%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN704-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:39:52 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN704-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:40:39 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.48 % SZS status Unsatisfiable
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(p4_type, type, (
% 0.20/0.48 p4: ( $i * $i ) > $o)).
% 0.20/0.48 tff(f5_type, type, (
% 0.20/0.48 f5: ( $i * $i ) > $i)).
% 0.20/0.48 tff(f13_type, type, (
% 0.20/0.48 f13: ( $i * $i ) > $i)).
% 0.20/0.48 tff(f40_type, type, (
% 0.20/0.48 f40: ( $i * $i ) > $i)).
% 0.20/0.48 tff(c54_type, type, (
% 0.20/0.48 c54: $i)).
% 0.20/0.48 tff(f42_type, type, (
% 0.20/0.48 f42: ( $i * $i ) > $i)).
% 0.20/0.48 tff(c53_type, type, (
% 0.20/0.48 c53: $i)).
% 0.20/0.48 tff(f44_type, type, (
% 0.20/0.48 f44: ( $i * $i ) > $i)).
% 0.20/0.48 tff(c52_type, type, (
% 0.20/0.48 c52: $i)).
% 0.20/0.48 tff(f46_type, type, (
% 0.20/0.48 f46: ( $i * $i ) > $i)).
% 0.20/0.48 tff(c51_type, type, (
% 0.20/0.48 c51: $i)).
% 0.20/0.48 tff(c58_type, type, (
% 0.20/0.48 c58: $i)).
% 0.20/0.48 tff(f16_type, type, (
% 0.20/0.48 f16: ( $i * $i ) > $i)).
% 0.20/0.48 tff(f30_type, type, (
% 0.20/0.48 f30: ( $i * $i ) > $i)).
% 0.20/0.48 tff(f32_type, type, (
% 0.20/0.48 f32: ( $i * $i ) > $i)).
% 0.20/0.48 tff(f34_type, type, (
% 0.20/0.48 f34: ( $i * $i ) > $i)).
% 0.20/0.48 tff(f36_type, type, (
% 0.20/0.48 f36: ( $i * $i ) > $i)).
% 0.20/0.48 tff(c57_type, type, (
% 0.20/0.48 c57: $i)).
% 0.20/0.48 tff(f18_type, type, (
% 0.20/0.48 f18: ( $i * $i ) > $i)).
% 0.20/0.48 tff(f20_type, type, (
% 0.20/0.48 f20: ( $i * $i ) > $i)).
% 0.20/0.48 tff(f22_type, type, (
% 0.20/0.48 f22: ( $i * $i ) > $i)).
% 0.20/0.48 tff(f24_type, type, (
% 0.20/0.48 f24: ( $i * $i ) > $i)).
% 0.20/0.48 tff(f26_type, type, (
% 0.20/0.48 f26: ( $i * $i ) > $i)).
% 0.20/0.48 tff(c56_type, type, (
% 0.20/0.48 c56: $i)).
% 0.20/0.48 tff(c50_type, type, (
% 0.20/0.48 c50: $i)).
% 0.20/0.48 tff(c48_type, type, (
% 0.20/0.48 c48: $i)).
% 0.20/0.48 tff(f8_type, type, (
% 0.20/0.48 f8: ( $i * $i ) > $i)).
% 0.20/0.48 tff(f10_type, type, (
% 0.20/0.48 f10: ( $i * $i ) > $i)).
% 0.20/0.48 tff(c49_type, type, (
% 0.20/0.48 c49: $i)).
% 0.20/0.48 tff(p3_type, type, (
% 0.20/0.48 p3: ( $i * $i ) > $o)).
% 0.20/0.48 tff(p2_type, type, (
% 0.20/0.48 p2: ( $i * $i ) > $o)).
% 0.20/0.48 tff(p47_type, type, (
% 0.20/0.48 p47: ( $i * $i ) > $o)).
% 0.20/0.48 tff(c55_type, type, (
% 0.20/0.48 c55: $i)).
% 0.20/0.48 tff(p7_type, type, (
% 0.20/0.48 p7: ( $i * $i ) > $o)).
% 0.20/0.48 tff(p19_type, type, (
% 0.20/0.48 p19: ( $i * $i ) > $o)).
% 0.20/0.48 tff(p12_type, type, (
% 0.20/0.48 p12: ( $i * $i ) > $o)).
% 0.20/0.48 tff(p21_type, type, (
% 0.20/0.48 p21: ( $i * $i ) > $o)).
% 0.20/0.48 tff(1,plain,
% 0.20/0.48 (^[X67: $i, X68: $i, X66: $i, X65: $i] : refl(p3(f8(f10(c49, f13(f16(f18(c50, X65), X66), X67)), X68), f13(f16(f18(c50, f20(f22(f24(f26(c56, X65), X66), X67), X68)), f30(f32(f34(f36(c57, X65), X66), X67), X68)), f40(f42(f44(f46(c58, X65), X66), X67), X68))) <=> p3(f8(f10(c49, f13(f16(f18(c50, X65), X66), X67)), X68), f13(f16(f18(c50, f20(f22(f24(f26(c56, X65), X66), X67), X68)), f30(f32(f34(f36(c57, X65), X66), X67), X68)), f40(f42(f44(f46(c58, X65), X66), X67), X68))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(2,plain,
% 0.20/0.48 (![X67: $i, X68: $i, X66: $i, X65: $i] : p3(f8(f10(c49, f13(f16(f18(c50, X65), X66), X67)), X68), f13(f16(f18(c50, f20(f22(f24(f26(c56, X65), X66), X67), X68)), f30(f32(f34(f36(c57, X65), X66), X67), X68)), f40(f42(f44(f46(c58, X65), X66), X67), X68))) <=> ![X67: $i, X68: $i, X66: $i, X65: $i] : p3(f8(f10(c49, f13(f16(f18(c50, X65), X66), X67)), X68), f13(f16(f18(c50, f20(f22(f24(f26(c56, X65), X66), X67), X68)), f30(f32(f34(f36(c57, X65), X66), X67), X68)), f40(f42(f44(f46(c58, X65), X66), X67), X68)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.48 tff(3,plain,
% 0.20/0.48 (![X67: $i, X68: $i, X66: $i, X65: $i] : p3(f8(f10(c49, f13(f16(f18(c50, X65), X66), X67)), X68), f13(f16(f18(c50, f20(f22(f24(f26(c56, X65), X66), X67), X68)), f30(f32(f34(f36(c57, X65), X66), X67), X68)), f40(f42(f44(f46(c58, X65), X66), X67), X68))) <=> ![X67: $i, X68: $i, X66: $i, X65: $i] : p3(f8(f10(c49, f13(f16(f18(c50, X65), X66), X67)), X68), f13(f16(f18(c50, f20(f22(f24(f26(c56, X65), X66), X67), X68)), f30(f32(f34(f36(c57, X65), X66), X67), X68)), f40(f42(f44(f46(c58, X65), X66), X67), X68)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(4,axiom,(![X67: $i, X68: $i, X66: $i, X65: $i] : p3(f8(f10(c49, f13(f16(f18(c50, X65), X66), X67)), X68), f13(f16(f18(c50, f20(f22(f24(f26(c56, X65), X66), X67), X68)), f30(f32(f34(f36(c57, X65), X66), X67), X68)), f40(f42(f44(f46(c58, X65), X66), X67), X68)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_80')).
