%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEV606+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 : Tue May 5 06:56:00 PM UTC 2026
% Result : Theorem 3.42s 3.80s
% Output : Proof 3.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.18 % Problem : SEV606+1 : TPTP v9.3.0. Released v9.3.0.
% 0.02/0.18 % Command : run_E %s %d THM
% 0.10/0.40 % Computer : n006.cluster.edu
% 0.10/0.40 % Model : x86_64 x86_64
% 0.10/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.40 % Memory : 8042.1875MB
% 0.10/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.40 % CPULimit : 300
% 0.10/0.40 % WCLimit : 300
% 0.10/0.40 % DateTime : Tue May 5 05:21:17 EDT 2026
% 0.10/0.40 % CPUTime :
% 3.42/3.80 % SZS status Theorem
% 3.42/3.80 % SZS output start Proof
% 3.42/3.80 tff(p_type, type, (
% 3.42/3.80 p: $i > $o)).
% 3.42/3.80 tff(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2_type, type, (
% 3.42/3.80 cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2: ( $i * $i ) > $i)).
% 3.42/3.80 tff(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2_type, type, (
% 3.42/3.80 cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2: ( $i * $i ) > $i)).
% 3.42/3.80 tff(tptp_fun_V1__m_550_type, type, (
% 3.42/3.80 tptp_fun_V1__m_550: $i)).
% 3.42/3.80 tff(cCoq_2eNumbers_2eBinNums_2eZ0_type, type, (
% 3.42/3.80 cCoq_2eNumbers_2eBinNums_2eZ0: $i)).
% 3.42/3.80 tff(cCoq_2eNumbers_2eBinNums_2eZ___24t_type, type, (
% 3.42/3.80 cCoq_2eNumbers_2eBinNums_2eZ___24t: $i > $o)).
% 3.42/3.80 tff(tptp_fun_V0__n_549_type, type, (
% 3.42/3.80 tptp_fun_V0__n_549: $i)).
% 3.42/3.80 tff(1,plain,
% 3.42/3.80 ((cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!549) & (~(p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V0__n!549)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m!550)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m!550))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n!549))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!549, V0__n!549))))))) <=> (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!549) & (~((~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n!549))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V0__n!549)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m!550)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m!550))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!549, V0__n!549)))))))),
% 3.42/3.80 inference(rewrite,[status(thm)],[])).
% 3.42/3.80 tff(2,plain,
% 3.42/3.80 ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m, V0__n)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n))))))) <=> (~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m, V0__n)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n)))))))),
% 3.42/3.80 inference(rewrite,[status(thm)],[])).
% 3.42/3.80 tff(3,plain,
% 3.42/3.80 ((~![V0__n: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => ![V1__m: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n)) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m)) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n))) => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m, V0__n)))))))) <=> (~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m, V0__n)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n)))))))),
% 3.42/3.80 inference(rewrite,[status(thm)],[])).
% 3.42/3.80 tff(4,axiom,(~![V0__n: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => ![V1__m: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n)) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m)) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n))) => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m, V0__n)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''_HAMMER_GOAL'')).
% 3.42/3.80 tff(5,plain,
% 3.42/3.80 (~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m, V0__n)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n))))))),
% 3.42/3.80 inference(modus_ponens,[status(thm)],[4, 3])).
% 3.42/3.80 tff(6,plain,
% 3.42/3.80 (~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m, V0__n)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n))))))),
% 3.42/3.80 inference(modus_ponens,[status(thm)],[5, 2])).
% 3.42/3.80 tff(7,plain,
% 3.42/3.80 (~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m, V0__n)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n))))))),
% 3.42/3.80 inference(modus_ponens,[status(thm)],[6, 2])).
% 3.42/3.80 tff(8,plain,
% 3.42/3.80 (~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m, V0__n)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n))))))),
% 3.42/3.80 inference(modus_ponens,[status(thm)],[7, 2])).
% 3.42/3.80 tff(9,plain,
% 3.42/3.80 (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!549) & (~((~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n!549))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V0__n!549)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m!550)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m!550))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!549, V0__n!549))))))),
% 3.42/3.80 inference(modus_ponens,[status(thm)],[8, 1])).
