%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN687-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:39:50 AM UTC 2025
% Result : Unsatisfiable 0.47s 0.66s
% Output : Proof 0.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN687-1 : TPTP v9.0.0. Released v2.5.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:39:54 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.47/0.66 % SZS status Unsatisfiable
% 0.47/0.66 % SZS output start Proof
% 0.47/0.66 tff(p4_type, type, (
% 0.47/0.66 p4: ( $i * $i ) > $o)).
% 0.47/0.66 tff(f5_type, type, (
% 0.47/0.66 f5: ( $i * $i ) > $i)).
% 0.47/0.66 tff(f7_type, type, (
% 0.47/0.66 f7: ( $i * $i ) > $i)).
% 0.47/0.66 tff(f26_type, type, (
% 0.47/0.66 f26: ( $i * $i ) > $i)).
% 0.47/0.66 tff(c39_type, type, (
% 0.47/0.66 c39: $i)).
% 0.47/0.66 tff(f28_type, type, (
% 0.47/0.66 f28: ( $i * $i ) > $i)).
% 0.47/0.66 tff(c37_type, type, (
% 0.47/0.66 c37: $i)).
% 0.47/0.66 tff(c46_type, type, (
% 0.47/0.66 c46: $i)).
% 0.47/0.66 tff(c38_type, type, (
% 0.47/0.66 c38: $i)).
% 0.47/0.66 tff(f9_type, type, (
% 0.47/0.66 f9: ( $i * $i ) > $i)).
% 0.47/0.66 tff(f30_type, type, (
% 0.47/0.66 f30: ( $i * $i ) > $i)).
% 0.47/0.66 tff(f32_type, type, (
% 0.47/0.66 f32: ( $i * $i ) > $i)).
% 0.47/0.66 tff(c45_type, type, (
% 0.47/0.66 c45: $i)).
% 0.47/0.66 tff(c47_type, type, (
% 0.47/0.66 c47: $i)).
% 0.47/0.66 tff(f14_type, type, (
% 0.47/0.66 f14: ( $i * $i ) > $i)).
% 0.47/0.66 tff(f16_type, type, (
% 0.47/0.66 f16: ( $i * $i ) > $i)).
% 0.47/0.66 tff(f18_type, type, (
% 0.47/0.66 f18: ( $i * $i ) > $i)).
% 0.47/0.66 tff(c40_type, type, (
% 0.47/0.66 c40: $i)).
% 0.47/0.66 tff(p35_type, type, (
% 0.47/0.66 p35: ( $i * $i ) > $o)).
% 0.47/0.66 tff(f12_type, type, (
% 0.47/0.66 f12: ( $i * $i ) > $i)).
% 0.47/0.66 tff(p34_type, type, (
% 0.47/0.66 p34: ( $i * $i ) > $o)).
% 0.47/0.66 tff(c36_type, type, (
% 0.47/0.66 c36: $i)).
% 0.47/0.66 tff(1,plain,
% 0.47/0.66 (^[X130: $i] : refl((~p4(f5(X130, f7(c38, X130)), f5(f9(c39, X130), f7(c38, X130)))) <=> (~p4(f5(X130, f7(c38, X130)), f5(f9(c39, X130), f7(c38, X130)))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(2,plain,
% 0.47/0.66 (![X130: $i] : (~p4(f5(X130, f7(c38, X130)), f5(f9(c39, X130), f7(c38, X130)))) <=> ![X130: $i] : (~p4(f5(X130, f7(c38, X130)), f5(f9(c39, X130), f7(c38, X130))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[1])).
% 0.47/0.66 tff(3,plain,
% 0.47/0.66 (![X130: $i] : (~p4(f5(X130, f7(c38, X130)), f5(f9(c39, X130), f7(c38, X130)))) <=> ![X130: $i] : (~p4(f5(X130, f7(c38, X130)), f5(f9(c39, X130), f7(c38, X130))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(4,axiom,(![X130: $i] : (~p4(f5(X130, f7(c38, X130)), f5(f9(c39, X130), f7(c38, X130))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p4_40')).
% 0.47/0.66 tff(5,plain,
% 0.47/0.66 (![X130: $i] : (~p4(f5(X130, f7(c38, X130)), f5(f9(c39, X130), f7(c38, X130))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.47/0.66 tff(6,plain,(
% 0.47/0.66 ![X130: $i] : (~p4(f5(X130, f7(c38, X130)), f5(f9(c39, X130), f7(c38, X130))))),
% 0.47/0.66 inference(skolemize,[status(sab)],[5])).
% 0.47/0.66 tff(7,plain,
% 0.47/0.66 (![X130: $i] : (~p4(f5(X130, f7(c38, X130)), f5(f9(c39, X130), f7(c38, X130))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.47/0.66 tff(8,plain,
% 0.47/0.66 ((~![X130: $i] : (~p4(f5(X130, f7(c38, X130)), f5(f9(c39, X130), f7(c38, X130))))) | (~p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39)))))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(9,plain,
% 0.47/0.66 (~p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39))))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.47/0.66 tff(10,assumption,(~p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))), introduced(assumption)).