% 0.20/0.48 tff(5,plain,
% 0.20/0.48 (![X67: $i, X68: $i, X66: $i, X65: $i] : p3(f8(f10(c49, f13(f16(f18(c50, X65), X66), X67)), X68), f13(f16(f18(c50, f20(f22(f24(f26(c56, X65), X66), X67), X68)), f30(f32(f34(f36(c57, X65), X66), X67), X68)), f40(f42(f44(f46(c58, X65), X66), X67), X68)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.48 tff(6,plain,(
% 0.20/0.48 ![X67: $i, X68: $i, X66: $i, X65: $i] : p3(f8(f10(c49, f13(f16(f18(c50, X65), X66), X67)), X68), f13(f16(f18(c50, f20(f22(f24(f26(c56, X65), X66), X67), X68)), f30(f32(f34(f36(c57, X65), X66), X67), X68)), f40(f42(f44(f46(c58, X65), X66), X67), X68)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[5])).
% 0.20/0.48 tff(7,plain,
% 0.20/0.48 (![X67: $i, X68: $i, X66: $i, X65: $i] : p3(f8(f10(c49, f13(f16(f18(c50, X65), X66), X67)), X68), f13(f16(f18(c50, f20(f22(f24(f26(c56, X65), X66), X67), X68)), f30(f32(f34(f36(c57, X65), X66), X67), X68)), f40(f42(f44(f46(c58, X65), X66), X67), X68)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.48 tff(8,plain,
% 0.20/0.48 ((~![X67: $i, X68: $i, X66: $i, X65: $i] : p3(f8(f10(c49, f13(f16(f18(c50, X65), X66), X67)), X68), f13(f16(f18(c50, f20(f22(f24(f26(c56, X65), X66), X67), X68)), f30(f32(f34(f36(c57, X65), X66), X67), X68)), f40(f42(f44(f46(c58, X65), X66), X67), X68)))) | p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(9,plain,
% 0.20/0.48 (p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.48 tff(10,assumption,(~p2(c48, c48)), introduced(assumption)).
% 0.20/0.48 tff(11,plain,
% 0.20/0.48 (^[X38: $i] : refl(p2(X38, X38) <=> p2(X38, X38))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(12,plain,
% 0.20/0.48 (![X38: $i] : p2(X38, X38) <=> ![X38: $i] : p2(X38, X38)),
% 0.20/0.48 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.48 tff(13,plain,
% 0.20/0.48 (![X38: $i] : p2(X38, X38) <=> ![X38: $i] : p2(X38, X38)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(14,axiom,(![X38: $i] : p2(X38, X38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_20')).
% 0.20/0.48 tff(15,plain,
% 0.20/0.48 (![X38: $i] : p2(X38, X38)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.48 tff(16,plain,(
% 0.20/0.48 ![X38: $i] : p2(X38, X38)),
% 0.20/0.48 inference(skolemize,[status(sab)],[15])).
% 0.20/0.48 tff(17,plain,
% 0.20/0.48 (![X38: $i] : p2(X38, X38)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 ((~![X38: $i] : p2(X38, X38)) | p2(c48, c48)),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[18, 17, 10])).
% 0.20/0.48 tff(20,plain,(p2(c48, c48)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 (^[X129: $i, X126: $i, X127: $i, X128: $i] : refl(((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129))) <=> ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 (![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129))) <=> ![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.48 tff(23,plain,
% 0.20/0.48 (![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129))) <=> ![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 (^[X129: $i, X126: $i, X127: $i, X128: $i] : trans(monotonicity(rewrite((p4(f5(X126, X127), f5(X128, X129)) | (~p2(X126, X128))) <=> ((~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))), (((p4(f5(X126, X127), f5(X128, X129)) | (~p2(X126, X128))) | (~p3(X127, X129))) <=> (((~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129))) | (~p3(X127, X129))))), rewrite((((~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129))) | (~p3(X127, X129))) <=> ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))), (((p4(f5(X126, X127), f5(X128, X129)) | (~p2(X126, X128))) | (~p3(X127, X129))) <=> ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(25,plain,
% 0.20/0.48 (![X129: $i, X126: $i, X127: $i, X128: $i] : ((p4(f5(X126, X127), f5(X128, X129)) | (~p2(X126, X128))) | (~p3(X127, X129))) <=> ![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.48 tff(26,axiom,(![X129: $i, X126: $i, X127: $i, X128: $i] : ((p4(f5(X126, X127), f5(X128, X129)) | (~p2(X126, X128))) | (~p3(X127, X129)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_58')).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 (![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.48 tff(28,plain,
% 0.20/0.48 (![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.20/0.48 tff(29,plain,(
% 0.20/0.48 ![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[28])).
% 0.20/0.48 tff(30,plain,
% 0.20/0.48 (![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.20/0.48 tff(31,plain,
% 0.20/0.48 (((~![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))) | ((~p2(c48, c48)) | (~p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54)))) | p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54)))))) <=> ((~![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))) | (~p2(c48, c48)) | (~p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54)))) | p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 (((~p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54)))) | (~p2(c48, c48)) | p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))))) <=> ((~p2(c48, c48)) | (~p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54)))) | p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 (((~![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))) | ((~p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54)))) | (~p2(c48, c48)) | p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54)))))) <=> ((~![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))) | ((~p2(c48, c48)) | (~p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54)))) | p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[32])).