% 3.42/3.80 tff(10,plain,
% 3.42/3.80 (~((~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n!549))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V0__n!549)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m!550)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m!550))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!549, V0__n!549)))))),
% 3.42/3.80 inference(and_elim,[status(thm)],[9])).
% 3.42/3.80 tff(11,plain,
% 3.42/3.80 (cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m!550)),
% 3.42/3.80 inference(or_elim,[status(thm)],[10])).
% 3.42/3.80 tff(12,plain,
% 3.42/3.80 (^[V0__n: $i] : refl(((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))) <=> ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))))),
% 3.42/3.80 inference(bind,[status(th)],[])).
% 3.42/3.80 tff(13,plain,
% 3.42/3.80 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))) <=> ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))),
% 3.42/3.80 inference(quant_intro,[status(thm)],[12])).
% 3.42/3.80 tff(14,plain,
% 3.42/3.80 (^[V0__n: $i] : rewrite(((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))) <=> ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))))),
% 3.42/3.80 inference(bind,[status(th)],[])).
% 3.42/3.80 tff(15,plain,
% 3.42/3.80 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))) <=> ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))),
% 3.42/3.80 inference(quant_intro,[status(thm)],[14])).
% 3.42/3.80 tff(16,plain,
% 3.42/3.80 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))) <=> ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))),
% 3.42/3.80 inference(transitivity,[status(thm)],[15, 13])).
% 3.42/3.80 tff(17,plain,
% 3.42/3.80 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))) <=> ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))),
% 3.42/3.80 inference(rewrite,[status(thm)],[])).
% 3.42/3.80 tff(18,plain,
% 3.42/3.80 (^[V0__n: $i] : trans(monotonicity(quant_intro(proof_bind(^[V1__m: $i] : trans(monotonicity(trans(monotonicity(rewrite((p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))) => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m))) <=> (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))), ((p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m)) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))) => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)))) <=> (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m)) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))))), rewrite((p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m)) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))) <=> (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))), ((p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m)) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))) => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)))) <=> (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))), ((cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m)) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))) => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m))))) <=> (cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))))), rewrite((cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))) <=> (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))), ((cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m)) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))) => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m))))) <=> (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))))), (![V1__m: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m)) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))) => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m))))) <=> ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))), ((cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => ![V1__m: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m)) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))) => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)))))) <=> (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))))), rewrite((cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))) <=> ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))), ((cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => ![V1__m: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m)) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))) => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)))))) <=> ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))))),
% 3.42/3.80 inference(bind,[status(th)],[])).
% 3.42/3.80 tff(19,plain,
% 3.42/3.80 (![V0__n: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => ![V1__m: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m)) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))) => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)))))) <=> ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))),
% 3.42/3.80 inference(quant_intro,[status(thm)],[18])).
% 3.42/3.80 tff(20,axiom,(![V0__n: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => ![V1__m: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m)) => (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))) => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Coq.ZArith.BinInt.Z.square_le_simpl_nonneg'')).
% 3.42/3.80 tff(21,plain,
% 3.42/3.80 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))),
% 3.42/3.80 inference(modus_ponens,[status(thm)],[20, 19])).
% 3.42/3.80 tff(22,plain,
% 3.42/3.80 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))),
% 3.42/3.80 inference(modus_ponens,[status(thm)],[21, 17])).
% 3.42/3.80 tff(23,plain,(
% 3.42/3.80 ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))),
% 3.42/3.80 inference(skolemize,[status(sab)],[22])).
% 3.42/3.80 tff(24,plain,
% 3.42/3.80 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))),
% 3.42/3.80 inference(modus_ponens,[status(thm)],[23, 16])).
% 3.42/3.80 tff(25,plain,
% 3.42/3.80 (((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m!550)) | ![V1__m: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))) <=> ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m!550)) | ![V1__m: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))),
% 3.42/3.80 inference(rewrite,[status(thm)],[])).
% 3.42/3.80 tff(26,plain,
% 3.42/3.80 (((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m!550)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))) <=> ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m!550)) | ![V1__m: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))),
% 3.42/3.80 inference(rewrite,[status(thm)],[])).