% 0.47/0.66 tff(11,plain,
% 0.47/0.66 (^[X107: $i, X106: $i, X108: $i] : refl((p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | p35(f12(c37, f14(f16(f18(c40, X106), X107), X108)), X108)) <=> (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | p35(f12(c37, f14(f16(f18(c40, X106), X107), X108)), X108)))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(12,plain,
% 0.47/0.66 (![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | p35(f12(c37, f14(f16(f18(c40, X106), X107), X108)), X108)) <=> ![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | p35(f12(c37, f14(f16(f18(c40, X106), X107), X108)), X108))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[11])).
% 0.47/0.66 tff(13,plain,
% 0.47/0.66 (![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | p35(f12(c37, f14(f16(f18(c40, X106), X107), X108)), X108)) <=> ![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | p35(f12(c37, f14(f16(f18(c40, X106), X107), X108)), X108))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(14,axiom,(![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | p35(f12(c37, f14(f16(f18(c40, X106), X107), X108)), X108))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_55')).
% 0.47/0.66 tff(15,plain,
% 0.47/0.66 (![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | p35(f12(c37, f14(f16(f18(c40, X106), X107), X108)), X108))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.47/0.66 tff(16,plain,(
% 0.47/0.66 ![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | p35(f12(c37, f14(f16(f18(c40, X106), X107), X108)), X108))),
% 0.47/0.66 inference(skolemize,[status(sab)],[15])).
% 0.47/0.66 tff(17,plain,
% 0.47/0.66 (![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | p35(f12(c37, f14(f16(f18(c40, X106), X107), X108)), X108))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.47/0.66 tff(18,plain,
% 0.47/0.66 (((~![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | p35(f12(c37, f14(f16(f18(c40, X106), X107), X108)), X108))) | (p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))) | p35(f12(c37, f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f30(f32(c45, c37), c39)))) <=> ((~![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | p35(f12(c37, f14(f16(f18(c40, X106), X107), X108)), X108))) | p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))) | p35(f12(c37, f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f30(f32(c45, c37), c39)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(19,plain,
% 0.47/0.66 ((~![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | p35(f12(c37, f14(f16(f18(c40, X106), X107), X108)), X108))) | (p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))) | p35(f12(c37, f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f30(f32(c45, c37), c39)))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(20,plain,
% 0.47/0.66 ((~![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | p35(f12(c37, f14(f16(f18(c40, X106), X107), X108)), X108))) | p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))) | p35(f12(c37, f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f30(f32(c45, c37), c39))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.47/0.66 tff(21,plain,
% 0.47/0.66 (p35(f12(c37, f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f30(f32(c45, c37), c39))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[20, 17, 10])).
% 0.47/0.66 tff(22,assumption,(~p4(f5(f26(f28(c46, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f5(f26(f28(c47, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))))), introduced(assumption)).
% 0.47/0.66 tff(23,plain,
% 0.47/0.66 (^[X118: $i, X119: $i, X116: $i, X117: $i] : refl(((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118))) <=> ((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(24,plain,
% 0.47/0.66 (![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118))) <=> ![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[23])).
% 0.47/0.66 tff(25,plain,
% 0.47/0.66 (![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118))) <=> ![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(26,plain,
% 0.47/0.66 (^[X118: $i, X119: $i, X116: $i, X117: $i] : trans(monotonicity(rewrite(((p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119))) | (~p34(c36, X116))) <=> ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)))), ((((p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119))) | (~p34(c36, X116))) | (~p35(f12(X116, X118), f30(f32(c45, X116), X117)))) <=> (((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118))) | (~p35(f12(X116, X118), f30(f32(c45, X116), X117)))))), rewrite((((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118))) | (~p35(f12(X116, X118), f30(f32(c45, X116), X117)))) <=> ((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)))), ((((p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119))) | (~p34(c36, X116))) | (~p35(f12(X116, X118), f30(f32(c45, X116), X117)))) <=> ((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(27,plain,
% 0.47/0.66 (![X118: $i, X119: $i, X116: $i, X117: $i] : (((p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119))) | (~p34(c36, X116))) | (~p35(f12(X116, X118), f30(f32(c45, X116), X117)))) <=> ![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[26])).
% 0.47/0.66 tff(28,axiom,(![X118: $i, X119: $i, X116: $i, X117: $i] : (((p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119))) | (~p34(c36, X116))) | (~p35(f12(X116, X118), f30(f32(c45, X116), X117))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_57')).
% 0.47/0.66 tff(29,plain,
% 0.47/0.66 (![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.50/0.67 tff(30,plain,
% 0.50/0.67 (![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.50/0.67 tff(31,plain,(
% 0.50/0.67 ![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)))),
% 0.50/0.67 inference(skolemize,[status(sab)],[30])).
% 0.50/0.67 tff(32,plain,
% 0.50/0.67 (![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.50/0.67 tff(33,plain,
% 0.50/0.67 (p34(c36, c37) <=> p34(c36, c37)),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(34,axiom,(p34(c36, c37)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p34_19')).
