) = e12) | (j(e21) = e13) | (j(e21) = e14)) & ((j(e22) = e10) | (j(e22) = e11) | (j(e22) = e12) | (j(e22) = e13) | (j(e22) = e14)) & ((j(e23) = e10) | (j(e23) = e11) | (j(e23) = e12) | (j(e23) = e13) | (j(e23) = e14)) & ((j(e24) = e10) | (j(e24) = e11) | (j(e24) = e12) | (j(e24) = e13) | (j(e24) = e14))),
% 0.18/0.45 inference(or_elim,[status(thm)],[4])).
% 0.18/0.45 tff(160,plain,
% 0.18/0.45 ((j(e20) = e10) | (j(e20) = e11) | (j(e20) = e12) | (j(e20) = e13) | (j(e20) = e14)),
% 0.18/0.45 inference(and_elim,[status(thm)],[159])).
% 0.18/0.45 tff(161,plain,
% 0.18/0.45 ((j(e20) = e10) | (j(e20) = e11) | (j(e20) = e12) | (j(e20) = e13) | (j(e20) = e14)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[160, 158])).
% 0.18/0.45 tff(162,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[161, 157, 128, 9, 105, 104])).
% 0.18/0.45 tff(163,plain,((j(e23) = e14) | (j(e20) = e12) | (j(e20) = e11) | (j(e20) = e13) | (~(j(e21) = e12))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(164,plain,
% 0.18/0.45 (j(e23) = e14),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[163, 103, 9, 82, 10])).
% 0.18/0.45 tff(165,plain,
% 0.18/0.45 (e14 = j(e23)),
% 0.18/0.45 inference(symmetry,[status(thm)],[164])).
% 0.18/0.45 tff(166,plain,
% 0.18/0.45 (op1(e14, e12) = op1(j(e23), j(e21))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[165, 17])).
% 0.18/0.45 tff(167,plain,
% 0.18/0.45 (op1(j(e23), j(e21)) = op1(e14, e12)),
% 0.18/0.45 inference(symmetry,[status(thm)],[166])).
% 0.18/0.45 tff(168,plain,
% 0.18/0.45 ((j(op2(e23, e21)) = op1(j(e23), j(e21))) <=> (j(op2(e23, e21)) = op1(j(e23), j(e21)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(169,plain,
% 0.18/0.45 (j(op2(e23, e21)) = op1(j(e23), j(e21))),
% 0.18/0.45 inference(and_elim,[status(thm)],[5])).
% 0.18/0.45 tff(170,plain,
% 0.18/0.45 (j(op2(e23, e21)) = op1(j(e23), j(e21))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.18/0.45 tff(171,plain,
% 0.18/0.45 ((op2(e23, e21) = e20) <=> (op2(e23, e21) = e20)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(172,plain,
% 0.18/0.45 (op2(e23, e21) = e20),
% 0.18/0.45 inference(and_elim,[status(thm)],[33])).
% 0.18/0.45 tff(173,plain,
% 0.18/0.45 (op2(e23, e21) = e20),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.18/0.45 tff(174,plain,
% 0.18/0.45 (j(op2(e23, e21)) = j(e20)),
% 0.18/0.45 inference(monotonicity,[status(thm)],[173])).
% 0.18/0.45 tff(175,plain,
% 0.18/0.45 (j(e20) = j(op2(e23, e21))),
% 0.18/0.45 inference(symmetry,[status(thm)],[174])).
% 0.18/0.45 tff(176,plain,
% 0.18/0.45 (j(e20) = e11),
% 0.18/0.45 inference(transitivity,[status(thm)],[175, 170, 167, 16])).
% 0.18/0.45 tff(177,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[103, 176])).
% 0.18/0.45 tff(178,plain,((~(j(e21) = e12)) | (j(e20) = e12) | (j(e24) = e11) | (h(e10) = e22)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(179,plain,
% 0.18/0.45 (h(e10) = e22),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[178, 10, 8, 9])).
% 0.18/0.45 tff(180,plain,
% 0.18/0.45 (h(op1(e12, e11)) = h(e10)),
% 0.18/0.45 inference(monotonicity,[status(thm)],[91])).
% 0.18/0.45 tff(181,plain,
% 0.18/0.45 ((h(op1(e12, e11)) = op2(h(e12), h(e11))) <=> (h(op1(e12, e11)) = op2(h(e12), h(e11)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(182,plain,
% 0.18/0.45 (h(op1(e12, e11)) = op2(h(e12), h(e11))),
% 0.18/0.45 inference(and_elim,[status(thm)],[5])).
% 0.18/0.45 tff(183,plain,
% 0.18/0.45 (h(op1(e12, e11)) = op2(h(e12), h(e11))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.18/0.45 tff(184,plain,
% 0.18/0.45 (op2(h(e12), h(e11)) = h(op1(e12, e11))),
% 0.18/0.45 inference(symmetry,[status(thm)],[183])).
% 0.18/0.45 tff(185,plain,
% 0.18/0.45 ((op1(e12, e10) = e11) <=> (op1(e12, e10) = e11)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(186,plain,
% 0.18/0.45 (op1(e12, e10) = e11),
% 0.18/0.45 inference(and_elim,[status(thm)],[130])).
% 0.18/0.45 tff(187,plain,
% 0.18/0.45 (op1(e12, e10) = e11),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.18/0.45 tff(188,plain,
% 0.18/0.45 (h(op1(e12, e10)) = h(e11)),
% 0.18/0.45 inference(monotonicity,[status(thm)],[187])).
% 0.18/0.45 tff(189,plain,
% 0.18/0.45 ((h(op1(e12, e10)) = op2(h(e12), h(e10))) <=> (h(op1(e12, e10)) = op2(h(e12), h(e10)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(190,plain,
% 0.18/0.45 (h(op1(e12, e10)) = op2(h(e12), h(e10))),
% 0.18/0.45 inference(and_elim,[status(thm)],[5])).
% 0.18/0.45 tff(191,plain,
% 0.18/0.45 (h(op1(e12, e10)) = op2(h(e12), h(e10))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.18/0.45 tff(192,plain,
% 0.18/0.45 (op2(h(e12), h(e10)) = h(op1(e12, e10))),
% 0.18/0.45 inference(symmetry,[status(thm)],[191])).
% 0.18/0.45 tff(193,plain,
% 0.18/0.45 (e22 = h(e10)),
% 0.18/0.45 inference(symmetry,[status(thm)],[179])).
% 0.18/0.45 tff(194,plain,
% 0.18/0.45 (h(e12) = h(j(e21))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[17])).
% 0.18/0.45 tff(195,plain,
% 0.18/0.45 (h(j(e21)) = h(e12)),
% 0.18/0.45 inference(symmetry,[status(thm)],[194])).
% 0.18/0.45 tff(196,plain,
% 0.18/0.45 ((h(j(e21)) = e21) <=> (h(j(e21)) = e21)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(197,plain,
% 0.18/0.45 (h(j(e21)) = e21),
% 0.18/0.45 inference(and_elim,[status(thm)],[5])).
% 0.18/0.45 tff(198,plain,
% 0.18/0.45 (h(j(e21)) = e21),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.18/0.45 tff(199,plain,
% 0.18/0.45 (e21 = h(j(e21))),
% 0.18/0.45 inference(symmetry,[status(thm)],[198])).
% 0.18/0.45 tff(200,plain,
% 0.18/0.45 (e21 = h(e12)),
% 0.18/0.45 inference(transitivity,[status(thm)],[199, 195])).
% 0.18/0.45 tff(201,plain,
% 0.18/0.45 (op2(e21, e22) = op2(h(e12), h(e10))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[200, 193])).
% 0.18/0.45 tff(202,plain,
% 0.18/0.45 (e23 = op2(e21, e22)),
% 0.18/0.45 inference(symmetry,[status(thm)],[122])).
% 0.18/0.45 tff(203,plain,
% 0.18/0.45 (e23 = h(e11)),
% 0.18/0.45 inference(transitivity,[status(thm)],[202, 201, 192, 188])).
% 0.18/0.45 tff(204,plain,
% 0.18/0.45 (op2(e21, e23) = op2(h(e12), h(e11))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[200, 203])).
% 0.18/0.45 tff(205,plain,
% 0.18/0.45 ((op2(e21, e23) = e24) <=> (op2(e21, e23) = e24)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(206,plain,
% 0.18/0.45 (op2(e21, e23) = e24),
% 0.18/0.45 inference(and_elim,[status(thm)],[41])).
% 0.18/0.45 tff(207,plain,
% 0.18/0.45 (op2(e21, e23) = e24),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.18/0.45 tff(208,plain,
% 0.18/0.45 (e24 = op2(e21, e23)),
% 0.18/0.45 inference(symmetry,[status(thm)],[207])).
% 0.18/0.45 tff(209,plain,
% 0.18/0.45 ((op2(e22, e21) = e24) <=> (op2(e22, e21) = e24)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(210,plain,
% 0.18/0.45 (op2(e22, e21) = e24),
% 0.18/0.45 inference(and_elim,[status(thm)],[38])).
% 0.18/0.45 tff(211,plain,
% 0.18/0.45 (op2(e22, e21) = e24),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.18/0.45 tff(212,plain,
% 0.18/0.45 (h(e12) = e21),
% 0.18/0.45 inference(transitivity,[status(thm)],[194, 198])).
% 0.18/0.45 tff(213,plain,
% 0.18/0.45 (op2(h(e10), h(e12)) = op2(e22, e21)),
% 0.18/0.45 inference(monotonicity,[status(thm)],[179, 212])).
% 0.18/0.45 tff(214,plain,
% 0.18/0.45 ((h(op1(e10, e12)) = op2(h(e10), h(e12))) <=> (h(op1(e10, e12)) = op2(h(e10), h(e12)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(215,plain,
% 0.18/0.45 (h(op1(e10, e12)) = op2(h(e10), h(e12))),
% 0.18/0.45 inference(and_elim,[status(thm)],[5])).
% 0.18/0.45 tff(216,plain,
% 0.18/0.45 (h(op1(e10, e12)) = op2(h(e10), h(e12))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.18/0.45 tff(217,plain,
% 0.18/0.45 (e14 = op1(e10, e12)),
% 0.18/0.45 inference(symmetry,[status(thm)],[140])).
% 0.18/0.45 tff(218,plain,
% 0.18/0.45 (h(e14) = h(op1(e10, e12))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[217])).
% 0.18/0.45 tff(219,plain,
% 0.18/0.45 ((op1(e11, e10) = e14) <=> (op1(e11, e10) = e14)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(220,plain,
% 0.18/0.45 (op1(e11, e10) = e14),
% 0.18/0.45 inference(and_elim,[status(thm)],[135])).
% 0.18/0.45 tff(221,plain,
% 0.18/0.45 (op1(e11, e10) = e14),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.18/0.45 tff(222,plain,
% 0.18/0.45 (h(op1(e11, e10)) = h(e14)),
% 0.18/0.45 inference(monotonicity,[status(thm)],[221])).
% 0.18/0.45 tff(223,plain,
% 0.18/0.45 ((h(op1(e11, e10)) = op2(h(e11), h(e10))) <=> (h(op1(e11, e10)) = op2(h(e11), h(e10)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(224,plain,
% 0.18/0.45 (h(op1(e11, e10)) = op2(h(e11), h(e10))),
% 0.18/0.45 inference(and_elim,[status(thm)],[5])).
% 0.18/0.45 tff(225,plain,
% 0.18/0.45 (h(op1(e11, e10)) = op2(h(e11), h(e10))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.18/0.45 tff(226,plain,
% 0.18/0.45 (op2(h(e11), h(e10)) = h(op1(e11, e10))),
% 0.18/0.45 inference(symmetry,[status(thm)],[225])).
% 0.18/0.45 tff(227,plain,
% 0.18/0.45 (op2(e23, e22) = op2(h(e11), h(e10))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[203, 193])).
% 0.18/0.45 tff(228,plain,
% 0.18/0.45 ((op2(e23, e22) = e21) <=> (op2(e23, e22) = e21)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(229,plain,
% 0.18/0.45 (op2(e23, e22) = e21),
% 0.18/0.45 inference(and_elim,[status(thm)],[32])).
% 0.18/0.45 tff(230,plain,
% 0.18/0.45 (op2(e23, e22) = e21),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.18/0.45 tff(231,plain,
% 0.18/0.45 (e21 = op2(e23, e22)),
% 0.18/0.45 inference(symmetry,[status(thm)],[230])).
% 0.18/0.45 tff(232,plain,
% 0.18/0.45 (h(e12) = e22),
% 0.18/0.45 inference(transitivity,[status(thm)],[194, 198, 231, 227, 226, 222, 218, 216, 213, 211, 208, 204, 184, 180, 179])).
% 0.18/0.45 tff(233,plain,
% 0.18/0.45 ((e21 = h(e10)) <=> (h(e10) = e21)),
% 0.18/0.45 inference(commutativity,[status(thm)],[])).
% 0.18/0.45 tff(234,plain,
% 0.18/0.45 ((h(e12) = e22) <=> (e21 = h(e10))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[212, 193])).
% 0.18/0.45 tff(235,plain,
% 0.18/0.45 ((h(e12) = e22) <=> (h(e10) = e21)),
% 0.18/0.45 inference(transitivity,[status(thm)],[234, 233])).
% 0.18/0.45 tff(236,plain,
% 0.18/0.45 ((h(e10) = e21) <=> (h(e12) = e22)),
% 0.18/0.45 inference(symmetry,[status(thm)],[235])).
% 0.18/0.45 tff(237,plain,
% 0.18/0.45 ((~(h(e10) = e21)) <=> (~(h(e12) = e22))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[236])).
% 0.18/0.45 tff(238,plain,
% 0.18/0.45 ((e21 = e22) <=> (e21 = h(e10))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[193])).