% 0.20/0.49 tff(34,plain,
% 0.20/0.49 (((~![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))) | ((~p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54)))) | (~p2(c48, c48)) | p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54)))))) <=> ((~![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))) | (~p2(c48, c48)) | (~p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54)))) | p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[33, 31])).
% 0.20/0.49 tff(35,plain,
% 0.20/0.49 ((~![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))) | ((~p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54)))) | (~p2(c48, c48)) | p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(36,plain,
% 0.20/0.49 ((~![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))) | (~p2(c48, c48)) | (~p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54)))) | p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.49 tff(37,plain,
% 0.20/0.49 (p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[36, 30, 20, 9])).
% 0.20/0.49 tff(38,assumption,(~p7(c54, c54)), introduced(assumption)).
% 0.20/0.49 tff(39,plain,
% 0.20/0.49 (^[X162: $i] : refl(p7(X162, X162) <=> p7(X162, X162))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(40,plain,
% 0.20/0.49 (![X162: $i] : p7(X162, X162) <=> ![X162: $i] : p7(X162, X162)),
% 0.20/0.49 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.49 tff(41,plain,
% 0.20/0.49 (![X162: $i] : p7(X162, X162) <=> ![X162: $i] : p7(X162, X162)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(42,axiom,(![X162: $i] : p7(X162, X162)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_3')).
% 0.20/0.49 tff(43,plain,
% 0.20/0.49 (![X162: $i] : p7(X162, X162)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.49 tff(44,plain,(
% 0.20/0.49 ![X162: $i] : p7(X162, X162)),
% 0.20/0.49 inference(skolemize,[status(sab)],[43])).
% 0.20/0.49 tff(45,plain,
% 0.20/0.49 (![X162: $i] : p7(X162, X162)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.49 tff(46,plain,
% 0.20/0.49 ((~![X162: $i] : p7(X162, X162)) | p7(c54, c54)),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(47,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[46, 45, 38])).
% 0.20/0.49 tff(48,plain,(p7(c54, c54)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(49,plain,
% 0.20/0.49 (^[X163: $i, X162: $i, X164: $i] : refl(((~p7(X162, X164)) | (~p7(X162, X163)) | p7(X163, X164)) <=> ((~p7(X162, X164)) | (~p7(X162, X163)) | p7(X163, X164)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(50,plain,
% 0.20/0.49 (![X163: $i, X162: $i, X164: $i] : ((~p7(X162, X164)) | (~p7(X162, X163)) | p7(X163, X164)) <=> ![X163: $i, X162: $i, X164: $i] : ((~p7(X162, X164)) | (~p7(X162, X163)) | p7(X163, X164))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.49 tff(51,plain,
% 0.20/0.49 (![X163: $i, X162: $i, X164: $i] : ((~p7(X162, X164)) | (~p7(X162, X163)) | p7(X163, X164)) <=> ![X163: $i, X162: $i, X164: $i] : ((~p7(X162, X164)) | (~p7(X162, X163)) | p7(X163, X164))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(52,plain,
% 0.20/0.49 (^[X163: $i, X162: $i, X164: $i] : trans(monotonicity(rewrite((p7(X163, X164) | (~p7(X162, X163))) <=> ((~p7(X162, X163)) | p7(X163, X164))), (((p7(X163, X164) | (~p7(X162, X163))) | (~p7(X162, X164))) <=> (((~p7(X162, X163)) | p7(X163, X164)) | (~p7(X162, X164))))), rewrite((((~p7(X162, X163)) | p7(X163, X164)) | (~p7(X162, X164))) <=> ((~p7(X162, X164)) | (~p7(X162, X163)) | p7(X163, X164))), (((p7(X163, X164) | (~p7(X162, X163))) | (~p7(X162, X164))) <=> ((~p7(X162, X164)) | (~p7(X162, X163)) | p7(X163, X164))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(53,plain,
% 0.20/0.49 (![X163: $i, X162: $i, X164: $i] : ((p7(X163, X164) | (~p7(X162, X163))) | (~p7(X162, X164))) <=> ![X163: $i, X162: $i, X164: $i] : ((~p7(X162, X164)) | (~p7(X162, X163)) | p7(X163, X164))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.49 tff(54,axiom,(![X163: $i, X162: $i, X164: $i] : ((p7(X163, X164) | (~p7(X162, X163))) | (~p7(X162, X164)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_29')).
% 0.20/0.49 tff(55,plain,
% 0.20/0.49 (![X163: $i, X162: $i, X164: $i] : ((~p7(X162, X164)) | (~p7(X162, X163)) | p7(X163, X164))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.49 tff(56,plain,
% 0.20/0.49 (![X163: $i, X162: $i, X164: $i] : ((~p7(X162, X164)) | (~p7(X162, X163)) | p7(X163, X164))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.49 tff(57,plain,(
% 0.20/0.49 ![X163: $i, X162: $i, X164: $i] : ((~p7(X162, X164)) | (~p7(X162, X163)) | p7(X163, X164))),
% 0.20/0.49 inference(skolemize,[status(sab)],[56])).
% 0.20/0.49 tff(58,plain,
% 0.20/0.49 (![X163: $i, X162: $i, X164: $i] : ((~p7(X162, X164)) | (~p7(X162, X163)) | p7(X163, X164))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.49 tff(59,plain,
% 0.20/0.49 (p7(c54, c55) <=> p7(c54, c55)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(60,axiom,(p7(c54, c55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_26')).
% 0.20/0.49 tff(61,plain,
% 0.20/0.49 (p7(c54, c55)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.49 tff(62,plain,
% 0.20/0.49 (((~![X163: $i, X162: $i, X164: $i] : ((~p7(X162, X164)) | (~p7(X162, X163)) | p7(X163, X164))) | ((~p7(c54, c54)) | (~p7(c54, c55)) | p7(c55, c54))) <=> ((~![X163: $i, X162: $i, X164: $i] : ((~p7(X162, X164)) | (~p7(X162, X163)) | p7(X163, X164))) | (~p7(c54, c54)) | (~p7(c54, c55)) | p7(c55, c54))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(63,plain,
% 0.20/0.49 ((~![X163: $i, X162: $i, X164: $i] : ((~p7(X162, X164)) | (~p7(X162, X163)) | p7(X163, X164))) | ((~p7(c54, c54)) | (~p7(c54, c55)) | p7(c55, c54))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(64,plain,
% 0.20/0.49 ((~![X163: $i, X162: $i, X164: $i] : ((~p7(X162, X164)) | (~p7(X162, X163)) | p7(X163, X164))) | (~p7(c54, c54)) | (~p7(c54, c55)) | p7(c55, c54)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.49 tff(65,plain,
% 0.20/0.49 (p7(c55, c54)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[64, 61, 58, 48])).