% 3.42/3.80 tff(27,plain,
% 3.42/3.80 (((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m!550)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))) <=> ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m!550)) | ![V1__m: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))))),
% 3.42/3.80 inference(monotonicity,[status(thm)],[26])).
% 3.42/3.80 tff(28,plain,
% 3.42/3.80 (((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m!550)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))) <=> ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m!550)) | ![V1__m: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))),
% 3.42/3.80 inference(transitivity,[status(thm)],[27, 25])).
% 3.42/3.80 tff(29,plain,
% 3.42/3.80 ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m!550)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))),
% 3.42/3.80 inference(quant_inst,[status(thm)],[])).
% 3.42/3.80 tff(30,plain,
% 3.42/3.80 ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ![V1__m: $i] : (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n, V1__m)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m))))))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m!550)) | ![V1__m: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))),
% 3.42/3.80 inference(modus_ponens,[status(thm)],[29, 28])).
% 3.42/3.80 tff(31,plain,
% 3.42/3.80 (![V1__m: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))),
% 3.42/3.80 inference(unit_resolution,[status(thm)],[30, 24, 11])).
% 3.42/3.80 tff(32,plain,
% 3.42/3.80 (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!549, V0__n!549)))),
% 3.42/3.80 inference(or_elim,[status(thm)],[10])).
% 3.42/3.80 tff(33,plain,
% 3.42/3.80 (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V0__n!549))),
% 3.42/3.80 inference(or_elim,[status(thm)],[10])).
% 3.42/3.80 tff(34,plain,
% 3.42/3.80 (p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n!549))),
% 3.42/3.80 inference(or_elim,[status(thm)],[10])).
% 3.42/3.80 tff(35,plain,
% 3.42/3.80 (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!549)),
% 3.42/3.80 inference(and_elim,[status(thm)],[9])).
% 3.42/3.80 tff(36,plain,
% 3.42/3.80 (((~![V1__m: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))) | ((~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n!549))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!549)) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V0__n!549)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!549, V0__n!549)))))) <=> ((~![V1__m: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n!549))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!549)) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V0__n!549)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!549, V0__n!549)))))),
% 3.42/3.80 inference(rewrite,[status(thm)],[])).
% 3.42/3.80 tff(37,plain,
% 3.42/3.80 (((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!549)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n!549))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V0__n!549)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!549, V0__n!549))))) <=> ((~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n!549))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!549)) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V0__n!549)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!549, V0__n!549)))))),
% 3.42/3.80 inference(rewrite,[status(thm)],[])).
% 3.42/3.80 tff(38,plain,
% 3.42/3.80 (((~![V1__m: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!549)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n!549))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V0__n!549)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!549, V0__n!549)))))) <=> ((~![V1__m: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))) | ((~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n!549))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!549)) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V0__n!549)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!549, V0__n!549))))))),
% 3.42/3.80 inference(monotonicity,[status(thm)],[37])).
% 3.42/3.80 tff(39,plain,
% 3.42/3.80 (((~![V1__m: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!549)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n!549))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V0__n!549)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!549, V0__n!549)))))) <=> ((~![V1__m: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n!549))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!549)) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V0__n!549)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!549, V0__n!549)))))),
% 3.42/3.80 inference(transitivity,[status(thm)],[38, 36])).
% 3.42/3.80 tff(40,plain,
% 3.42/3.80 ((~![V1__m: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!549)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n!549))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V0__n!549)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!549, V0__n!549)))))),
% 3.42/3.89 inference(quant_inst,[status(thm)],[])).
% 3.42/3.89 tff(41,plain,
% 3.42/3.89 ((~![V1__m: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V1__m))) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V1__m)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m, V1__m)))))) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0, V0__n!549))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!549)) | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m!550, V0__n!549)) | (~p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m!550, V1__m!550), cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!549, V0__n!549))))),
% 3.42/3.89 inference(modus_ponens,[status(thm)],[40, 39])).
% 3.42/3.89 tff(42,plain,
% 3.42/3.89 ($false),
% 3.42/3.89 inference(unit_resolution,[status(thm)],[41, 35, 34, 33, 32, 31])).
% 3.42/3.89 % SZS output end Proof
% 0.14/3.90 % E exiting
%------------------------------------------------------------------------------