% 0.18/0.45 tff(239,plain,
% 0.18/0.45 ((e21 = e22) <=> (h(e10) = e21)),
% 0.18/0.45 inference(transitivity,[status(thm)],[238, 233])).
% 0.18/0.45 tff(240,plain,
% 0.18/0.45 ((~(e21 = e22)) <=> (~(h(e10) = e21))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[239])).
% 0.18/0.45 tff(241,plain,
% 0.18/0.45 ((~(e21 = e22)) <=> (~(e21 = e22))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(242,axiom,((((((((((~(e20 = e21)) & (~(e20 = e22))) & (~(e20 = e23))) & (~(e20 = e24))) & (~(e21 = e22))) & (~(e21 = e23))) & (~(e21 = e24))) & (~(e22 = e23))) & (~(e22 = e24))) & (~(e23 = e24))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax2')).
% 0.18/0.45 tff(243,plain,
% 0.18/0.45 (((((((((~(e20 = e21)) & (~(e20 = e22))) & (~(e20 = e23))) & (~(e20 = e24))) & (~(e21 = e22))) & (~(e21 = e23))) & (~(e21 = e24))) & (~(e22 = e23))) & (~(e22 = e24))),
% 0.18/0.45 inference(and_elim,[status(thm)],[242])).
% 0.18/0.45 tff(244,plain,
% 0.18/0.45 ((((((((~(e20 = e21)) & (~(e20 = e22))) & (~(e20 = e23))) & (~(e20 = e24))) & (~(e21 = e22))) & (~(e21 = e23))) & (~(e21 = e24))) & (~(e22 = e23))),
% 0.18/0.45 inference(and_elim,[status(thm)],[243])).
% 0.18/0.45 tff(245,plain,
% 0.18/0.45 (((((((~(e20 = e21)) & (~(e20 = e22))) & (~(e20 = e23))) & (~(e20 = e24))) & (~(e21 = e22))) & (~(e21 = e23))) & (~(e21 = e24))),
% 0.18/0.45 inference(and_elim,[status(thm)],[244])).
% 0.18/0.45 tff(246,plain,
% 0.18/0.45 ((((((~(e20 = e21)) & (~(e20 = e22))) & (~(e20 = e23))) & (~(e20 = e24))) & (~(e21 = e22))) & (~(e21 = e23))),
% 0.18/0.45 inference(and_elim,[status(thm)],[245])).
% 0.18/0.45 tff(247,plain,
% 0.18/0.45 (((((~(e20 = e21)) & (~(e20 = e22))) & (~(e20 = e23))) & (~(e20 = e24))) & (~(e21 = e22))),
% 0.18/0.45 inference(and_elim,[status(thm)],[246])).
% 0.18/0.45 tff(248,plain,
% 0.18/0.45 (~(e21 = e22)),
% 0.18/0.45 inference(and_elim,[status(thm)],[247])).
% 0.18/0.45 tff(249,plain,
% 0.18/0.45 (~(e21 = e22)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[248, 241])).
% 0.18/0.45 tff(250,plain,
% 0.18/0.45 (~(h(e10) = e21)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[249, 240])).
% 0.18/0.45 tff(251,plain,
% 0.18/0.45 (~(h(e12) = e22)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[250, 237])).
% 0.18/0.45 tff(252,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[251, 232])).
% 0.18/0.45 tff(253,plain,((~(j(e21) = e12)) | (j(e24) = e11) | (j(e20) = e12)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(254,plain,
% 0.18/0.45 (~(j(e21) = e12)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[253, 9, 8])).
% 0.18/0.45 tff(255,plain,
% 0.18/0.45 ((op1(e13, e12) = e10) <=> (op1(e13, e12) = e10)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(256,plain,
% 0.18/0.45 (op1(e13, e12) = e10),
% 0.18/0.45 inference(and_elim,[status(thm)],[57])).
% 0.18/0.45 tff(257,plain,
% 0.18/0.45 (op1(e13, e12) = e10),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.18/0.45 tff(258,assumption,(j(e21) = e10), introduced(assumption)).
% 0.18/0.45 tff(259,plain,
% 0.18/0.45 ((op1(e13, e10) = e12) <=> (op1(e13, e10) = e12)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(260,plain,
% 0.18/0.45 (op1(e13, e10) = e12),
% 0.18/0.45 inference(and_elim,[status(thm)],[59])).
% 0.18/0.45 tff(261,plain,
% 0.18/0.45 (op1(e13, e10) = e12),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.18/0.45 tff(262,plain,
% 0.18/0.45 (e10 = j(e21)),
% 0.18/0.45 inference(symmetry,[status(thm)],[258])).
% 0.18/0.45 tff(263,plain,
% 0.18/0.45 ((op1(e14, e10) = e13) <=> (op1(e14, e10) = e13)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(264,plain,
% 0.18/0.45 (op1(e14, e10) = e13),
% 0.18/0.45 inference(and_elim,[status(thm)],[20])).
% 0.18/0.45 tff(265,plain,
% 0.18/0.45 (op1(e14, e10) = e13),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.18/0.45 tff(266,plain,
% 0.18/0.45 ((h(j(e20)) = e20) <=> (h(j(e20)) = e20)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(267,plain,
% 0.18/0.45 (h(j(e20)) = e20),
% 0.18/0.45 inference(and_elim,[status(thm)],[5])).
% 0.18/0.45 tff(268,plain,
% 0.18/0.45 (h(j(e20)) = e20),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.18/0.45 tff(269,plain,
% 0.18/0.45 (j(e20) = j(e21)),
% 0.18/0.45 inference(transitivity,[status(thm)],[141, 262])).
% 0.18/0.45 tff(270,plain,
% 0.18/0.45 (h(j(e20)) = h(j(e21))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[269])).
% 0.18/0.45 tff(271,plain,
% 0.18/0.45 (h(j(e21)) = h(j(e20))),
% 0.18/0.45 inference(symmetry,[status(thm)],[270])).
% 0.18/0.45 tff(272,plain,
% 0.18/0.45 (h(j(e21)) = h(e10)),
% 0.18/0.45 inference(monotonicity,[status(thm)],[258])).
% 0.18/0.45 tff(273,plain,
% 0.18/0.45 (h(e10) = h(j(e21))),
% 0.18/0.45 inference(symmetry,[status(thm)],[272])).
% 0.18/0.45 tff(274,plain,
% 0.18/0.45 (h(e10) = e20),
% 0.18/0.45 inference(transitivity,[status(thm)],[273, 271, 268])).
% 0.18/0.45 tff(275,plain,
% 0.18/0.45 ((e20 = h(e10)) <=> (h(e10) = e20)),
% 0.18/0.45 inference(commutativity,[status(thm)],[])).
% 0.18/0.45 tff(276,plain,
% 0.18/0.45 (e21 = h(e10)),
% 0.18/0.45 inference(transitivity,[status(thm)],[199, 272])).
% 0.18/0.45 tff(277,plain,
% 0.18/0.45 ((e20 = e21) <=> (e20 = h(e10))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[276])).
% 0.18/0.45 tff(278,plain,
% 0.18/0.45 ((e20 = e21) <=> (h(e10) = e20)),
% 0.18/0.45 inference(transitivity,[status(thm)],[277, 275])).
% 0.18/0.45 tff(279,plain,
% 0.18/0.45 ((~(e20 = e21)) <=> (~(h(e10) = e20))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[278])).
% 0.18/0.45 tff(280,plain,
% 0.18/0.45 ((~(e20 = e21)) <=> (~(e20 = e21))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(281,plain,
% 0.18/0.45 ((((~(e20 = e21)) & (~(e20 = e22))) & (~(e20 = e23))) & (~(e20 = e24))),
% 0.18/0.45 inference(and_elim,[status(thm)],[247])).
% 0.18/0.45 tff(282,plain,
% 0.18/0.45 (((~(e20 = e21)) & (~(e20 = e22))) & (~(e20 = e23))),
% 0.18/0.45 inference(and_elim,[status(thm)],[281])).
% 0.18/0.45 tff(283,plain,
% 0.18/0.45 ((~(e20 = e21)) & (~(e20 = e22))),
% 0.18/0.45 inference(and_elim,[status(thm)],[282])).
% 0.18/0.45 tff(284,plain,
% 0.18/0.45 (~(e20 = e21)),
% 0.18/0.45 inference(and_elim,[status(thm)],[283])).
% 0.18/0.45 tff(285,plain,
% 0.18/0.45 (~(e20 = e21)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[284, 280])).
% 0.18/0.45 tff(286,plain,
% 0.18/0.45 (~(h(e10) = e20)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[285, 279])).
% 0.18/0.45 tff(287,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[286, 274])).
% 0.18/0.45 tff(288,plain,((~(j(e20) = e10)) | (~(j(e21) = e10))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(289,plain,
% 0.18/0.45 (~(j(e20) = e10)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[288, 258])).
% 0.18/0.45 tff(290,plain,
% 0.18/0.45 (op1(e11, e10) = op1(j(e20), j(e21))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[93, 262])).
% 0.18/0.45 tff(291,plain,
% 0.18/0.45 (op1(j(e20), j(e21)) = op1(e11, e10)),
% 0.18/0.45 inference(symmetry,[status(thm)],[290])).
% 0.18/0.45 tff(292,plain,
% 0.18/0.45 (j(e23) = e14),
% 0.18/0.45 inference(transitivity,[status(thm)],[153, 147, 291, 221])).
% 0.18/0.45 tff(293,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[106, 292])).
% 0.18/0.45 tff(294,plain,((~(j(e20) = e11)) | (j(e23) = e14) | (~(j(e21) = e10))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(295,plain,
% 0.18/0.45 (~(j(e20) = e11)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[294, 106, 258])).
% 0.18/0.45 tff(296,plain,
% 0.18/0.45 (j(e20) = e14),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[161, 295, 9, 289, 104])).
% 0.18/0.45 tff(297,plain,
% 0.18/0.45 (e14 = j(e20)),
% 0.18/0.45 inference(symmetry,[status(thm)],[296])).
% 0.18/0.45 tff(298,plain,
% 0.18/0.45 (op1(e10, e14) = op1(j(e21), j(e20))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[262, 297])).
% 0.18/0.45 tff(299,plain,
% 0.18/0.45 ((op1(e10, e14) = e12) <=> (op1(e10, e14) = e12)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(300,plain,
% 0.18/0.45 (op1(e10, e14) = e12),
% 0.18/0.45 inference(and_elim,[status(thm)],[136])).
% 0.18/0.45 tff(301,plain,
% 0.18/0.45 (op1(e10, e14) = e12),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.18/0.45 tff(302,plain,
% 0.18/0.45 (e12 = op1(e10, e14)),
% 0.18/0.45 inference(symmetry,[status(thm)],[301])).
% 0.18/0.45 tff(303,plain,
% 0.18/0.45 (e12 = j(e22)),
% 0.18/0.45 inference(transitivity,[status(thm)],[302, 298, 51, 47])).
% 0.18/0.45 tff(304,plain,
% 0.18/0.45 (op1(e10, e12) = op1(j(e21), j(e22))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[262, 303])).
% 0.18/0.45 tff(305,plain,
% 0.18/0.45 (op1(j(e21), j(e22)) = op1(e10, e12)),
% 0.18/0.45 inference(symmetry,[status(thm)],[304])).
% 0.18/0.45 tff(306,plain,
% 0.18/0.45 (j(e23) = e14),
% 0.18/0.45 inference(transitivity,[status(thm)],[124, 119, 305, 140])).
% 0.18/0.45 tff(307,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[106, 306])).
% 0.18/0.45 tff(308,plain,((j(e23) = e14) | (~(j(e21) = e10)) | (j(e20) = e12) | (j(e20) = e13)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(309,plain,
% 0.18/0.45 (j(e23) = e14),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[308, 104, 9, 258])).
% 0.18/0.45 tff(310,plain,
% 0.18/0.45 (e14 = j(e23)),
% 0.18/0.45 inference(symmetry,[status(thm)],[309])).
% 0.18/0.45 tff(311,plain,
% 0.18/0.45 (op1(e14, e10) = op1(j(e23), j(e21))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[310, 262])).
% 0.18/0.45 tff(312,plain,
% 0.18/0.45 (op1(j(e23), j(e21)) = op1(e14, e10)),
% 0.18/0.45 inference(symmetry,[status(thm)],[311])).
% 0.18/0.45 tff(313,plain,
% 0.18/0.45 (j(e20) = e13),
% 0.18/0.45 inference(transitivity,[status(thm)],[175, 170, 312, 265])).
% 0.18/0.45 tff(314,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[104, 313])).
% 0.18/0.45 tff(315,plain,((j(e20) = e13) | (~(j(e21) = e10)) | (j(e20) = e12)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(316,plain,
% 0.18/0.45 (j(e20) = e13),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[315, 258, 9])).
% 0.18/0.45 tff(317,plain,
% 0.18/0.45 (e13 = j(e20)),
% 0.18/0.45 inference(symmetry,[status(thm)],[316])).
% 0.18/0.45 tff(318,plain,
% 0.18/0.45 (op1(e13, e10) = op1(j(e20), j(e21))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[317, 262])).
% 0.18/0.45 tff(319,plain,
% 0.18/0.45 (op1(j(e20), j(e21)) = op1(e13, e10)),
% 0.18/0.45 inference(symmetry,[status(thm)],[318])).
% 0.18/0.45 tff(320,plain,
% 0.18/0.46 (j(e23) = e12),
% 0.18/0.46 inference(transitivity,[status(thm)],[153, 147, 319, 261])).
% 0.18/0.46 tff(321,assumption,(~(j(e23) = e12)), introduced(assumption)).
% 0.18/0.46 tff(322,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[321, 320])).
% 0.18/0.46 tff(323,plain,((~(j(e21) = e10)) | (j(e23) = e12) | (j(e20) = e12)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(324,plain,
% 0.18/0.46 (j(e23) = e12),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[323, 258, 9])).