% 0.20/0.49 tff(66,plain,
% 0.20/0.49 (^[X67: $i, X68: $i, X66: $i, X65: $i] : refl((~p47(f20(f22(f24(f26(c56, X65), X66), X67), X68), X68)) <=> (~p47(f20(f22(f24(f26(c56, X65), X66), X67), X68), X68)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(67,plain,
% 0.20/0.49 (![X67: $i, X68: $i, X66: $i, X65: $i] : (~p47(f20(f22(f24(f26(c56, X65), X66), X67), X68), X68)) <=> ![X67: $i, X68: $i, X66: $i, X65: $i] : (~p47(f20(f22(f24(f26(c56, X65), X66), X67), X68), X68))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.49 tff(68,plain,
% 0.20/0.49 (![X67: $i, X68: $i, X66: $i, X65: $i] : (~p47(f20(f22(f24(f26(c56, X65), X66), X67), X68), X68)) <=> ![X67: $i, X68: $i, X66: $i, X65: $i] : (~p47(f20(f22(f24(f26(c56, X65), X66), X67), X68), X68))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(69,axiom,(![X67: $i, X68: $i, X66: $i, X65: $i] : (~p47(f20(f22(f24(f26(c56, X65), X66), X67), X68), X68))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p47_52')).
% 0.20/0.49 tff(70,plain,
% 0.20/0.49 (![X67: $i, X68: $i, X66: $i, X65: $i] : (~p47(f20(f22(f24(f26(c56, X65), X66), X67), X68), X68))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.49 tff(71,plain,(
% 0.20/0.49 ![X67: $i, X68: $i, X66: $i, X65: $i] : (~p47(f20(f22(f24(f26(c56, X65), X66), X67), X68), X68))),
% 0.20/0.49 inference(skolemize,[status(sab)],[70])).
% 0.20/0.49 tff(72,plain,
% 0.20/0.49 (![X67: $i, X68: $i, X66: $i, X65: $i] : (~p47(f20(f22(f24(f26(c56, X65), X66), X67), X68), X68))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.20/0.49 tff(73,plain,
% 0.20/0.49 ((~![X67: $i, X68: $i, X66: $i, X65: $i] : (~p47(f20(f22(f24(f26(c56, X65), X66), X67), X68), X68))) | (~p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c54))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(74,plain,
% 0.20/0.49 (~p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c54)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.20/0.49 tff(75,assumption,(~p12(c53, c53)), introduced(assumption)).
% 0.20/0.49 tff(76,plain,
% 0.20/0.49 (^[X7: $i] : refl(p12(X7, X7) <=> p12(X7, X7))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(77,plain,
% 0.20/0.49 (![X7: $i] : p12(X7, X7) <=> ![X7: $i] : p12(X7, X7)),
% 0.20/0.49 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.49 tff(78,plain,
% 0.20/0.49 (![X7: $i] : p12(X7, X7) <=> ![X7: $i] : p12(X7, X7)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(79,axiom,(![X7: $i] : p12(X7, X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p12_25')).
% 0.20/0.49 tff(80,plain,
% 0.20/0.49 (![X7: $i] : p12(X7, X7)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.49 tff(81,plain,(
% 0.20/0.49 ![X7: $i] : p12(X7, X7)),
% 0.20/0.49 inference(skolemize,[status(sab)],[80])).
% 0.20/0.49 tff(82,plain,
% 0.20/0.49 (![X7: $i] : p12(X7, X7)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.20/0.49 tff(83,plain,
% 0.20/0.49 ((~![X7: $i] : p12(X7, X7)) | p12(c53, c53)),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(84,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[83, 82, 75])).
% 0.20/0.49 tff(85,plain,(p12(c53, c53)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(86,assumption,(~p21(f24(f26(c56, c51), c52), f24(f26(c56, c51), c52))), introduced(assumption)).
% 0.20/0.49 tff(87,plain,
% 0.20/0.49 (^[X41: $i] : refl(p21(X41, X41) <=> p21(X41, X41))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 (![X41: $i] : p21(X41, X41) <=> ![X41: $i] : p21(X41, X41)),
% 0.20/0.49 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.49 tff(89,plain,
% 0.20/0.49 (![X41: $i] : p21(X41, X41) <=> ![X41: $i] : p21(X41, X41)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(90,axiom,(![X41: $i] : p21(X41, X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p21_19')).
% 0.20/0.49 tff(91,plain,
% 0.20/0.49 (![X41: $i] : p21(X41, X41)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.49 tff(92,plain,(
% 0.20/0.49 ![X41: $i] : p21(X41, X41)),
% 0.20/0.49 inference(skolemize,[status(sab)],[91])).
% 0.20/0.49 tff(93,plain,
% 0.20/0.49 (![X41: $i] : p21(X41, X41)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.20/0.49 tff(94,plain,
% 0.20/0.49 ((~![X41: $i] : p21(X41, X41)) | p21(f24(f26(c56, c51), c52), f24(f26(c56, c51), c52))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(95,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[94, 93, 86])).