% 0.18/0.46 tff(325,plain,
% 0.18/0.46 (e12 = j(e23)),
% 0.18/0.46 inference(symmetry,[status(thm)],[324])).
% 0.18/0.46 tff(326,plain,
% 0.18/0.46 (op1(e13, e12) = op1(j(e20), j(e23))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[317, 325])).
% 0.18/0.46 tff(327,plain,
% 0.18/0.46 (op1(j(e20), j(e23)) = op1(e13, e12)),
% 0.18/0.46 inference(symmetry,[status(thm)],[326])).
% 0.18/0.46 tff(328,plain,
% 0.18/0.46 ((j(op2(e20, e23)) = op1(j(e20), j(e23))) <=> (j(op2(e20, e23)) = op1(j(e20), j(e23)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(329,plain,
% 0.18/0.46 (j(op2(e20, e23)) = op1(j(e20), j(e23))),
% 0.18/0.46 inference(and_elim,[status(thm)],[5])).
% 0.18/0.46 tff(330,plain,
% 0.18/0.46 (j(op2(e20, e23)) = op1(j(e20), j(e23))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.18/0.46 tff(331,plain,
% 0.18/0.46 ((op2(e20, e23) = e22) <=> (op2(e20, e23) = e22)),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(332,plain,
% 0.18/0.46 (op2(e20, e23) = e22),
% 0.18/0.46 inference(and_elim,[status(thm)],[73])).
% 0.18/0.46 tff(333,plain,
% 0.18/0.46 (op2(e20, e23) = e22),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.18/0.46 tff(334,plain,
% 0.18/0.46 (j(op2(e20, e23)) = j(e22)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[333])).
% 0.18/0.46 tff(335,plain,
% 0.18/0.46 (j(e22) = j(op2(e20, e23))),
% 0.18/0.46 inference(symmetry,[status(thm)],[334])).
% 0.18/0.46 tff(336,plain,
% 0.18/0.46 ((op1(e10, e13) = e11) <=> (op1(e10, e13) = e11)),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(337,plain,
% 0.18/0.46 (op1(e10, e13) = e11),
% 0.18/0.46 inference(and_elim,[status(thm)],[137])).
% 0.18/0.46 tff(338,plain,
% 0.18/0.46 (op1(e10, e13) = e11),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.18/0.46 tff(339,plain,
% 0.18/0.46 (op1(e10, e13) = op1(j(e21), j(e20))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[262, 53])).
% 0.18/0.46 tff(340,plain,
% 0.18/0.46 (op1(j(e21), j(e20)) = op1(e10, e13)),
% 0.18/0.46 inference(symmetry,[status(thm)],[339])).
% 0.18/0.46 tff(341,plain,
% 0.18/0.46 (j(e22) = e11),
% 0.18/0.46 inference(transitivity,[status(thm)],[96, 50, 340, 338])).
% 0.18/0.46 tff(342,assumption,(~(j(e22) = e11)), introduced(assumption)).
% 0.18/0.46 tff(343,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[342, 341])).
% 0.18/0.46 tff(344,plain,((~(j(e20) = e13)) | (j(e22) = e11) | (~(j(e21) = e10))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(345,plain,
% 0.18/0.46 (j(e22) = e11),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[344, 258, 316])).
% 0.18/0.46 tff(346,plain,
% 0.18/0.46 (e11 = j(e22)),
% 0.18/0.46 inference(symmetry,[status(thm)],[345])).
% 0.18/0.46 tff(347,plain,
% 0.18/0.46 (op1(e12, e10) = op1(j(e23), j(e21))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[325, 262])).
% 0.18/0.46 tff(348,plain,
% 0.18/0.46 (op1(j(e23), j(e21)) = op1(e12, e10)),
% 0.18/0.46 inference(symmetry,[status(thm)],[347])).
% 0.18/0.46 tff(349,plain,
% 0.18/0.46 (j(e20) = e10),
% 0.18/0.46 inference(transitivity,[status(thm)],[175, 170, 348, 187, 346, 335, 330, 327, 257])).
% 0.18/0.46 tff(350,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[289, 349])).
% 0.18/0.46 tff(351,plain,((~(j(e21) = e10)) | (j(e20) = e12)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(352,plain,
% 0.18/0.46 (~(j(e21) = e10)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[351, 9])).
% 0.18/0.46 tff(353,assumption,(~(j(e21) = e12)), introduced(assumption)).
% 0.18/0.46 tff(354,plain,
% 0.18/0.46 (op1(j(e23), j(e21)) = j(op2(e23, e21))),
% 0.18/0.46 inference(symmetry,[status(thm)],[170])).
% 0.18/0.46 tff(355,plain,
% 0.18/0.46 (h(j(e20)) = h(e14)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[107])).
% 0.18/0.46 tff(356,plain,
% 0.18/0.46 (e20 = h(j(e20))),
% 0.18/0.46 inference(symmetry,[status(thm)],[268])).
% 0.18/0.46 tff(357,plain,
% 0.18/0.46 (e20 = h(e14)),
% 0.18/0.46 inference(transitivity,[status(thm)],[356, 355])).
% 0.18/0.46 tff(358,plain,
% 0.18/0.46 ((e20 = e21) <=> (h(e14) = e21)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[357])).
% 0.18/0.46 tff(359,plain,
% 0.18/0.46 ((~(e20 = e21)) <=> (~(h(e14) = e21))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[358])).
% 0.18/0.46 tff(360,plain,
% 0.18/0.46 (~(h(e14) = e21)),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[285, 359])).
% 0.18/0.46 tff(361,assumption,(j(e21) = e14), introduced(assumption)).
% 0.18/0.46 tff(362,plain,
% 0.18/0.46 (h(j(e21)) = h(e14)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[361])).
% 0.18/0.46 tff(363,plain,
% 0.18/0.46 (h(e14) = h(j(e21))),
% 0.18/0.46 inference(symmetry,[status(thm)],[362])).
% 0.18/0.46 tff(364,plain,
% 0.18/0.46 (h(e14) = e21),
% 0.18/0.46 inference(transitivity,[status(thm)],[363, 198])).
% 0.18/0.46 tff(365,assumption,(~(h(e14) = e21)), introduced(assumption)).
% 0.18/0.46 tff(366,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[365, 364])).
% 0.18/0.46 tff(367,plain,((~(j(e21) = e14)) | (h(e14) = e21)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(368,plain,
% 0.18/0.46 (~(j(e21) = e14)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[367, 360])).
% 0.18/0.46 tff(369,assumption,(~(j(e21) = e10)), introduced(assumption)).
% 0.18/0.46 tff(370,plain,
% 0.18/0.46 ((op1(e13, e11) = e14) <=> (op1(e13, e11) = e14)),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(371,plain,
% 0.18/0.46 (op1(e13, e11) = e14),
% 0.18/0.46 inference(and_elim,[status(thm)],[58])).
% 0.18/0.46 tff(372,plain,
% 0.18/0.46 (op1(e13, e11) = e14),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.18/0.46 tff(373,assumption,(j(e21) = e13), introduced(assumption)).
% 0.18/0.46 tff(374,plain,
% 0.18/0.46 (e13 = j(e21)),
% 0.18/0.46 inference(symmetry,[status(thm)],[373])).
% 0.18/0.46 tff(375,plain,
% 0.18/0.46 (op1(e13, e14) = op1(j(e21), j(e20))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[374, 108])).
% 0.18/0.46 tff(376,plain,
% 0.18/0.46 (e11 = op1(e13, e14)),
% 0.18/0.46 inference(symmetry,[status(thm)],[23])).
% 0.18/0.46 tff(377,plain,
% 0.18/0.46 (e11 = j(e22)),
% 0.18/0.46 inference(transitivity,[status(thm)],[376, 375, 51, 47])).
% 0.18/0.46 tff(378,plain,
% 0.18/0.46 (op1(e13, e11) = op1(j(e21), j(e22))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[374, 377])).
% 0.18/0.46 tff(379,plain,
% 0.18/0.46 (op1(j(e21), j(e22)) = op1(e13, e11)),
% 0.18/0.46 inference(symmetry,[status(thm)],[378])).
% 0.18/0.46 tff(380,plain,
% 0.18/0.46 (j(op2(e20, e21)) = j(e23)),
% 0.18/0.46 inference(symmetry,[status(thm)],[153])).
% 0.18/0.46 tff(381,plain,
% 0.18/0.46 (op1(j(e20), j(e21)) = j(op2(e20, e21))),
% 0.18/0.46 inference(symmetry,[status(thm)],[147])).
% 0.18/0.46 tff(382,plain,
% 0.18/0.46 (op1(j(e20), j(e21)) = op1(e14, e13)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[107, 373])).
% 0.18/0.46 tff(383,plain,
% 0.18/0.46 (op1(e14, e13) = op1(j(e20), j(e21))),
% 0.18/0.46 inference(symmetry,[status(thm)],[382])).
% 0.18/0.46 tff(384,plain,
% 0.18/0.46 ((op1(e14, e13) = e10) <=> (op1(e14, e13) = e10)),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(385,plain,
% 0.18/0.46 (op1(e14, e13) = e10),
% 0.18/0.46 inference(and_elim,[status(thm)],[13])).
% 0.18/0.46 tff(386,plain,
% 0.18/0.46 (op1(e14, e13) = e10),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.18/0.46 tff(387,plain,
% 0.18/0.46 (e10 = op1(e14, e13)),
% 0.18/0.46 inference(symmetry,[status(thm)],[386])).
% 0.18/0.46 tff(388,plain,
% 0.18/0.46 ((op1(e11, e14) = e10) <=> (op1(e11, e14) = e10)),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(389,plain,
% 0.18/0.46 (op1(e11, e14) = e10),
% 0.18/0.46 inference(and_elim,[status(thm)],[131])).
% 0.18/0.46 tff(390,plain,
% 0.18/0.46 (op1(e11, e14) = e10),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.18/0.46 tff(391,plain,
% 0.18/0.46 (op1(e11, e14) = op1(j(e22), j(e20))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[377, 108])).
% 0.18/0.46 tff(392,plain,
% 0.18/0.46 (op1(j(e22), j(e20)) = op1(e11, e14)),
% 0.18/0.46 inference(symmetry,[status(thm)],[391])).
% 0.18/0.46 tff(393,plain,
% 0.18/0.46 ((j(op2(e22, e20)) = op1(j(e22), j(e20))) <=> (j(op2(e22, e20)) = op1(j(e22), j(e20)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(394,plain,
% 0.18/0.46 (j(op2(e22, e20)) = op1(j(e22), j(e20))),
% 0.18/0.46 inference(and_elim,[status(thm)],[5])).
% 0.18/0.46 tff(395,plain,
% 0.18/0.46 (j(op2(e22, e20)) = op1(j(e22), j(e20))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[394, 393])).
% 0.18/0.46 tff(396,plain,
% 0.18/0.46 ((op2(e22, e20) = e21) <=> (op2(e22, e20) = e21)),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(397,plain,
% 0.18/0.46 (op2(e22, e20) = e21),
% 0.18/0.46 inference(and_elim,[status(thm)],[39])).
% 0.18/0.46 tff(398,plain,
% 0.18/0.46 (op2(e22, e20) = e21),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[397, 396])).
% 0.18/0.46 tff(399,plain,
% 0.18/0.46 (j(op2(e22, e20)) = j(e21)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[398])).
% 0.18/0.46 tff(400,plain,
% 0.18/0.46 (j(e21) = j(op2(e22, e20))),
% 0.18/0.46 inference(symmetry,[status(thm)],[399])).
% 0.18/0.46 tff(401,plain,
% 0.18/0.46 (j(e21) = e14),
% 0.18/0.46 inference(transitivity,[status(thm)],[400, 395, 392, 390, 387, 383, 381, 380, 124, 119, 379, 372])).
% 0.18/0.46 tff(402,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[368, 401])).
% 0.18/0.46 tff(403,plain,((~(j(e21) = e13)) | (~(j(e20) = e14))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(404,plain,
% 0.18/0.46 (~(j(e21) = e13)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[403, 107])).
% 0.18/0.46 tff(405,plain,
% 0.18/0.46 (((j(e21) = e10) | (j(e21) = e11) | (j(e21) = e12) | (j(e21) = e13) | (j(e21) = e14)) <=> ((j(e21) = e10) | (j(e21) = e11) | (j(e21) = e12) | (j(e21) = e13) | (j(e21) = e14))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(406,plain,
% 0.18/0.46 ((j(e21) = e10) | (j(e21) = e11) | (j(e21) = e12) | (j(e21) = e13) | (j(e21) = e14)),
% 0.18/0.46 inference(and_elim,[status(thm)],[159])).
% 0.18/0.46 tff(407,plain,
% 0.18/0.46 ((j(e21) = e10) | (j(e21) = e11) | (j(e21) = e12) | (j(e21) = e13) | (j(e21) = e14)),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[406, 405])).
% 0.18/0.46 tff(408,plain,
% 0.18/0.46 (j(e21) = e11),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[407, 404, 369, 353, 368])).
% 0.18/0.46 tff(409,plain,
% 0.18/0.46 (e11 = j(e21)),
% 0.18/0.46 inference(symmetry,[status(thm)],[408])).
% 0.18/0.46 tff(410,plain,
% 0.18/0.46 ((op1(e14, e11) = e12) <=> (op1(e14, e11) = e12)),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(411,plain,
% 0.18/0.46 (op1(e14, e11) = e12),
% 0.18/0.46 inference(and_elim,[status(thm)],[19])).
% 0.18/0.46 tff(412,plain,
% 0.18/0.46 (op1(e14, e11) = e12),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[411, 410])).
% 0.18/0.46 tff(413,assumption,(j(e21) = e11), introduced(assumption)).
% 0.18/0.46 tff(414,plain,
% 0.18/0.46 (e11 = j(e21)),
% 0.18/0.46 inference(symmetry,[status(thm)],[413])).
% 0.18/0.46 tff(415,plain,
% 0.18/0.46 (op1(e14, e11) = op1(j(e20), j(e21))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[108, 414])).
% 0.18/0.46 tff(416,plain,
% 0.18/0.46 (op1(j(e20), j(e21)) = op1(e14, e11)),
% 0.18/0.46 inference(symmetry,[status(thm)],[415])).
% 0.18/0.46 tff(417,plain,
% 0.18/0.46 (j(e23) = e12),
% 0.18/0.46 inference(transitivity,[status(thm)],[153, 147, 416, 412])).
% 0.18/0.46 tff(418,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[321, 417])).
% 0.18/0.46 tff(419,plain,((~(j(e21) = e11)) | (j(e23) = e12) | (~(j(e20) = e14))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(420,plain,
% 0.18/0.46 (j(e23) = e12),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[419, 408, 107])).
% 0.18/0.46 tff(421,plain,
% 0.18/0.46 (e12 = j(e23)),
% 0.18/0.46 inference(symmetry,[status(thm)],[420])).
% 0.18/0.46 tff(422,plain,
% 0.18/0.46 (op1(e12, e11) = op1(j(e23), j(e21))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[421, 409])).
% 0.18/0.46 tff(423,plain,
% 0.18/0.46 (e10 = op1(e12, e11)),
% 0.18/0.46 inference(symmetry,[status(thm)],[91])).
% 0.18/0.46 tff(424,plain,
% 0.18/0.46 (op1(j(e21), j(e20)) = op1(e11, e14)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[408, 107])).
% 0.18/0.46 tff(425,plain,
% 0.18/0.46 (e22 = op2(e21, e20)),
% 0.18/0.46 inference(symmetry,[status(thm)],[46])).
% 0.18/0.46 tff(426,plain,
% 0.18/0.46 (j(e22) = j(op2(e21, e20))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[425])).
% 0.18/0.46 tff(427,plain,
% 0.18/0.46 (op1(j(e20), j(e23)) = j(op2(e20, e23))),
% 0.18/0.46 inference(symmetry,[status(thm)],[330])).
% 0.18/0.46 tff(428,plain,
% 0.18/0.46 (op1(e14, e12) = op1(j(e20), j(e23))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[108, 421])).
% 0.18/0.46 tff(429,plain,
% 0.18/0.46 (e11 = op1(e14, e12)),
% 0.18/0.46 inference(symmetry,[status(thm)],[16])).
% 0.18/0.46 tff(430,plain,
% 0.18/0.46 (j(e21) = e14),
% 0.18/0.46 inference(transitivity,[status(thm)],[408, 429, 428, 427, 334, 426, 50, 424, 390, 423, 422, 354, 174, 107])).
% 0.18/0.46 tff(431,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[368, 430])).
% 0.18/0.46 tff(432,plain,((~(j(e20) = e14)) | (j(e21) = e10) | (j(e21) = e12)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(433,plain,
% 0.18/0.46 (~(j(e20) = e14)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[432, 353, 352])).
% 0.18/0.46 tff(434,plain,
% 0.18/0.46 ((e12 = j(e20)) <=> (j(e20) = e12)),
% 0.18/0.46 inference(commutativity,[status(thm)],[])).
% 0.18/0.46 tff(435,plain,
% 0.18/0.46 (h(j(e20)) = h(e11)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[92])).
% 0.18/0.46 tff(436,plain,
% 0.18/0.46 (e20 = h(e11)),
% 0.18/0.46 inference(transitivity,[status(thm)],[356, 435])).
% 0.18/0.46 tff(437,plain,
% 0.18/0.46 ((e20 = e21) <=> (h(e11) = e21)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[436])).
% 0.18/0.46 tff(438,plain,
% 0.18/0.46 ((~(e20 = e21)) <=> (~(h(e11) = e21))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[437])).
% 0.18/0.46 tff(439,plain,
% 0.18/0.46 (~(h(e11) = e21)),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[285, 438])).
% 0.18/0.46 tff(440,plain,
% 0.18/0.46 (h(j(e21)) = h(e11)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[413])).
% 0.18/0.46 tff(441,plain,
% 0.18/0.46 (h(e11) = h(j(e21))),
% 0.18/0.46 inference(symmetry,[status(thm)],[440])).
% 0.18/0.46 tff(442,plain,
% 0.18/0.46 (h(e11) = e21),
% 0.18/0.46 inference(transitivity,[status(thm)],[441, 198])).
% 0.18/0.46 tff(443,assumption,(~(h(e11) = e21)), introduced(assumption)).
% 0.18/0.46 tff(444,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[443, 442])).
% 0.18/0.46 tff(445,plain,((~(j(e21) = e11)) | (h(e11) = e21)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(446,plain,
% 0.18/0.46 (~(j(e21) = e11)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[445, 439])).
% 0.18/0.46 tff(447,plain,
% 0.18/0.46 ((op1(e11, e13) = e12) <=> (op1(e11, e13) = e12)),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(448,plain,
% 0.18/0.46 (op1(e11, e13) = e12),
% 0.18/0.46 inference(and_elim,[status(thm)],[132])).
% 0.18/0.46 tff(449,plain,
% 0.18/0.46 (op1(e11, e13) = e12),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[448, 447])).
% 0.18/0.46 tff(450,plain,
% 0.18/0.46 (op1(e11, e13) = op1(j(e20), j(e21))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[93, 374])).
% 0.18/0.46 tff(451,plain,
% 0.18/0.46 (op1(j(e20), j(e21)) = op1(e11, e13)),
% 0.18/0.46 inference(symmetry,[status(thm)],[450])).
% 0.18/0.46 tff(452,plain,
% 0.18/0.46 (j(e23) = e12),
% 0.18/0.46 inference(transitivity,[status(thm)],[153, 147, 451, 449])).
% 0.18/0.46 tff(453,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[321, 452])).
% 0.18/0.46 tff(454,plain,((~(j(e21) = e13)) | (j(e23) = e12) | (~(j(e20) = e11))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(455,plain,
% 0.18/0.46 (~(j(e21) = e13)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[454, 92, 321])).
% 0.18/0.46 tff(456,plain,
% 0.18/0.46 (j(e21) = e14),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[407, 455, 369, 353, 446])).
% 0.18/0.46 tff(457,plain,
% 0.18/0.46 (e14 = j(e21)),
% 0.18/0.46 inference(symmetry,[status(thm)],[456])).
% 0.18/0.46 tff(458,plain,
% 0.18/0.46 (op1(e11, e14) = op1(j(e20), j(e21))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[93, 457])).
% 0.18/0.46 tff(459,plain,
% 0.18/0.46 (e10 = op1(e11, e14)),
% 0.18/0.46 inference(symmetry,[status(thm)],[390])).
% 0.18/0.46 tff(460,plain,
% 0.18/0.46 (e10 = j(e23)),
% 0.18/0.46 inference(transitivity,[status(thm)],[459, 458, 381, 380])).
% 0.18/0.46 tff(461,plain,
% 0.18/0.46 (op1(e10, e14) = op1(j(e23), j(e21))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[460, 457])).
% 0.18/0.46 tff(462,plain,
% 0.18/0.46 (op1(j(e21), j(e20)) = op1(e14, e11)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[456, 92])).
% 0.18/0.46 tff(463,plain,
% 0.18/0.46 (op1(e11, e10) = op1(j(e20), j(e23))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[93, 460])).
% 0.18/0.46 tff(464,plain,
% 0.18/0.46 (e14 = op1(e11, e10)),
% 0.18/0.46 inference(symmetry,[status(thm)],[221])).
% 0.18/0.46 tff(465,plain,
% 0.18/0.46 (j(e21) = e11),
% 0.18/0.46 inference(transitivity,[status(thm)],[456, 464, 463, 427, 334, 426, 50, 462, 412, 302, 461, 354, 174, 92])).
% 0.18/0.46 tff(466,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[446, 465])).
% 0.18/0.46 tff(467,plain,((~(j(e20) = e11)) | (j(e21) = e10) | (j(e21) = e12) | (j(e23) = e12)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(468,plain,
% 0.18/0.46 (~(j(e20) = e11)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[467, 321, 353, 352])).
% 0.18/0.46 tff(469,plain,
% 0.18/0.46 (j(e20) = e10),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[161, 468, 9, 433, 104])).
% 0.18/0.46 tff(470,plain,
% 0.18/0.46 (e10 = j(e20)),
% 0.18/0.46 inference(symmetry,[status(thm)],[469])).
% 0.18/0.46 tff(471,plain,
% 0.18/0.46 ((e14 = j(e20)) <=> (j(e20) = e14)),
% 0.18/0.46 inference(commutativity,[status(thm)],[])).
% 0.18/0.46 tff(472,plain,
% 0.18/0.46 (op1(e11, e10) = op1(j(e21), j(e20))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[414, 142])).
% 0.18/0.46 tff(473,plain,
% 0.18/0.46 (op1(j(e21), j(e20)) = op1(e11, e10)),
% 0.18/0.46 inference(symmetry,[status(thm)],[472])).
% 0.18/0.46 tff(474,plain,
% 0.18/0.46 (j(e22) = e14),
% 0.18/0.46 inference(transitivity,[status(thm)],[96, 50, 473, 221])).
% 0.18/0.46 tff(475,plain,
% 0.18/0.46 ((j(e22) = e10) <=> (e14 = j(e20))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[474, 142])).
% 0.18/0.46 tff(476,plain,
% 0.18/0.46 ((j(e22) = e10) <=> (j(e20) = e14)),
% 0.18/0.46 inference(transitivity,[status(thm)],[475, 471])).
% 0.18/0.46 tff(477,plain,
% 0.18/0.46 ((j(e20) = e14) <=> (j(e22) = e10)),
% 0.18/0.46 inference(symmetry,[status(thm)],[476])).
% 0.18/0.46 tff(478,plain,
% 0.18/0.46 ((~(j(e20) = e14)) <=> (~(j(e22) = e10))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[477])).
% 0.18/0.46 tff(479,assumption,(~(j(e20) = e14)), introduced(assumption)).
% 0.18/0.46 tff(480,plain,
% 0.18/0.46 (~(j(e22) = e10)),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[479, 478])).
% 0.18/0.46 tff(481,plain,
% 0.18/0.46 (e20 = op2(e23, e21)),
% 0.18/0.46 inference(symmetry,[status(thm)],[173])).
% 0.18/0.46 tff(482,plain,
% 0.18/0.46 (j(e20) = j(op2(e23, e21))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[481])).
% 0.18/0.46 tff(483,plain,
% 0.18/0.46 (j(op2(e23, e21)) = j(e20)),
% 0.18/0.46 inference(symmetry,[status(thm)],[482])).
% 0.18/0.46 tff(484,plain,
% 0.18/0.46 ((op1(e10, e11) = e13) <=> (op1(e10, e11) = e13)),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(485,plain,
% 0.18/0.46 ((op1(e10, e10) = e10) & (op1(e10, e11) = e13)),
% 0.18/0.46 inference(and_elim,[status(thm)],[138])).
% 0.18/0.46 tff(486,plain,
% 0.18/0.46 (op1(e10, e11) = e13),
% 0.18/0.46 inference(and_elim,[status(thm)],[485])).
% 0.18/0.46 tff(487,plain,
% 0.18/0.46 (op1(e10, e11) = e13),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[486, 484])).
% 0.18/0.46 tff(488,plain,
% 0.18/0.46 (op1(e10, e11) = op1(j(e20), j(e21))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[142, 414])).
% 0.18/0.46 tff(489,plain,
% 0.18/0.46 (op1(j(e20), j(e21)) = op1(e10, e11)),
% 0.18/0.46 inference(symmetry,[status(thm)],[488])).
% 0.18/0.46 tff(490,plain,
% 0.18/0.46 (j(op2(e20, e21)) = j(e23)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[151])).
% 0.18/0.46 tff(491,plain,
% 0.18/0.46 (j(e23) = j(op2(e20, e21))),
% 0.18/0.46 inference(symmetry,[status(thm)],[490])).
% 0.18/0.46 tff(492,plain,
% 0.18/0.46 (j(e23) = e13),
% 0.18/0.46 inference(transitivity,[status(thm)],[491, 147, 489, 487])).
% 0.18/0.46 tff(493,plain,
% 0.18/0.46 (op1(j(e23), j(e21)) = op1(e13, e11)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[492, 413])).
% 0.18/0.46 tff(494,plain,
% 0.18/0.46 (op1(e13, e11) = op1(j(e23), j(e21))),
% 0.18/0.46 inference(symmetry,[status(thm)],[493])).
% 0.18/0.46 tff(495,plain,
% 0.18/0.46 (e14 = op1(e13, e11)),
% 0.18/0.46 inference(symmetry,[status(thm)],[372])).
% 0.18/0.46 tff(496,plain,
% 0.18/0.46 (j(e22) = e10),
% 0.18/0.46 inference(transitivity,[status(thm)],[96, 50, 473, 221, 495, 494, 354, 483, 141])).
% 0.18/0.46 tff(497,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[496, 480])).
% 0.18/0.46 tff(498,plain,((~(j(e21) = e11)) | (j(e20) = e14) | (~(j(e20) = e10))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(499,plain,
% 0.18/0.46 (~(j(e21) = e11)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[498, 469, 433])).
% 0.18/0.46 tff(500,plain,
% 0.18/0.46 (e14 = j(e21)),
% 0.18/0.46 inference(symmetry,[status(thm)],[361])).
% 0.18/0.46 tff(501,plain,
% 0.18/0.46 (op1(e10, e14) = op1(j(e20), j(e21))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[142, 500])).