% 0.20/0.49 tff(96,plain,(p21(f24(f26(c56, c51), c52), f24(f26(c56, c51), c52))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(97,plain,
% 0.20/0.49 (^[X37: $i, X35: $i, X34: $i, X36: $i] : refl(((~p12(X35, X37)) | (~p21(X34, X36)) | p19(f22(X34, X35), f22(X36, X37))) <=> ((~p12(X35, X37)) | (~p21(X34, X36)) | p19(f22(X34, X35), f22(X36, X37))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(98,plain,
% 0.20/0.49 (![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p12(X35, X37)) | (~p21(X34, X36)) | p19(f22(X34, X35), f22(X36, X37))) <=> ![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p12(X35, X37)) | (~p21(X34, X36)) | p19(f22(X34, X35), f22(X36, X37)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.49 tff(99,plain,
% 0.20/0.49 (![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p12(X35, X37)) | (~p21(X34, X36)) | p19(f22(X34, X35), f22(X36, X37))) <=> ![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p12(X35, X37)) | (~p21(X34, X36)) | p19(f22(X34, X35), f22(X36, X37)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(100,plain,
% 0.20/0.49 (^[X37: $i, X35: $i, X34: $i, X36: $i] : trans(monotonicity(rewrite((p19(f22(X34, X35), f22(X36, X37)) | (~p12(X35, X37))) <=> ((~p12(X35, X37)) | p19(f22(X34, X35), f22(X36, X37)))), (((p19(f22(X34, X35), f22(X36, X37)) | (~p12(X35, X37))) | (~p21(X34, X36))) <=> (((~p12(X35, X37)) | p19(f22(X34, X35), f22(X36, X37))) | (~p21(X34, X36))))), rewrite((((~p12(X35, X37)) | p19(f22(X34, X35), f22(X36, X37))) | (~p21(X34, X36))) <=> ((~p12(X35, X37)) | (~p21(X34, X36)) | p19(f22(X34, X35), f22(X36, X37)))), (((p19(f22(X34, X35), f22(X36, X37)) | (~p12(X35, X37))) | (~p21(X34, X36))) <=> ((~p12(X35, X37)) | (~p21(X34, X36)) | p19(f22(X34, X35), f22(X36, X37)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(101,plain,
% 0.20/0.49 (![X37: $i, X35: $i, X34: $i, X36: $i] : ((p19(f22(X34, X35), f22(X36, X37)) | (~p12(X35, X37))) | (~p21(X34, X36))) <=> ![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p12(X35, X37)) | (~p21(X34, X36)) | p19(f22(X34, X35), f22(X36, X37)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.49 tff(102,axiom,(![X37: $i, X35: $i, X34: $i, X36: $i] : ((p19(f22(X34, X35), f22(X36, X37)) | (~p12(X35, X37))) | (~p21(X34, X36)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p19_70')).
% 0.20/0.49 tff(103,plain,
% 0.20/0.49 (![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p12(X35, X37)) | (~p21(X34, X36)) | p19(f22(X34, X35), f22(X36, X37)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.49 tff(104,plain,
% 0.20/0.49 (![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p12(X35, X37)) | (~p21(X34, X36)) | p19(f22(X34, X35), f22(X36, X37)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.20/0.49 tff(105,plain,(
% 0.20/0.49 ![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p12(X35, X37)) | (~p21(X34, X36)) | p19(f22(X34, X35), f22(X36, X37)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[104])).
% 0.20/0.49 tff(106,plain,
% 0.20/0.49 (![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p12(X35, X37)) | (~p21(X34, X36)) | p19(f22(X34, X35), f22(X36, X37)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.20/0.49 tff(107,plain,
% 0.20/0.49 (((~![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p12(X35, X37)) | (~p21(X34, X36)) | p19(f22(X34, X35), f22(X36, X37)))) | ((~p12(c53, c53)) | (~p21(f24(f26(c56, c51), c52), f24(f26(c56, c51), c52))) | p19(f22(f24(f26(c56, c51), c52), c53), f22(f24(f26(c56, c51), c52), c53)))) <=> ((~![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p12(X35, X37)) | (~p21(X34, X36)) | p19(f22(X34, X35), f22(X36, X37)))) | (~p12(c53, c53)) | (~p21(f24(f26(c56, c51), c52), f24(f26(c56, c51), c52))) | p19(f22(f24(f26(c56, c51), c52), c53), f22(f24(f26(c56, c51), c52), c53)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(108,plain,
% 0.20/0.49 ((~![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p12(X35, X37)) | (~p21(X34, X36)) | p19(f22(X34, X35), f22(X36, X37)))) | ((~p12(c53, c53)) | (~p21(f24(f26(c56, c51), c52), f24(f26(c56, c51), c52))) | p19(f22(f24(f26(c56, c51), c52), c53), f22(f24(f26(c56, c51), c52), c53)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(109,plain,
% 0.20/0.49 ((~![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p12(X35, X37)) | (~p21(X34, X36)) | p19(f22(X34, X35), f22(X36, X37)))) | (~p12(c53, c53)) | (~p21(f24(f26(c56, c51), c52), f24(f26(c56, c51), c52))) | p19(f22(f24(f26(c56, c51), c52), c53), f22(f24(f26(c56, c51), c52), c53))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.49 tff(110,plain,
% 0.20/0.49 ((~p12(c53, c53)) | (~p21(f24(f26(c56, c51), c52), f24(f26(c56, c51), c52))) | p19(f22(f24(f26(c56, c51), c52), c53), f22(f24(f26(c56, c51), c52), c53))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[109, 106])).
% 0.20/0.49 tff(111,plain,
% 0.20/0.49 (p19(f22(f24(f26(c56, c51), c52), c53), f22(f24(f26(c56, c51), c52), c53))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[110, 96, 85])).
% 0.20/0.49 tff(112,plain,
% 0.20/0.49 (^[X122: $i, X124: $i, X123: $i, X125: $i] : refl(((~p7(X123, X125)) | (~p19(X122, X124)) | p4(f20(X122, X123), f20(X124, X125))) <=> ((~p7(X123, X125)) | (~p19(X122, X124)) | p4(f20(X122, X123), f20(X124, X125))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(113,plain,
% 0.20/0.49 (![X122: $i, X124: $i, X123: $i, X125: $i] : ((~p7(X123, X125)) | (~p19(X122, X124)) | p4(f20(X122, X123), f20(X124, X125))) <=> ![X122: $i, X124: $i, X123: $i, X125: $i] : ((~p7(X123, X125)) | (~p19(X122, X124)) | p4(f20(X122, X123), f20(X124, X125)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[112])).
% 0.20/0.49 tff(114,plain,
% 0.20/0.49 (![X122: $i, X124: $i, X123: $i, X125: $i] : ((~p7(X123, X125)) | (~p19(X122, X124)) | p4(f20(X122, X123), f20(X124, X125))) <=> ![X122: $i, X124: $i, X123: $i, X125: $i] : ((~p7(X123, X125)) | (~p19(X122, X124)) | p4(f20(X122, X123), f20(X124, X125)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(115,plain,
% 0.20/0.49 (^[X122: $i, X124: $i, X123: $i, X125: $i] : trans(monotonicity(rewrite((p4(f20(X122, X123), f20(X124, X125)) | (~p19(X122, X124))) <=> ((~p19(X122, X124)) | p4(f20(X122, X123), f20(X124, X125)))), (((p4(f20(X122, X123), f20(X124, X125)) | (~p19(X122, X124))) | (~p7(X123, X125))) <=> (((~p19(X122, X124)) | p4(f20(X122, X123), f20(X124, X125))) | (~p7(X123, X125))))), rewrite((((~p19(X122, X124)) | p4(f20(X122, X123), f20(X124, X125))) | (~p7(X123, X125))) <=> ((~p7(X123, X125)) | (~p19(X122, X124)) | p4(f20(X122, X123), f20(X124, X125)))), (((p4(f20(X122, X123), f20(X124, X125)) | (~p19(X122, X124))) | (~p7(X123, X125))) <=> ((~p7(X123, X125)) | (~p19(X122, X124)) | p4(f20(X122, X123), f20(X124, X125)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(116,plain,
% 0.20/0.49 (![X122: $i, X124: $i, X123: $i, X125: $i] : ((p4(f20(X122, X123), f20(X124, X125)) | (~p19(X122, X124))) | (~p7(X123, X125))) <=> ![X122: $i, X124: $i, X123: $i, X125: $i] : ((~p7(X123, X125)) | (~p19(X122, X124)) | p4(f20(X122, X123), f20(X124, X125)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[115])).