% 0.18/0.46 tff(502,plain,
% 0.18/0.46 (op1(j(e20), j(e21)) = op1(e10, e14)),
% 0.18/0.46 inference(symmetry,[status(thm)],[501])).
% 0.18/0.46 tff(503,plain,
% 0.18/0.46 (j(e23) = e12),
% 0.18/0.46 inference(transitivity,[status(thm)],[153, 147, 502, 301])).
% 0.18/0.46 tff(504,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[321, 503])).
% 0.18/0.46 tff(505,plain,((~(j(e21) = e14)) | (j(e23) = e12) | (~(j(e20) = e10))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(506,plain,
% 0.18/0.46 (~(j(e21) = e14)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[505, 321, 469])).
% 0.18/0.46 tff(507,plain,
% 0.18/0.46 (j(e21) = e13),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[407, 506, 352, 353, 499])).
% 0.18/0.46 tff(508,plain,
% 0.18/0.46 (e13 = j(e21)),
% 0.18/0.46 inference(symmetry,[status(thm)],[507])).
% 0.18/0.46 tff(509,plain,
% 0.18/0.46 (op1(e13, e10) = op1(j(e21), j(e20))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[508, 470])).
% 0.18/0.46 tff(510,plain,
% 0.18/0.46 (op1(j(e21), j(e20)) = op1(e13, e10)),
% 0.18/0.46 inference(symmetry,[status(thm)],[509])).
% 0.18/0.46 tff(511,plain,
% 0.18/0.46 (j(e22) = e12),
% 0.18/0.46 inference(transitivity,[status(thm)],[96, 50, 510, 261])).
% 0.18/0.46 tff(512,plain,
% 0.18/0.46 ((j(e22) = e10) <=> (e12 = j(e20))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[511, 470])).
% 0.18/0.46 tff(513,plain,
% 0.18/0.46 ((j(e22) = e10) <=> (j(e20) = e12)),
% 0.18/0.46 inference(transitivity,[status(thm)],[512, 434])).
% 0.18/0.46 tff(514,plain,
% 0.18/0.46 ((j(e20) = e12) <=> (j(e22) = e10)),
% 0.18/0.46 inference(symmetry,[status(thm)],[513])).
% 0.18/0.46 tff(515,plain,
% 0.18/0.46 ((~(j(e20) = e12)) <=> (~(j(e22) = e10))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[514])).
% 0.18/0.46 tff(516,plain,
% 0.18/0.46 (~(j(e22) = e10)),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[9, 515])).
% 0.18/0.46 tff(517,plain,
% 0.18/0.46 (op1(j(e20), j(e21)) = op1(e10, e13)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[469, 507])).
% 0.18/0.46 tff(518,plain,
% 0.18/0.46 (j(e23) = e11),
% 0.18/0.46 inference(transitivity,[status(thm)],[153, 147, 517, 338])).
% 0.18/0.46 tff(519,plain,
% 0.18/0.46 (op1(j(e23), j(e21)) = op1(e11, e13)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[518, 507])).
% 0.18/0.46 tff(520,plain,
% 0.18/0.46 (op1(e11, e13) = op1(j(e23), j(e21))),
% 0.18/0.46 inference(symmetry,[status(thm)],[519])).
% 0.18/0.46 tff(521,plain,
% 0.18/0.46 (e12 = op1(e11, e13)),
% 0.18/0.46 inference(symmetry,[status(thm)],[449])).
% 0.18/0.46 tff(522,plain,
% 0.18/0.46 (j(e22) = e10),
% 0.18/0.46 inference(transitivity,[status(thm)],[96, 50, 510, 261, 521, 520, 354, 483, 469])).
% 0.18/0.46 tff(523,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[522, 516])).
% 0.18/0.46 tff(524,plain,((j(e23) = e12) | (j(e20) = e12) | (j(e21) = e12) | (j(e20) = e13)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(525,plain,
% 0.18/0.46 (j(e23) = e12),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[524, 353, 9, 104])).
% 0.18/0.46 tff(526,plain,
% 0.18/0.46 ((op2(e22, e23) = e20) <=> (op2(e22, e23) = e20)),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(527,plain,
% 0.18/0.46 (op2(e22, e23) = e20),
% 0.18/0.46 inference(and_elim,[status(thm)],[36])).
% 0.18/0.46 tff(528,plain,
% 0.18/0.46 (op2(e22, e23) = e20),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[527, 526])).
% 0.18/0.46 tff(529,plain,
% 0.18/0.46 (e20 = op2(e22, e23)),
% 0.18/0.46 inference(symmetry,[status(thm)],[528])).
% 0.18/0.46 tff(530,plain,
% 0.18/0.46 (j(e20) = j(op2(e22, e23))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[529])).
% 0.18/0.46 tff(531,plain,
% 0.18/0.46 (j(op2(e22, e23)) = j(e20)),
% 0.18/0.46 inference(symmetry,[status(thm)],[530])).
% 0.18/0.46 tff(532,plain,
% 0.18/0.46 ((j(op2(e22, e23)) = op1(j(e22), j(e23))) <=> (j(op2(e22, e23)) = op1(j(e22), j(e23)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(533,plain,
% 0.18/0.46 (j(op2(e22, e23)) = op1(j(e22), j(e23))),
% 0.18/0.46 inference(and_elim,[status(thm)],[5])).
% 0.18/0.46 tff(534,plain,
% 0.18/0.46 (j(op2(e22, e23)) = op1(j(e22), j(e23))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[533, 532])).
% 0.18/0.46 tff(535,plain,
% 0.18/0.46 (op1(j(e22), j(e23)) = j(op2(e22, e23))),
% 0.18/0.46 inference(symmetry,[status(thm)],[534])).
% 0.18/0.46 tff(536,assumption,(j(e23) = e12), introduced(assumption)).
% 0.18/0.46 tff(537,plain,
% 0.18/0.46 ((op1(e11, e12) = e13) <=> (op1(e11, e12) = e13)),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(538,plain,
% 0.18/0.46 (op1(e11, e12) = e13),
% 0.18/0.46 inference(and_elim,[status(thm)],[133])).
% 0.18/0.46 tff(539,plain,
% 0.18/0.46 (op1(e11, e12) = e13),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[538, 537])).
% 0.18/0.46 tff(540,plain,
% 0.18/0.46 (e12 = j(e23)),
% 0.18/0.46 inference(symmetry,[status(thm)],[536])).
% 0.18/0.46 tff(541,plain,
% 0.18/0.46 (op1(e11, e12) = op1(j(e20), j(e23))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[93, 540])).
% 0.18/0.46 tff(542,plain,
% 0.18/0.46 (op1(j(e20), j(e23)) = op1(e11, e12)),
% 0.18/0.46 inference(symmetry,[status(thm)],[541])).
% 0.18/0.46 tff(543,plain,
% 0.18/0.46 (e22 = op2(e20, e23)),
% 0.18/0.46 inference(symmetry,[status(thm)],[333])).
% 0.18/0.46 tff(544,plain,
% 0.18/0.46 (j(e22) = j(op2(e20, e23))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[543])).
% 0.18/0.46 tff(545,plain,
% 0.18/0.46 (j(e22) = e13),
% 0.18/0.46 inference(transitivity,[status(thm)],[544, 330, 542, 539])).
% 0.18/0.46 tff(546,plain,
% 0.18/0.46 (op1(j(e22), j(e23)) = op1(e13, e12)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[545, 536])).
% 0.18/0.46 tff(547,plain,
% 0.18/0.46 (op1(e13, e12) = op1(j(e22), j(e23))),
% 0.18/0.46 inference(symmetry,[status(thm)],[546])).
% 0.18/0.46 tff(548,plain,
% 0.18/0.46 (e10 = op1(e13, e12)),
% 0.18/0.46 inference(symmetry,[status(thm)],[257])).
% 0.18/0.46 tff(549,plain,
% 0.18/0.46 (op1(e12, e11) = op1(j(e23), j(e20))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[540, 93])).
% 0.18/0.46 tff(550,plain,
% 0.18/0.46 (op1(j(e23), j(e20)) = op1(e12, e11)),
% 0.18/0.46 inference(symmetry,[status(thm)],[549])).
% 0.18/0.46 tff(551,plain,
% 0.18/0.46 ((j(op2(e23, e20)) = op1(j(e23), j(e20))) <=> (j(op2(e23, e20)) = op1(j(e23), j(e20)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(552,plain,
% 0.18/0.46 (j(op2(e23, e20)) = op1(j(e23), j(e20))),
% 0.18/0.46 inference(and_elim,[status(thm)],[5])).
% 0.18/0.46 tff(553,plain,
% 0.18/0.46 (j(op2(e23, e20)) = op1(j(e23), j(e20))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[552, 551])).
% 0.18/0.46 tff(554,plain,
% 0.18/0.46 ((op2(e23, e20) = e24) <=> (op2(e23, e20) = e24)),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(555,plain,
% 0.18/0.46 (op2(e23, e20) = e24),
% 0.18/0.46 inference(and_elim,[status(thm)],[34])).
% 0.18/0.46 tff(556,plain,
% 0.18/0.46 (op2(e23, e20) = e24),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[555, 554])).
% 0.18/0.46 tff(557,plain,
% 0.18/0.46 (j(op2(e23, e20)) = j(e24)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[556])).
% 0.18/0.46 tff(558,plain,
% 0.18/0.46 (j(e24) = j(op2(e23, e20))),
% 0.18/0.46 inference(symmetry,[status(thm)],[557])).
% 0.18/0.46 tff(559,plain,
% 0.18/0.46 (j(e24) = e11),
% 0.18/0.46 inference(transitivity,[status(thm)],[558, 553, 550, 91, 548, 547, 535, 531, 92])).
% 0.18/0.46 tff(560,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[8, 559])).
% 0.18/0.46 tff(561,plain,((~(j(e20) = e11)) | (j(e24) = e11) | (~(j(e23) = e12))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(562,plain,
% 0.18/0.46 (~(j(e20) = e11)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[561, 525, 8])).
% 0.18/0.46 tff(563,plain,
% 0.18/0.46 (j(e20) = e10),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[161, 562, 9, 433, 104])).
% 0.18/0.46 tff(564,plain,
% 0.18/0.46 (e10 = j(e20)),
% 0.18/0.46 inference(symmetry,[status(thm)],[563])).
% 0.18/0.46 tff(565,plain,
% 0.18/0.46 (e12 = j(e23)),
% 0.18/0.46 inference(symmetry,[status(thm)],[525])).
% 0.18/0.46 tff(566,plain,
% 0.18/0.46 (op1(e12, e10) = op1(j(e23), j(e20))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[565, 564])).
% 0.18/0.46 tff(567,plain,
% 0.18/0.46 (op1(j(e23), j(e20)) = op1(e12, e10)),
% 0.18/0.46 inference(symmetry,[status(thm)],[566])).
% 0.18/0.46 tff(568,plain,
% 0.18/0.46 (j(e24) = e11),
% 0.18/0.46 inference(transitivity,[status(thm)],[558, 553, 567, 187])).
% 0.18/0.46 tff(569,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[8, 568])).
% 0.18/0.46 tff(570,plain,((j(e21) = e12) | (j(e24) = e11) | (j(e20) = e12) | (j(e20) = e13)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(571,plain,
% 0.18/0.46 (j(e20) = e13),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[570, 254, 9, 8])).
% 0.18/0.46 tff(572,plain,
% 0.18/0.46 (h(j(e20)) = h(e13)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[571])).
% 0.18/0.46 tff(573,plain,
% 0.18/0.46 (e20 = h(e13)),
% 0.18/0.46 inference(transitivity,[status(thm)],[356, 572])).
% 0.18/0.46 tff(574,plain,
% 0.18/0.46 ((e20 = e21) <=> (h(e13) = e21)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[573])).
% 0.18/0.47 tff(575,plain,
% 0.18/0.47 ((~(e20 = e21)) <=> (~(h(e13) = e21))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[574])).
% 0.18/0.47 tff(576,plain,
% 0.18/0.47 (~(h(e13) = e21)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[285, 575])).
% 0.18/0.47 tff(577,plain,
% 0.18/0.47 (h(j(e21)) = h(e13)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[373])).
% 0.18/0.47 tff(578,plain,
% 0.18/0.47 (h(e13) = h(j(e21))),
% 0.18/0.47 inference(symmetry,[status(thm)],[577])).
% 0.18/0.47 tff(579,plain,
% 0.18/0.47 (h(e13) = e21),
% 0.18/0.47 inference(transitivity,[status(thm)],[578, 198])).
% 0.18/0.47 tff(580,assumption,(~(h(e13) = e21)), introduced(assumption)).
% 0.18/0.47 tff(581,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[580, 579])).
% 0.18/0.47 tff(582,plain,((~(j(e21) = e13)) | (h(e13) = e21)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(583,plain,
% 0.18/0.47 (~(j(e21) = e13)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[582, 576])).
% 0.18/0.47 tff(584,plain,
% 0.18/0.47 (op1(e13, e14) = op1(j(e20), j(e21))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[53, 500])).
% 0.18/0.47 tff(585,plain,
% 0.18/0.47 (e11 = j(e23)),
% 0.18/0.47 inference(transitivity,[status(thm)],[376, 584, 381, 380])).
% 0.18/0.47 tff(586,plain,
% 0.18/0.47 (op1(e11, e14) = op1(j(e23), j(e21))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[585, 500])).
% 0.18/0.47 tff(587,plain,
% 0.18/0.47 (op1(j(e21), j(e20)) = op1(e14, e13)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[361, 52])).
% 0.18/0.47 tff(588,plain,
% 0.18/0.47 (op1(e13, e11) = op1(j(e20), j(e23))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[53, 585])).
% 0.18/0.47 tff(589,plain,
% 0.18/0.47 (j(e21) = e13),
% 0.18/0.47 inference(transitivity,[status(thm)],[361, 495, 588, 427, 334, 426, 50, 587, 386, 459, 586, 354, 174, 52])).