% 0.20/0.49 tff(117,axiom,(![X122: $i, X124: $i, X123: $i, X125: $i] : ((p4(f20(X122, X123), f20(X124, X125)) | (~p19(X122, X124))) | (~p7(X123, X125)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_59')).
% 0.20/0.49 tff(118,plain,
% 0.20/0.49 (![X122: $i, X124: $i, X123: $i, X125: $i] : ((~p7(X123, X125)) | (~p19(X122, X124)) | p4(f20(X122, X123), f20(X124, X125)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.49 tff(119,plain,
% 0.20/0.49 (![X122: $i, X124: $i, X123: $i, X125: $i] : ((~p7(X123, X125)) | (~p19(X122, X124)) | p4(f20(X122, X123), f20(X124, X125)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.20/0.49 tff(120,plain,(
% 0.20/0.49 ![X122: $i, X124: $i, X123: $i, X125: $i] : ((~p7(X123, X125)) | (~p19(X122, X124)) | p4(f20(X122, X123), f20(X124, X125)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[119])).
% 0.20/0.49 tff(121,plain,
% 0.20/0.49 (![X122: $i, X124: $i, X123: $i, X125: $i] : ((~p7(X123, X125)) | (~p19(X122, X124)) | p4(f20(X122, X123), f20(X124, X125)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.20/0.49 tff(122,plain,
% 0.20/0.49 (((~![X122: $i, X124: $i, X123: $i, X125: $i] : ((~p7(X123, X125)) | (~p19(X122, X124)) | p4(f20(X122, X123), f20(X124, X125)))) | ((~p7(c54, c54)) | (~p19(f22(f24(f26(c56, c51), c52), c53), f22(f24(f26(c56, c51), c52), c53))) | p4(f20(f22(f24(f26(c56, c51), c52), c53), c54), f20(f22(f24(f26(c56, c51), c52), c53), c54)))) <=> ((~![X122: $i, X124: $i, X123: $i, X125: $i] : ((~p7(X123, X125)) | (~p19(X122, X124)) | p4(f20(X122, X123), f20(X124, X125)))) | (~p7(c54, c54)) | (~p19(f22(f24(f26(c56, c51), c52), c53), f22(f24(f26(c56, c51), c52), c53))) | p4(f20(f22(f24(f26(c56, c51), c52), c53), c54), f20(f22(f24(f26(c56, c51), c52), c53), c54)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(123,plain,
% 0.20/0.49 ((~![X122: $i, X124: $i, X123: $i, X125: $i] : ((~p7(X123, X125)) | (~p19(X122, X124)) | p4(f20(X122, X123), f20(X124, X125)))) | ((~p7(c54, c54)) | (~p19(f22(f24(f26(c56, c51), c52), c53), f22(f24(f26(c56, c51), c52), c53))) | p4(f20(f22(f24(f26(c56, c51), c52), c53), c54), f20(f22(f24(f26(c56, c51), c52), c53), c54)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(124,plain,
% 0.20/0.49 ((~![X122: $i, X124: $i, X123: $i, X125: $i] : ((~p7(X123, X125)) | (~p19(X122, X124)) | p4(f20(X122, X123), f20(X124, X125)))) | (~p7(c54, c54)) | (~p19(f22(f24(f26(c56, c51), c52), c53), f22(f24(f26(c56, c51), c52), c53))) | p4(f20(f22(f24(f26(c56, c51), c52), c53), c54), f20(f22(f24(f26(c56, c51), c52), c53), c54))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.20/0.49 tff(125,plain,
% 0.20/0.49 ((~p7(c54, c54)) | (~p19(f22(f24(f26(c56, c51), c52), c53), f22(f24(f26(c56, c51), c52), c53))) | p4(f20(f22(f24(f26(c56, c51), c52), c53), c54), f20(f22(f24(f26(c56, c51), c52), c53), c54))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[124, 121])).
% 0.20/0.49 tff(126,plain,
% 0.20/0.49 ((~p7(c54, c54)) | p4(f20(f22(f24(f26(c56, c51), c52), c53), c54), f20(f22(f24(f26(c56, c51), c52), c53), c54))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[125, 111])).
% 0.20/0.49 tff(127,plain,
% 0.20/0.49 (p4(f20(f22(f24(f26(c56, c51), c52), c53), c54), f20(f22(f24(f26(c56, c51), c52), c53), c54))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[126, 48])).
% 0.20/0.49 tff(128,plain,
% 0.20/0.49 (^[X152: $i, X154: $i, X151: $i, X153: $i] : refl(((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152)) <=> ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(129,plain,
% 0.20/0.49 (![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152)) <=> ![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[128])).
% 0.20/0.49 tff(130,plain,
% 0.20/0.49 (![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152)) <=> ![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(131,plain,
% 0.20/0.49 (^[X152: $i, X154: $i, X151: $i, X153: $i] : trans(monotonicity(trans(monotonicity(rewrite((p47(X151, X152) | (~p47(X153, X154))) <=> ((~p47(X153, X154)) | p47(X151, X152))), (((p47(X151, X152) | (~p47(X153, X154))) | (~p7(X154, X152))) <=> (((~p47(X153, X154)) | p47(X151, X152)) | (~p7(X154, X152))))), rewrite((((~p47(X153, X154)) | p47(X151, X152)) | (~p7(X154, X152))) <=> ((~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))), (((p47(X151, X152) | (~p47(X153, X154))) | (~p7(X154, X152))) <=> ((~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152)))), ((((p47(X151, X152) | (~p47(X153, X154))) | (~p7(X154, X152))) | (~p4(X153, X151))) <=> (((~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152)) | (~p4(X153, X151))))), rewrite((((~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152)) | (~p4(X153, X151))) <=> ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))), ((((p47(X151, X152) | (~p47(X153, X154))) | (~p7(X154, X152))) | (~p4(X153, X151))) <=> ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(132,plain,
% 0.20/0.49 (![X152: $i, X154: $i, X151: $i, X153: $i] : (((p47(X151, X152) | (~p47(X153, X154))) | (~p7(X154, X152))) | (~p4(X153, X151))) <=> ![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[131])).