% 0.18/0.47 tff(590,plain,
% 0.18/0.47 (h(j(e20)) = h(e13)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[52])).
% 0.18/0.47 tff(591,plain,
% 0.18/0.47 (e20 = h(e13)),
% 0.18/0.47 inference(transitivity,[status(thm)],[356, 590])).
% 0.18/0.47 tff(592,plain,
% 0.18/0.47 ((e20 = e21) <=> (h(e13) = e21)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[591])).
% 0.18/0.47 tff(593,plain,
% 0.18/0.47 ((~(e20 = e21)) <=> (~(h(e13) = e21))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[592])).
% 0.18/0.47 tff(594,plain,
% 0.18/0.47 (~(h(e13) = e21)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[285, 593])).
% 0.18/0.47 tff(595,plain,
% 0.18/0.47 (~(j(e21) = e13)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[582, 594])).
% 0.18/0.47 tff(596,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[595, 589])).
% 0.18/0.47 tff(597,plain,((~(j(e21) = e14)) | (~(j(e20) = e13))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(598,plain,
% 0.18/0.47 (~(j(e21) = e14)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[597, 571])).
% 0.18/0.47 tff(599,plain,
% 0.18/0.47 (j(e21) = e11),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[407, 598, 352, 254, 583])).
% 0.18/0.47 tff(600,plain,
% 0.18/0.47 (op1(e11, e13) = op1(j(e21), j(e20))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[414, 53])).
% 0.18/0.47 tff(601,plain,
% 0.18/0.47 (op1(j(e21), j(e20)) = op1(e11, e13)),
% 0.18/0.47 inference(symmetry,[status(thm)],[600])).
% 0.18/0.47 tff(602,plain,
% 0.18/0.47 (j(op2(e20, e23)) = j(e22)),
% 0.18/0.47 inference(symmetry,[status(thm)],[544])).
% 0.18/0.47 tff(603,plain,
% 0.18/0.47 (op1(e13, e11) = op1(j(e20), j(e21))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[53, 414])).
% 0.18/0.47 tff(604,plain,
% 0.18/0.47 (op1(j(e20), j(e21)) = op1(e13, e11)),
% 0.18/0.47 inference(symmetry,[status(thm)],[603])).
% 0.18/0.47 tff(605,plain,
% 0.18/0.47 (j(e23) = e14),
% 0.18/0.47 inference(transitivity,[status(thm)],[153, 147, 604, 372])).
% 0.18/0.47 tff(606,plain,
% 0.18/0.47 (op1(j(e20), j(e23)) = op1(e13, e14)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[52, 605])).
% 0.18/0.47 tff(607,plain,
% 0.18/0.47 (op1(e13, e14) = op1(j(e20), j(e23))),
% 0.18/0.47 inference(symmetry,[status(thm)],[606])).
% 0.18/0.47 tff(608,plain,
% 0.18/0.47 (e21 = op2(e22, e20)),
% 0.18/0.47 inference(symmetry,[status(thm)],[398])).
% 0.18/0.47 tff(609,plain,
% 0.18/0.47 (j(e21) = j(op2(e22, e20))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[608])).
% 0.18/0.47 tff(610,plain,
% 0.18/0.47 (j(op2(e22, e20)) = j(e21)),
% 0.18/0.47 inference(symmetry,[status(thm)],[609])).
% 0.18/0.47 tff(611,plain,
% 0.18/0.47 (op1(j(e22), j(e20)) = j(op2(e22, e20))),
% 0.18/0.47 inference(symmetry,[status(thm)],[395])).
% 0.18/0.47 tff(612,plain,
% 0.18/0.47 (j(e22) = e12),
% 0.18/0.47 inference(transitivity,[status(thm)],[96, 50, 601, 449])).
% 0.18/0.47 tff(613,plain,
% 0.18/0.47 (op1(j(e22), j(e20)) = op1(e12, e13)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[612, 52])).
% 0.18/0.47 tff(614,plain,
% 0.18/0.47 (op1(e12, e13) = op1(j(e22), j(e20))),
% 0.18/0.47 inference(symmetry,[status(thm)],[613])).
% 0.18/0.47 tff(615,plain,
% 0.18/0.47 (j(e23) = e12),
% 0.18/0.47 inference(transitivity,[status(thm)],[153, 147, 604, 372, 64, 614, 611, 610, 413, 376, 607, 427, 602, 96, 50, 601, 449])).
% 0.18/0.47 tff(616,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[321, 615])).
% 0.18/0.47 tff(617,plain,((~(j(e21) = e11)) | (j(e23) = e12) | (~(j(e20) = e13))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(618,plain,
% 0.18/0.47 (j(e23) = e12),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[617, 599, 571])).
% 0.18/0.47 tff(619,plain,
% 0.18/0.47 (e12 = j(e23)),
% 0.18/0.47 inference(symmetry,[status(thm)],[618])).
% 0.18/0.47 tff(620,plain,
% 0.18/0.47 ((e12 = e14) <=> (j(e23) = e14)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[619])).
% 0.18/0.47 tff(621,plain,
% 0.18/0.47 ((j(e23) = e14) <=> (e12 = e14)),
% 0.18/0.47 inference(symmetry,[status(thm)],[620])).
% 0.18/0.47 tff(622,plain,
% 0.18/0.47 (e11 = j(e21)),
% 0.18/0.47 inference(symmetry,[status(thm)],[599])).
% 0.18/0.47 tff(623,plain,
% 0.18/0.47 (e13 = j(e20)),
% 0.18/0.47 inference(symmetry,[status(thm)],[571])).
% 0.18/0.47 tff(624,plain,
% 0.18/0.47 (op1(e13, e11) = op1(j(e20), j(e21))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[623, 622])).
% 0.18/0.47 tff(625,plain,
% 0.18/0.47 (op1(j(e20), j(e21)) = op1(e13, e11)),
% 0.18/0.47 inference(symmetry,[status(thm)],[624])).
% 0.18/0.47 tff(626,plain,
% 0.18/0.47 (j(e23) = e14),
% 0.18/0.47 inference(transitivity,[status(thm)],[153, 147, 625, 372])).
% 0.18/0.47 tff(627,plain,
% 0.18/0.47 (e12 = e14),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[626, 621])).
% 0.18/0.47 tff(628,plain,
% 0.18/0.47 ((~(e12 = e14)) <=> (~(e12 = e14))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(629,axiom,((((((((((~(e10 = e11)) & (~(e10 = e12))) & (~(e10 = e13))) & (~(e10 = e14))) & (~(e11 = e12))) & (~(e11 = e13))) & (~(e11 = e14))) & (~(e12 = e13))) & (~(e12 = e14))) & (~(e13 = e14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax1')).
% 0.18/0.47 tff(630,plain,
% 0.18/0.47 (((((((((~(e10 = e11)) & (~(e10 = e12))) & (~(e10 = e13))) & (~(e10 = e14))) & (~(e11 = e12))) & (~(e11 = e13))) & (~(e11 = e14))) & (~(e12 = e13))) & (~(e12 = e14))),
% 0.18/0.47 inference(and_elim,[status(thm)],[629])).
% 0.18/0.47 tff(631,plain,
% 0.18/0.47 (~(e12 = e14)),
% 0.18/0.47 inference(and_elim,[status(thm)],[630])).
% 0.18/0.47 tff(632,plain,
% 0.18/0.47 (~(e12 = e14)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[631, 628])).
% 0.18/0.47 tff(633,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[632, 627])).
% 0.18/0.47 tff(634,plain,((j(e20) = e12) | (j(e24) = e11)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(635,plain,
% 0.18/0.47 (j(e20) = e12),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[634, 8])).
% 0.18/0.47 tff(636,plain,
% 0.18/0.47 (e12 = j(e20)),
% 0.18/0.47 inference(symmetry,[status(thm)],[635])).
% 0.18/0.47 tff(637,plain,
% 0.18/0.47 (op1(e12, e13) = op1(j(e20), j(e21))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[636, 374])).
% 0.18/0.47 tff(638,plain,
% 0.18/0.47 (e14 = j(e23)),
% 0.18/0.47 inference(transitivity,[status(thm)],[64, 637, 381, 380])).
% 0.18/0.47 tff(639,plain,
% 0.18/0.47 (op1(e13, e14) = op1(j(e21), j(e23))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[374, 638])).
% 0.18/0.47 tff(640,plain,
% 0.18/0.47 (op1(j(e21), j(e23)) = op1(e13, e14)),
% 0.18/0.47 inference(symmetry,[status(thm)],[639])).
% 0.18/0.47 tff(641,plain,
% 0.18/0.47 ((j(op2(e21, e23)) = op1(j(e21), j(e23))) <=> (j(op2(e21, e23)) = op1(j(e21), j(e23)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(642,plain,
% 0.18/0.47 (j(op2(e21, e23)) = op1(j(e21), j(e23))),
% 0.18/0.47 inference(and_elim,[status(thm)],[5])).
% 0.18/0.47 tff(643,plain,
% 0.18/0.47 (j(op2(e21, e23)) = op1(j(e21), j(e23))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[642, 641])).
% 0.18/0.47 tff(644,plain,
% 0.18/0.47 (j(op2(e21, e23)) = j(e24)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[207])).
% 0.18/0.47 tff(645,plain,
% 0.18/0.47 (j(e24) = j(op2(e21, e23))),
% 0.18/0.47 inference(symmetry,[status(thm)],[644])).
% 0.18/0.47 tff(646,plain,
% 0.18/0.47 (j(e24) = e11),
% 0.18/0.47 inference(transitivity,[status(thm)],[645, 643, 640, 23])).
% 0.18/0.47 tff(647,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[8, 646])).
% 0.18/0.47 tff(648,plain,((~(j(e21) = e13)) | (j(e24) = e11)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(649,plain,
% 0.18/0.47 (~(j(e21) = e13)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[648, 8])).
% 0.18/0.47 tff(650,assumption,(j(e20) = e12), introduced(assumption)).
% 0.18/0.47 tff(651,plain,
% 0.18/0.47 ((op2(e20, e20) = e20) <=> (op2(e20, e20) = e20)),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(652,plain,
% 0.18/0.47 (op2(e20, e20) = e20),
% 0.18/0.47 inference(and_elim,[status(thm)],[149])).
% 0.18/0.47 tff(653,plain,
% 0.18/0.47 (op2(e20, e20) = e20),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[652, 651])).
% 0.18/0.47 tff(654,plain,
% 0.18/0.47 (e20 = op2(e20, e20)),
% 0.18/0.47 inference(symmetry,[status(thm)],[653])).
% 0.18/0.47 tff(655,plain,
% 0.18/0.47 (j(e20) = j(op2(e20, e20))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[654])).
% 0.18/0.47 tff(656,plain,
% 0.18/0.47 (j(op2(e20, e20)) = j(e20)),
% 0.18/0.47 inference(symmetry,[status(thm)],[655])).
% 0.18/0.47 tff(657,plain,
% 0.18/0.47 ((j(op2(e20, e20)) = op1(j(e20), j(e20))) <=> (j(op2(e20, e20)) = op1(j(e20), j(e20)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(658,plain,
% 0.18/0.47 (j(op2(e20, e20)) = op1(j(e20), j(e20))),
% 0.18/0.47 inference(and_elim,[status(thm)],[5])).
% 0.18/0.47 tff(659,plain,
% 0.18/0.47 (j(op2(e20, e20)) = op1(j(e20), j(e20))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[658, 657])).
% 0.18/0.47 tff(660,plain,
% 0.18/0.47 (op1(j(e20), j(e20)) = j(op2(e20, e20))),
% 0.18/0.47 inference(symmetry,[status(thm)],[659])).
% 0.18/0.47 tff(661,plain,
% 0.18/0.47 (e12 = j(e20)),
% 0.18/0.47 inference(symmetry,[status(thm)],[650])).
% 0.18/0.47 tff(662,assumption,(h(e11) = e21), introduced(assumption)).
% 0.18/0.47 tff(663,plain,
% 0.18/0.47 (e21 = h(e11)),
% 0.18/0.47 inference(symmetry,[status(thm)],[662])).
% 0.18/0.47 tff(664,plain,
% 0.18/0.47 (h(j(e20)) = h(e12)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[650])).
% 0.18/0.47 tff(665,plain,
% 0.18/0.47 (e20 = h(e12)),
% 0.18/0.47 inference(transitivity,[status(thm)],[356, 664])).
% 0.18/0.47 tff(666,plain,
% 0.18/0.47 (op2(e20, e21) = op2(h(e12), h(e11))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[665, 663])).
% 0.18/0.47 tff(667,plain,
% 0.18/0.47 (op2(h(e12), h(e11)) = op2(e20, e21)),
% 0.18/0.47 inference(symmetry,[status(thm)],[666])).
% 0.18/0.47 tff(668,plain,
% 0.18/0.47 (h(e10) = h(op1(e12, e11))),
% 0.18/0.47 inference(symmetry,[status(thm)],[180])).
% 0.18/0.47 tff(669,plain,
% 0.18/0.47 (h(e10) = e23),
% 0.18/0.47 inference(transitivity,[status(thm)],[668, 183, 667, 151])).
% 0.18/0.47 tff(670,assumption,(~(h(e10) = e23)), introduced(assumption)).
% 0.18/0.47 tff(671,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[670, 669])).
% 0.18/0.47 tff(672,plain,((~(h(e11) = e21)) | (h(e10) = e23) | (~(j(e20) = e12))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(673,plain,
% 0.18/0.47 (h(e10) = e23),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[672, 662, 650])).
% 0.18/0.47 tff(674,plain,
% 0.18/0.47 (e23 = h(e10)),
% 0.18/0.47 inference(symmetry,[status(thm)],[673])).