% 0.20/0.49 tff(133,axiom,(![X152: $i, X154: $i, X151: $i, X153: $i] : (((p47(X151, X152) | (~p47(X153, X154))) | (~p7(X154, X152))) | (~p4(X153, X151)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p47_53')).
% 0.20/0.50 tff(134,plain,
% 0.20/0.50 (![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.50 tff(135,plain,
% 0.20/0.50 (![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.20/0.50 tff(136,plain,(
% 0.20/0.50 ![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))),
% 0.20/0.50 inference(skolemize,[status(sab)],[135])).
% 0.20/0.50 tff(137,plain,
% 0.20/0.50 (![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[136, 129])).
% 0.20/0.50 tff(138,plain,
% 0.20/0.50 (((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | ((~p4(f20(f22(f24(f26(c56, c51), c52), c53), c54), f20(f22(f24(f26(c56, c51), c52), c53), c54))) | p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c54) | (~p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c55)) | (~p7(c55, c54)))) <=> ((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | (~p4(f20(f22(f24(f26(c56, c51), c52), c53), c54), f20(f22(f24(f26(c56, c51), c52), c53), c54))) | p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c54) | (~p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c55)) | (~p7(c55, c54)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(139,plain,
% 0.20/0.50 (((~p4(f20(f22(f24(f26(c56, c51), c52), c53), c54), f20(f22(f24(f26(c56, c51), c52), c53), c54))) | (~p7(c55, c54)) | (~p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c55)) | p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c54)) <=> ((~p4(f20(f22(f24(f26(c56, c51), c52), c53), c54), f20(f22(f24(f26(c56, c51), c52), c53), c54))) | p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c54) | (~p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c55)) | (~p7(c55, c54)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(140,plain,
% 0.20/0.50 (((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | ((~p4(f20(f22(f24(f26(c56, c51), c52), c53), c54), f20(f22(f24(f26(c56, c51), c52), c53), c54))) | (~p7(c55, c54)) | (~p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c55)) | p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c54))) <=> ((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | ((~p4(f20(f22(f24(f26(c56, c51), c52), c53), c54), f20(f22(f24(f26(c56, c51), c52), c53), c54))) | p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c54) | (~p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c55)) | (~p7(c55, c54))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[139])).
% 0.20/0.50 tff(141,plain,
% 0.20/0.50 (((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | ((~p4(f20(f22(f24(f26(c56, c51), c52), c53), c54), f20(f22(f24(f26(c56, c51), c52), c53), c54))) | (~p7(c55, c54)) | (~p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c55)) | p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c54))) <=> ((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | (~p4(f20(f22(f24(f26(c56, c51), c52), c53), c54), f20(f22(f24(f26(c56, c51), c52), c53), c54))) | p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c54) | (~p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c55)) | (~p7(c55, c54)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[140, 138])).
% 0.20/0.50 tff(142,plain,
% 0.20/0.50 ((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | ((~p4(f20(f22(f24(f26(c56, c51), c52), c53), c54), f20(f22(f24(f26(c56, c51), c52), c53), c54))) | (~p7(c55, c54)) | (~p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c55)) | p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c54))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(143,plain,
% 0.20/0.50 ((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | (~p4(f20(f22(f24(f26(c56, c51), c52), c53), c54), f20(f22(f24(f26(c56, c51), c52), c53), c54))) | p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c54) | (~p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c55)) | (~p7(c55, c54))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.50 tff(144,plain,
% 0.20/0.50 (~p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c55)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[143, 137, 127, 74, 65])).
% 0.20/0.50 tff(145,plain,
% 0.20/0.50 (^[X148: $i, X150: $i, X147: $i, X149: $i] : refl((p47(X147, X148) | (~p47(f5(c48, f13(f16(f18(c50, X147), X149), X150)), X148))) <=> (p47(X147, X148) | (~p47(f5(c48, f13(f16(f18(c50, X147), X149), X150)), X148))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(146,plain,
% 0.20/0.50 (![X148: $i, X150: $i, X147: $i, X149: $i] : (p47(X147, X148) | (~p47(f5(c48, f13(f16(f18(c50, X147), X149), X150)), X148))) <=> ![X148: $i, X150: $i, X147: $i, X149: $i] : (p47(X147, X148) | (~p47(f5(c48, f13(f16(f18(c50, X147), X149), X150)), X148)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[145])).
% 0.20/0.50 tff(147,plain,
% 0.20/0.50 (![X148: $i, X150: $i, X147: $i, X149: $i] : (p47(X147, X148) | (~p47(f5(c48, f13(f16(f18(c50, X147), X149), X150)), X148))) <=> ![X148: $i, X150: $i, X147: $i, X149: $i] : (p47(X147, X148) | (~p47(f5(c48, f13(f16(f18(c50, X147), X149), X150)), X148)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(148,axiom,(![X148: $i, X150: $i, X147: $i, X149: $i] : (p47(X147, X148) | (~p47(f5(c48, f13(f16(f18(c50, X147), X149), X150)), X148)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p47_74')).
% 0.20/0.50 tff(149,plain,
% 0.20/0.50 (![X148: $i, X150: $i, X147: $i, X149: $i] : (p47(X147, X148) | (~p47(f5(c48, f13(f16(f18(c50, X147), X149), X150)), X148)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.20/0.50 tff(150,plain,(
% 0.20/0.50 ![X148: $i, X150: $i, X147: $i, X149: $i] : (p47(X147, X148) | (~p47(f5(c48, f13(f16(f18(c50, X147), X149), X150)), X148)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[149])).