% 0.18/0.47 tff(675,plain,
% 0.18/0.47 (op2(e23, e21) = op2(h(e10), h(e11))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[674, 663])).
% 0.18/0.47 tff(676,plain,
% 0.18/0.47 (op2(h(e10), h(e11)) = op2(e23, e21)),
% 0.18/0.47 inference(symmetry,[status(thm)],[675])).
% 0.18/0.47 tff(677,plain,
% 0.18/0.47 ((h(op1(e10, e11)) = op2(h(e10), h(e11))) <=> (h(op1(e10, e11)) = op2(h(e10), h(e11)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(678,plain,
% 0.18/0.47 (h(op1(e10, e11)) = op2(h(e10), h(e11))),
% 0.18/0.47 inference(and_elim,[status(thm)],[5])).
% 0.18/0.47 tff(679,plain,
% 0.18/0.47 (h(op1(e10, e11)) = op2(h(e10), h(e11))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[678, 677])).
% 0.18/0.47 tff(680,plain,
% 0.18/0.47 (h(op1(e10, e11)) = h(e13)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[487])).
% 0.18/0.47 tff(681,plain,
% 0.18/0.47 (h(e13) = h(op1(e10, e11))),
% 0.18/0.47 inference(symmetry,[status(thm)],[680])).
% 0.18/0.47 tff(682,plain,
% 0.18/0.47 (e13 = op1(e11, e12)),
% 0.18/0.47 inference(symmetry,[status(thm)],[539])).
% 0.18/0.47 tff(683,plain,
% 0.18/0.47 (h(e13) = h(op1(e11, e12))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[682])).
% 0.18/0.47 tff(684,plain,
% 0.18/0.47 (h(op1(e11, e12)) = h(e13)),
% 0.18/0.47 inference(symmetry,[status(thm)],[683])).
% 0.18/0.47 tff(685,plain,
% 0.18/0.47 ((h(op1(e11, e12)) = op2(h(e11), h(e12))) <=> (h(op1(e11, e12)) = op2(h(e11), h(e12)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(686,plain,
% 0.18/0.47 (h(op1(e11, e12)) = op2(h(e11), h(e12))),
% 0.18/0.47 inference(and_elim,[status(thm)],[5])).
% 0.18/0.47 tff(687,plain,
% 0.18/0.47 (h(op1(e11, e12)) = op2(h(e11), h(e12))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[686, 685])).
% 0.18/0.47 tff(688,plain,
% 0.18/0.47 (op2(h(e11), h(e12)) = h(op1(e11, e12))),
% 0.18/0.47 inference(symmetry,[status(thm)],[687])).
% 0.18/0.47 tff(689,plain,
% 0.18/0.47 (h(e12) = h(j(e20))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[661])).
% 0.18/0.47 tff(690,plain,
% 0.18/0.47 (h(e12) = e20),
% 0.18/0.47 inference(transitivity,[status(thm)],[689, 268])).
% 0.18/0.47 tff(691,plain,
% 0.18/0.47 (op2(h(e11), h(e12)) = op2(e21, e20)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[662, 690])).
% 0.18/0.47 tff(692,plain,
% 0.18/0.47 (op2(e21, e20) = op2(h(e11), h(e12))),
% 0.18/0.47 inference(symmetry,[status(thm)],[691])).
% 0.18/0.47 tff(693,plain,
% 0.18/0.47 (h(j(e20)) = h(e12)),
% 0.18/0.47 inference(symmetry,[status(thm)],[689])).
% 0.18/0.47 tff(694,plain,
% 0.18/0.47 (e20 = h(e12)),
% 0.18/0.47 inference(transitivity,[status(thm)],[356, 693])).
% 0.18/0.47 tff(695,plain,
% 0.18/0.47 (op2(e20, e23) = op2(h(e12), h(e10))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[694, 674])).
% 0.18/0.47 tff(696,plain,
% 0.18/0.47 (op2(h(e12), h(e10)) = op2(e20, e23)),
% 0.18/0.47 inference(symmetry,[status(thm)],[695])).
% 0.18/0.47 tff(697,plain,
% 0.18/0.47 (h(e11) = h(op1(e12, e10))),
% 0.18/0.47 inference(symmetry,[status(thm)],[188])).
% 0.18/0.47 tff(698,plain,
% 0.18/0.47 (h(e11) = e20),
% 0.18/0.47 inference(transitivity,[status(thm)],[697, 191, 696, 333, 425, 692, 688, 684, 681, 679, 676, 173])).
% 0.18/0.47 tff(699,plain,
% 0.18/0.47 ((e21 = h(e12)) <=> (h(e12) = e21)),
% 0.18/0.47 inference(commutativity,[status(thm)],[])).
% 0.18/0.47 tff(700,plain,
% 0.18/0.47 ((h(e11) = e20) <=> (e21 = h(e12))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[662, 694])).
% 0.18/0.47 tff(701,plain,
% 0.18/0.47 ((h(e11) = e20) <=> (h(e12) = e21)),
% 0.18/0.47 inference(transitivity,[status(thm)],[700, 699])).
% 0.18/0.47 tff(702,plain,
% 0.18/0.47 ((h(e12) = e21) <=> (h(e11) = e20)),
% 0.18/0.47 inference(symmetry,[status(thm)],[701])).
% 0.18/0.47 tff(703,plain,
% 0.18/0.47 ((~(h(e12) = e21)) <=> (~(h(e11) = e20))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[702])).
% 0.18/0.47 tff(704,plain,
% 0.18/0.47 ((e20 = e21) <=> (h(e12) = e21)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[694])).
% 0.18/0.47 tff(705,plain,
% 0.18/0.47 ((~(e20 = e21)) <=> (~(h(e12) = e21))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[704])).
% 0.18/0.47 tff(706,plain,
% 0.18/0.47 (~(h(e12) = e21)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[285, 705])).
% 0.18/0.47 tff(707,plain,
% 0.18/0.47 (~(h(e11) = e20)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[706, 703])).
% 0.18/0.47 tff(708,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[707, 698])).
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% 0.18/0.47 tff(710,plain,
% 0.18/0.47 (~(h(e11) = e21)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[709, 650])).
% 0.18/0.47 tff(711,plain,
% 0.18/0.47 (~(j(e21) = e11)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[445, 710])).
% 0.18/0.47 tff(712,plain,
% 0.18/0.47 ((e11 = j(e20)) <=> (j(e20) = e11)),
% 0.18/0.47 inference(commutativity,[status(thm)],[])).
% 0.18/0.47 tff(713,plain,
% 0.18/0.47 (op1(e14, e12) = op1(j(e21), j(e20))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[500, 661])).
% 0.18/0.47 tff(714,plain,
% 0.18/0.47 (op1(j(e21), j(e20)) = op1(e14, e12)),
% 0.18/0.47 inference(symmetry,[status(thm)],[713])).
% 0.18/0.47 tff(715,plain,
% 0.18/0.47 (j(e22) = e11),
% 0.18/0.47 inference(transitivity,[status(thm)],[96, 50, 714, 16])).
% 0.18/0.47 tff(716,plain,
% 0.18/0.47 ((j(e22) = e12) <=> (e11 = j(e20))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[715, 661])).
% 0.18/0.47 tff(717,plain,
% 0.18/0.47 ((j(e22) = e12) <=> (j(e20) = e11)),
% 0.18/0.47 inference(transitivity,[status(thm)],[716, 712])).
% 0.18/0.47 tff(718,plain,
% 0.18/0.47 ((j(e20) = e11) <=> (j(e22) = e12)),
% 0.18/0.47 inference(symmetry,[status(thm)],[717])).
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% 0.18/0.47 ((~(j(e20) = e11)) <=> (~(j(e22) = e12))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[718])).
% 0.18/0.47 tff(720,plain,
% 0.18/0.47 ((e11 = e12) <=> (e11 = j(e20))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[661])).
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% 0.18/0.47 inference(transitivity,[status(thm)],[720, 712])).
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% 0.18/0.47 ((~(e11 = e12)) <=> (~(j(e20) = e11))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[721])).
% 0.18/0.47 tff(723,plain,
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% 0.18/0.47 ((((((((~(e10 = e11)) & (~(e10 = e12))) & (~(e10 = e13))) & (~(e10 = e14))) & (~(e11 = e12))) & (~(e11 = e13))) & (~(e11 = e14))) & (~(e12 = e13))),
% 0.18/0.47 inference(and_elim,[status(thm)],[630])).
% 0.18/0.47 tff(725,plain,
% 0.18/0.47 (((((((~(e10 = e11)) & (~(e10 = e12))) & (~(e10 = e13))) & (~(e10 = e14))) & (~(e11 = e12))) & (~(e11 = e13))) & (~(e11 = e14))),
% 0.18/0.47 inference(and_elim,[status(thm)],[724])).
% 0.18/0.47 tff(726,plain,
% 0.18/0.47 ((((((~(e10 = e11)) & (~(e10 = e12))) & (~(e10 = e13))) & (~(e10 = e14))) & (~(e11 = e12))) & (~(e11 = e13))),
% 0.18/0.47 inference(and_elim,[status(thm)],[725])).
% 0.18/0.47 tff(727,plain,
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% 0.18/0.47 inference(and_elim,[status(thm)],[726])).
% 0.18/0.47 tff(728,plain,
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% 0.18/0.47 inference(and_elim,[status(thm)],[727])).
% 0.18/0.47 tff(729,plain,
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% 0.18/0.47 inference(modus_ponens,[status(thm)],[728, 723])).
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% 0.18/0.47 inference(modus_ponens,[status(thm)],[729, 722])).
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% 0.18/0.47 inference(modus_ponens,[status(thm)],[730, 719])).
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% 0.18/0.47 inference(transitivity,[status(thm)],[153, 147, 732, 112])).
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% 0.18/0.47 inference(monotonicity,[status(thm)],[733, 361])).
% 0.18/0.47 tff(735,plain,
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% 0.18/0.47 inference(symmetry,[status(thm)],[734])).
% 0.18/0.47 tff(736,plain,
% 0.18/0.47 (j(e22) = e12),
% 0.18/0.47 inference(transitivity,[status(thm)],[96, 50, 714, 16, 376, 735, 354, 483, 650])).
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% 0.18/0.47 inference(unit_resolution,[status(thm)],[736, 731])).
% 0.18/0.47 tff(738,plain,((~(j(e21) = e14)) | (~(j(e20) = e12))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(739,plain,
% 0.18/0.47 (~(j(e21) = e14)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[738, 650])).
% 0.18/0.47 tff(740,assumption,(~(j(e21) = e13)), introduced(assumption)).
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% 0.18/0.47 (op1(e10, e12) = op1(j(e21), j(e20))),
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% 0.18/0.47 inference(monotonicity,[status(thm)],[262, 742])).
% 0.18/0.47 tff(744,plain,
% 0.18/0.47 (op1(j(e21), j(e22)) = op1(e10, e14)),
% 0.18/0.47 inference(symmetry,[status(thm)],[743])).
% 0.18/0.47 tff(745,plain,
% 0.18/0.47 (j(e23) = e12),
% 0.18/0.47 inference(transitivity,[status(thm)],[124, 119, 744, 301])).
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% 0.18/0.47 inference(unit_resolution,[status(thm)],[321, 745])).
% 0.18/0.47 tff(747,plain,((~(j(e21) = e10)) | (j(e23) = e12) | (~(j(e20) = e12))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(748,plain,
% 0.18/0.47 (~(j(e21) = e10)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[747, 321, 650])).
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% 0.18/0.47 inference(unit_resolution,[status(thm)],[407, 748, 740, 739, 711])).
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% 0.18/0.47 inference(transitivity,[status(thm)],[749, 661])).
% 0.18/0.47 tff(751,plain,
% 0.18/0.47 (op1(j(e20), j(e21)) = op1(j(e20), j(e20))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[750])).
% 0.18/0.47 tff(752,plain,
% 0.18/0.47 (j(e23) = e12),
% 0.18/0.47 inference(transitivity,[status(thm)],[153, 147, 751, 660, 656, 650])).
% 0.18/0.47 tff(753,plain,
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% 0.18/0.47 inference(unit_resolution,[status(thm)],[321, 752])).
% 0.18/0.47 tff(754,plain,((j(e23) = e12) | (~(j(e20) = e12)) | (j(e21) = e13)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(755,plain,
% 0.18/0.47 (j(e23) = e12),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[754, 635, 649])).
% 0.18/0.47 tff(756,plain,
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% 0.18/0.47 inference(transitivity,[status(thm)],[755, 636])).
% 0.18/0.47 tff(757,plain,
% 0.18/0.47 (h(j(e23)) = h(j(e20))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[756])).
% 0.18/0.47 tff(758,plain,
% 0.18/0.47 (h(j(e20)) = h(j(e23))),
% 0.18/0.47 inference(symmetry,[status(thm)],[757])).
% 0.18/0.47 tff(759,plain,
% 0.18/0.47 (h(j(e20)) = h(e12)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[635])).
% 0.18/0.47 tff(760,plain,
% 0.18/0.47 (h(e12) = h(j(e20))),
% 0.18/0.47 inference(symmetry,[status(thm)],[759])).
% 0.18/0.47 tff(761,plain,
% 0.18/0.47 (h(e12) = e23),
% 0.18/0.47 inference(transitivity,[status(thm)],[760, 758, 7])).
% 0.18/0.47 tff(762,plain,
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% 0.18/0.47 inference(transitivity,[status(thm)],[356, 759])).
% 0.18/0.47 tff(763,plain,
% 0.18/0.47 ((e20 = e23) <=> (h(e12) = e23)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[762])).
% 0.18/0.47 tff(764,plain,
% 0.18/0.47 ((~(e20 = e23)) <=> (~(h(e12) = e23))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[763])).
% 0.18/0.47 tff(765,plain,
% 0.18/0.47 ((~(e20 = e23)) <=> (~(e20 = e23))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(766,plain,
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% 0.18/0.47 inference(and_elim,[status(thm)],[282])).
% 0.18/0.47 tff(767,plain,
% 0.18/0.47 (~(e20 = e23)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[766, 765])).
% 0.18/0.47 tff(768,plain,
% 0.18/0.47 (~(h(e12) = e23)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[767, 764])).
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% 0.18/0.47 inference(unit_resolution,[status(thm)],[768, 761])).
% 0.18/0.47 tff(770,plain,(j(e24) = e11), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(771,plain,
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% 0.18/0.47 inference(symmetry,[status(thm)],[556])).
% 0.18/0.47 tff(772,plain,
% 0.18/0.47 (j(e24) = j(op2(e23, e20))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[771])).
% 0.18/0.47 tff(773,plain,
% 0.18/0.47 (j(op2(e23, e20)) = j(e24)),
% 0.18/0.47 inference(symmetry,[status(thm)],[772])).
% 0.18/0.47 tff(774,plain,
% 0.18/0.47 (op1(j(e23), j(e20)) = j(op2(e23, e20))),
% 0.18/0.47 inference(symmetry,[status(thm)],[553])).
% 0.18/0.47 tff(775,plain,
% 0.18/0.47 ((op2(e24, e23) = e21) <=> (op2(e24, e23) = e21)),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(776,plain,
% 0.18/0.47 (op2(e24, e23) = e21),
% 0.18/0.47 inference(and_elim,[status(thm)],[26])).
% 0.18/0.47 tff(777,plain,
% 0.18/0.47 (op2(e24, e23) = e21),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[776, 775])).
% 0.18/0.47 tff(778,plain,
% 0.18/0.47 (j(op2(e24, e23)) = j(e21)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[777])).
% 0.18/0.47 tff(779,plain,
% 0.18/0.47 ((j(op2(e24, e23)) = op1(j(e24), j(e23))) <=> (j(op2(e24, e23)) = op1(j(e24), j(e23)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(780,plain,
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% 0.18/0.47 inference(and_elim,[status(thm)],[5])).
% 0.18/0.47 tff(781,plain,
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% 0.18/0.47 inference(modus_ponens,[status(thm)],[780, 779])).
% 0.18/0.47 tff(782,plain,
% 0.18/0.47 (op1(j(e24), j(e23)) = j(op2(e24, e23))),
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% 0.18/0.47 tff(783,plain,
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% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(784,plain,
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% 0.18/0.47 tff(785,plain,
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% 0.18/0.47 inference(modus_ponens,[status(thm)],[784, 783])).
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% 0.18/0.47 inference(monotonicity,[status(thm)],[785])).
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% 0.18/0.47 ((j(op2(e24, e21)) = op1(j(e24), j(e21))) <=> (j(op2(e24, e21)) = op1(j(e24), j(e21)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(788,plain,
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% 0.18/0.47 inference(and_elim,[status(thm)],[5])).
% 0.18/0.47 tff(789,plain,
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% 0.18/0.47 inference(modus_ponens,[status(thm)],[788, 787])).
% 0.18/0.47 tff(790,plain,
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% 0.18/0.47 inference(symmetry,[status(thm)],[789])).
% 0.18/0.47 tff(791,plain,
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% 0.18/0.47 tff(792,plain,
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% 0.18/0.47 inference(monotonicity,[status(thm)],[791, 17])).
% 0.18/0.47 tff(793,plain,
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% 0.18/0.47 inference(monotonicity,[status(thm)],[791, 793])).
% 0.18/0.47 tff(795,plain,
% 0.18/0.47 (op1(j(e24), j(e22)) = op1(e11, e13)),
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% 0.18/0.47 ((j(op2(e24, e22)) = op1(j(e24), j(e22))) <=> (j(op2(e24, e22)) = op1(j(e24), j(e22)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
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% 0.18/0.47 inference(and_elim,[status(thm)],[5])).
% 0.18/0.47 tff(798,plain,
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% 0.18/0.47 inference(modus_ponens,[status(thm)],[797, 796])).
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% 0.18/0.47 ((op2(e24, e22) = e20) <=> (op2(e24, e22) = e20)),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(800,plain,
% 0.18/0.47 (op2(e24, e22) = e20),
% 0.18/0.47 inference(and_elim,[status(thm)],[27])).
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% 0.18/0.47 inference(modus_ponens,[status(thm)],[800, 799])).
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% 0.18/0.47 inference(monotonicity,[status(thm)],[801])).
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% 0.18/0.47 inference(symmetry,[status(thm)],[802])).
% 0.18/0.47 tff(804,plain,
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% 0.18/0.47 inference(transitivity,[status(thm)],[803, 798, 795, 449])).
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% 0.18/0.47 inference(unit_resolution,[status(thm)],[9, 804])).
% 0.18/0.47 tff(806,plain,((~(j(e21) = e12)) | (j(e20) = e12)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(807,plain,
% 0.18/0.47 (~(j(e21) = e12)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[806, 9])).
% 0.18/0.47 tff(808,plain,
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% 0.18/0.47 inference(unit_resolution,[status(thm)],[524, 321, 9, 807])).
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% 0.18/0.47 inference(symmetry,[status(thm)],[808])).
% 0.18/0.47 tff(810,plain,
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% 0.18/0.47 inference(monotonicity,[status(thm)],[791, 809])).
% 0.18/0.47 tff(811,plain,
% 0.18/0.47 (op1(j(e24), j(e20)) = op1(e11, e13)),
% 0.18/0.47 inference(symmetry,[status(thm)],[810])).
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% 0.18/0.47 ((j(op2(e24, e20)) = op1(j(e24), j(e20))) <=> (j(op2(e24, e20)) = op1(j(e24), j(e20)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(813,plain,
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% 0.18/0.48 inference(and_elim,[status(thm)],[5])).
% 0.18/0.48 tff(814,plain,
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% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(816,plain,
% 0.18/0.48 (op2(e24, e20) = e23),
% 0.18/0.48 inference(and_elim,[status(thm)],[29])).
% 0.18/0.48 tff(817,plain,
% 0.18/0.48 (op2(e24, e20) = e23),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[816, 815])).
% 0.18/0.48 tff(818,plain,
% 0.18/0.48 (j(op2(e24, e20)) = j(e23)),
% 0.18/0.48 inference(monotonicity,[status(thm)],[817])).
% 0.18/0.48 tff(819,plain,
% 0.18/0.48 (j(e23) = j(op2(e24, e20))),
% 0.18/0.48 inference(symmetry,[status(thm)],[818])).
% 0.18/0.48 tff(820,plain,
% 0.18/0.48 (j(e23) = e12),
% 0.18/0.48 inference(transitivity,[status(thm)],[819, 814, 811, 449])).
% 0.18/0.48 tff(821,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[321, 820])).
% 0.18/0.48 tff(822,plain,((j(e23) = e12) | (j(e20) = e12)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(823,plain,
% 0.18/0.48 (j(e23) = e12),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[822, 9])).
% 0.18/0.48 tff(824,plain,
% 0.18/0.48 (e12 = j(e23)),
% 0.18/0.48 inference(symmetry,[status(thm)],[823])).
% 0.18/0.48 tff(825,plain,
% 0.18/0.48 (op1(e11, e12) = op1(j(e24), j(e23))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[791, 824])).
% 0.18/0.48 tff(826,plain,
% 0.18/0.48 (e13 = j(e21)),
% 0.18/0.48 inference(transitivity,[status(thm)],[682, 825, 782, 778])).
% 0.18/0.48 tff(827,plain,
% 0.18/0.48 (op1(e12, e13) = op1(j(e23), j(e21))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[824, 826])).
% 0.18/0.48 tff(828,plain,
% 0.18/0.48 (op1(j(e23), j(e21)) = op1(e12, e13)),
% 0.18/0.48 inference(symmetry,[status(thm)],[827])).
% 0.18/0.48 tff(829,plain,
% 0.18/0.48 (j(e20) = e14),
% 0.18/0.48 inference(transitivity,[status(thm)],[175, 170, 828, 63])).
% 0.18/0.48 tff(830,plain,
% 0.18/0.48 (~(j(e20) = e14)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[432, 807, 352])).
% 0.18/0.48 tff(831,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[830, 829])).
% 0.18/0.48 tff(832,plain,(j(e20) = e12), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(833,plain,
% 0.18/0.48 (e12 = j(e20)),
% 0.18/0.48 inference(symmetry,[status(thm)],[832])).
% 0.18/0.48 tff(834,plain,
% 0.18/0.48 (op1(e11, e12) = op1(j(e24), j(e20))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[791, 833])).
% 0.18/0.48 tff(835,plain,
% 0.18/0.48 (op1(j(e24), j(e20)) = op1(e11, e12)),
% 0.18/0.48 inference(symmetry,[status(thm)],[834])).
% 0.18/0.48 tff(836,plain,
% 0.18/0.48 (j(e23) = e13),
% 0.18/0.48 inference(transitivity,[status(thm)],[819, 814, 835, 539])).
% 0.18/0.48 tff(837,plain,
% 0.18/0.48 (op1(j(e23), j(e20)) = op1(e13, e12)),
% 0.18/0.48 inference(monotonicity,[status(thm)],[836, 832])).
% 0.18/0.48 tff(838,plain,
% 0.18/0.48 (op1(e13, e12) = op1(j(e23), j(e20))),
% 0.18/0.48 inference(symmetry,[status(thm)],[837])).
% 0.18/0.48 tff(839,plain,
% 0.18/0.48 (op1(e12, e11) = op1(j(e20), j(e24))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[833, 791])).
% 0.18/0.48 tff(840,plain,
% 0.18/0.48 (op1(j(e20), j(e24)) = op1(e12, e11)),
% 0.18/0.48 inference(symmetry,[status(thm)],[839])).
% 0.18/0.48 tff(841,plain,
% 0.18/0.48 ((j(op2(e20, e24)) = op1(j(e20), j(e24))) <=> (j(op2(e20, e24)) = op1(j(e20), j(e24)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(842,plain,
% 0.18/0.48 (j(op2(e20, e24)) = op1(j(e20), j(e24))),
% 0.18/0.48 inference(and_elim,[status(thm)],[5])).
% 0.18/0.48 tff(843,plain,
% 0.18/0.48 (j(op2(e20, e24)) = op1(j(e20), j(e24))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[842, 841])).
% 0.18/0.48 tff(844,plain,
% 0.18/0.48 ((op2(e20, e24) = e21) <=> (op2(e20, e24) = e21)),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(845,plain,
% 0.18/0.48 (op2(e20, e24) = e21),
% 0.18/0.48 inference(and_elim,[status(thm)],[72])).
% 0.18/0.48 tff(846,plain,
% 0.18/0.48 (op2(e20, e24) = e21),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[845, 844])).
% 0.18/0.48 tff(847,plain,
% 0.18/0.48 (e21 = op2(e20, e24)),
% 0.18/0.48 inference(symmetry,[status(thm)],[846])).
% 0.18/0.48 tff(848,plain,
% 0.18/0.48 (j(e21) = j(op2(e20, e24))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[847])).
% 0.18/0.48 tff(849,plain,
% 0.18/0.48 (j(e21) = e11),
% 0.18/0.48 inference(transitivity,[status(thm)],[848, 843, 840, 91, 548, 838, 774, 773, 770])).
% 0.18/0.48 tff(850,plain,
% 0.18/0.48 ((e21 = h(e11)) <=> (h(e11) = e21)),
% 0.18/0.48 inference(commutativity,[status(thm)],[])).
% 0.18/0.48 tff(851,plain,
% 0.18/0.48 (h(j(e24)) = h(e11)),
% 0.18/0.48 inference(monotonicity,[status(thm)],[770])).
% 0.18/0.48 tff(852,plain,
% 0.18/0.48 ((h(j(e24)) = e24) <=> (h(j(e24)) = e24)),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(853,plain,
% 0.18/0.48 (h(j(e24)) = e24),
% 0.18/0.48 inference(and_elim,[status(thm)],[5])).
% 0.18/0.48 tff(854,plain,
% 0.18/0.48 (h(j(e24)) = e24),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[853, 852])).
% 0.18/0.48 tff(855,plain,
% 0.18/0.48 (e24 = h(j(e24))),
% 0.18/0.48 inference(symmetry,[status(thm)],[854])).
% 0.18/0.48 tff(856,plain,
% 0.18/0.48 (e24 = h(e11)),
% 0.18/0.48 inference(transitivity,[status(thm)],[855, 851])).
% 0.18/0.48 tff(857,plain,
% 0.18/0.48 ((e21 = e24) <=> (e21 = h(e11))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[856])).
% 0.18/0.48 tff(858,plain,
% 0.18/0.48 ((e21 = e24) <=> (h(e11) = e21)),
% 0.18/0.48 inference(transitivity,[status(thm)],[857, 850])).
% 0.18/0.48 tff(859,plain,
% 0.18/0.48 ((~(e21 = e24)) <=> (~(h(e11) = e21))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[858])).
% 0.18/0.48 tff(860,plain,
% 0.18/0.48 ((~(e21 = e24)) <=> (~(e21 = e24))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(861,plain,
% 0.18/0.48 (~(e21 = e24)),
% 0.18/0.48 inference(and_elim,[status(thm)],[245])).
% 0.18/0.48 tff(862,plain,
% 0.18/0.48 (~(e21 = e24)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[861, 860])).
% 0.18/0.48 tff(863,plain,
% 0.18/0.48 (~(h(e11) = e21)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[862, 859])).
% 0.18/0.48 tff(864,plain,
% 0.18/0.48 (~(j(e21) = e11)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[445, 863])).
% 0.18/0.48 tff(865,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[864, 849])).
% 0.18/0.48 % SZS output end Proof
% 0.18/0.48 % E exiting
%------------------------------------------------------------------------------