% 0.20/0.50 tff(151,plain,
% 0.20/0.50 (![X148: $i, X150: $i, X147: $i, X149: $i] : (p47(X147, X148) | (~p47(f5(c48, f13(f16(f18(c50, X147), X149), X150)), X148)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.20/0.50 tff(152,plain,
% 0.20/0.50 (((~![X148: $i, X150: $i, X147: $i, X149: $i] : (p47(X147, X148) | (~p47(f5(c48, f13(f16(f18(c50, X147), X149), X150)), X148)))) | (p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c55) | (~p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55)))) <=> ((~![X148: $i, X150: $i, X147: $i, X149: $i] : (p47(X147, X148) | (~p47(f5(c48, f13(f16(f18(c50, X147), X149), X150)), X148)))) | p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c55) | (~p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(153,plain,
% 0.20/0.50 ((~![X148: $i, X150: $i, X147: $i, X149: $i] : (p47(X147, X148) | (~p47(f5(c48, f13(f16(f18(c50, X147), X149), X150)), X148)))) | (p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c55) | (~p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(154,plain,
% 0.20/0.50 ((~![X148: $i, X150: $i, X147: $i, X149: $i] : (p47(X147, X148) | (~p47(f5(c48, f13(f16(f18(c50, X147), X149), X150)), X148)))) | p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c55) | (~p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.50 tff(155,plain,
% 0.20/0.50 (~p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[154, 151, 144])).
% 0.20/0.50 tff(156,assumption,(~p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54))), introduced(assumption)).
% 0.20/0.50 tff(157,plain,
% 0.20/0.50 (^[X77: $i] : refl(p3(X77, X77) <=> p3(X77, X77))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(158,plain,
% 0.20/0.50 (![X77: $i] : p3(X77, X77) <=> ![X77: $i] : p3(X77, X77)),
% 0.20/0.50 inference(quant_intro,[status(thm)],[157])).
% 0.20/0.50 tff(159,plain,
% 0.20/0.50 (![X77: $i] : p3(X77, X77) <=> ![X77: $i] : p3(X77, X77)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(160,axiom,(![X77: $i] : p3(X77, X77)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_14')).
% 0.20/0.50 tff(161,plain,
% 0.20/0.50 (![X77: $i] : p3(X77, X77)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.20/0.50 tff(162,plain,(
% 0.20/0.50 ![X77: $i] : p3(X77, X77)),
% 0.20/0.50 inference(skolemize,[status(sab)],[161])).
% 0.20/0.50 tff(163,plain,
% 0.20/0.50 (![X77: $i] : p3(X77, X77)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.20/0.50 tff(164,plain,
% 0.20/0.50 ((~![X77: $i] : p3(X77, X77)) | p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(165,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[164, 163, 156])).
% 0.20/0.50 tff(166,plain,(p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(167,plain,
% 0.20/0.50 (((~![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))) | ((~p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54))) | (~p2(c48, c48)) | p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54))))) <=> ((~![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))) | (~p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54))) | (~p2(c48, c48)) | p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(168,plain,
% 0.20/0.50 ((~![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))) | ((~p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54))) | (~p2(c48, c48)) | p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(169,plain,
% 0.20/0.50 ((~![X129: $i, X126: $i, X127: $i, X128: $i] : ((~p3(X127, X129)) | (~p2(X126, X128)) | p4(f5(X126, X127), f5(X128, X129)))) | (~p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54))) | (~p2(c48, c48)) | p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.20/0.50 tff(170,plain,
% 0.20/0.50 ((~p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54))) | (~p2(c48, c48)) | p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[169, 30])).
% 0.20/0.50 tff(171,plain,
% 0.20/0.50 (p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[170, 20, 166])).
% 0.20/0.50 tff(172,plain,
% 0.20/0.50 (p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c55) <=> p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c55)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(173,axiom,(p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p47_77')).
% 0.20/0.50 tff(174,plain,
% 0.20/0.50 (p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c55)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.50 tff(175,plain,
% 0.20/0.50 (((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | ((~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)))) | p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54) | (~p7(c55, c54)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c55)))) <=> ((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | (~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)))) | p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54) | (~p7(c55, c54)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c55)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(176,plain,
% 0.20/0.50 (((~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)))) | (~p7(c55, c54)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c55)) | p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54)) <=> ((~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)))) | p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54) | (~p7(c55, c54)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c55)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(177,plain,
% 0.20/0.50 (((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | ((~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)))) | (~p7(c55, c54)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c55)) | p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54))) <=> ((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | ((~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)))) | p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54) | (~p7(c55, c54)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c55))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[176])).
% 0.20/0.50 tff(178,plain,
% 0.20/0.50 (((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | ((~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)))) | (~p7(c55, c54)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c55)) | p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54))) <=> ((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | (~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)))) | p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54) | (~p7(c55, c54)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c55)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[177, 175])).
% 0.20/0.50 tff(179,plain,
% 0.20/0.50 ((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | ((~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)))) | (~p7(c55, c54)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c55)) | p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(180,plain,
% 0.20/0.51 ((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | (~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)))) | p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54) | (~p7(c55, c54)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c55))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.20/0.51 tff(181,plain,
% 0.20/0.51 (p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[180, 137, 174, 171, 65])).
% 0.20/0.51 tff(182,plain,
% 0.20/0.51 (((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | ((~p7(c54, c55)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54)) | (~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))))) | p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55))) <=> ((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | (~p7(c54, c55)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54)) | (~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))))) | p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(183,plain,
% 0.20/0.51 (((~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))))) | (~p7(c54, c55)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54)) | p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55)) <=> ((~p7(c54, c55)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54)) | (~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))))) | p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(184,plain,
% 0.20/0.51 (((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | ((~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))))) | (~p7(c54, c55)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54)) | p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55))) <=> ((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | ((~p7(c54, c55)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54)) | (~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))))) | p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[183])).
% 0.20/0.51 tff(185,plain,
% 0.20/0.51 (((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | ((~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))))) | (~p7(c54, c55)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54)) | p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55))) <=> ((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | (~p7(c54, c55)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54)) | (~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))))) | p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55))),
% 0.20/0.51 inference(transitivity,[status(thm)],[184, 182])).
% 0.20/0.51 tff(186,plain,
% 0.20/0.51 ((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | ((~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))))) | (~p7(c54, c55)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54)) | p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(187,plain,
% 0.20/0.51 ((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | (~p7(c54, c55)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54)) | (~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))))) | p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.20/0.51 tff(188,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[187, 61, 137, 181, 155, 37])).
% 0.20/0.51 % SZS output end Proof
% 0.20/0.52 % E exiting
%------------------------------------------------------------------------------