% 0.50/0.67 tff(35,plain,
% 0.50/0.67 (p34(c36, c37)),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.50/0.67 tff(36,plain,
% 0.50/0.67 (((~![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)))) | ((~p34(c36, c37)) | p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39)))) | p4(f5(f26(f28(c46, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f5(f26(f28(c47, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))) | (~p35(f12(c37, f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f30(f32(c45, c37), c39))))) <=> ((~![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)))) | (~p34(c36, c37)) | p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39)))) | p4(f5(f26(f28(c46, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f5(f26(f28(c47, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))) | (~p35(f12(c37, f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f30(f32(c45, c37), c39))))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(37,plain,
% 0.50/0.67 (((~p35(f12(c37, f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f30(f32(c45, c37), c39))) | (~p34(c36, c37)) | p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39)))) | p4(f5(f26(f28(c46, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f5(f26(f28(c47, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))))) <=> ((~p34(c36, c37)) | p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39)))) | p4(f5(f26(f28(c46, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f5(f26(f28(c47, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))) | (~p35(f12(c37, f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f30(f32(c45, c37), c39))))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(38,plain,
% 0.50/0.67 (((~![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)))) | ((~p35(f12(c37, f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f30(f32(c45, c37), c39))) | (~p34(c36, c37)) | p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39)))) | p4(f5(f26(f28(c46, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f5(f26(f28(c47, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))))) <=> ((~![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)))) | ((~p34(c36, c37)) | p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39)))) | p4(f5(f26(f28(c46, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f5(f26(f28(c47, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))) | (~p35(f12(c37, f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f30(f32(c45, c37), c39)))))),
% 0.50/0.67 inference(monotonicity,[status(thm)],[37])).
% 0.50/0.67 tff(39,plain,
% 0.50/0.67 (((~![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)))) | ((~p35(f12(c37, f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f30(f32(c45, c37), c39))) | (~p34(c36, c37)) | p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39)))) | p4(f5(f26(f28(c46, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f5(f26(f28(c47, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))))) <=> ((~![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)))) | (~p34(c36, c37)) | p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39)))) | p4(f5(f26(f28(c46, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f5(f26(f28(c47, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))) | (~p35(f12(c37, f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f30(f32(c45, c37), c39))))),
% 0.50/0.67 inference(transitivity,[status(thm)],[38, 36])).
% 0.50/0.67 tff(40,plain,
% 0.50/0.67 ((~![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)))) | ((~p35(f12(c37, f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f30(f32(c45, c37), c39))) | (~p34(c36, c37)) | p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39)))) | p4(f5(f26(f28(c46, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f5(f26(f28(c47, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))))),
% 0.50/0.67 inference(quant_inst,[status(thm)],[])).
% 0.50/0.67 tff(41,plain,
% 0.50/0.67 ((~![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p35(f12(X116, X118), f30(f32(c45, X116), X117))) | (~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | p4(f5(f26(f28(c46, X116), X117), X118), f5(f26(f28(c47, X116), X117), X118)))) | (~p34(c36, c37)) | p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39)))) | p4(f5(f26(f28(c46, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f5(f26(f28(c47, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))) | (~p35(f12(c37, f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f30(f32(c45, c37), c39)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.50/0.67 tff(42,plain,
% 0.50/0.67 ($false),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[41, 35, 32, 9, 22, 21])).
% 0.50/0.67 tff(43,plain,(p4(f5(f26(f28(c46, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f5(f26(f28(c47, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))) | p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.67 tff(44,plain,
% 0.50/0.67 (p4(f5(f26(f28(c46, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f5(f26(f28(c47, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))))),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[43, 10])).
% 0.50/0.67 tff(45,plain,
% 0.50/0.67 (^[X107: $i, X106: $i, X108: $i] : refl((p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | (~p4(f5(X106, f14(f16(f18(c40, X106), X107), X108)), f5(X107, f14(f16(f18(c40, X106), X107), X108))))) <=> (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | (~p4(f5(X106, f14(f16(f18(c40, X106), X107), X108)), f5(X107, f14(f16(f18(c40, X106), X107), X108))))))),
% 0.50/0.67 inference(bind,[status(th)],[])).
% 0.50/0.67 tff(46,plain,
% 0.50/0.67 (![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | (~p4(f5(X106, f14(f16(f18(c40, X106), X107), X108)), f5(X107, f14(f16(f18(c40, X106), X107), X108))))) <=> ![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | (~p4(f5(X106, f14(f16(f18(c40, X106), X107), X108)), f5(X107, f14(f16(f18(c40, X106), X107), X108)))))),
% 0.50/0.67 inference(quant_intro,[status(thm)],[45])).
% 0.50/0.67 tff(47,plain,
% 0.50/0.67 (![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | (~p4(f5(X106, f14(f16(f18(c40, X106), X107), X108)), f5(X107, f14(f16(f18(c40, X106), X107), X108))))) <=> ![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | (~p4(f5(X106, f14(f16(f18(c40, X106), X107), X108)), f5(X107, f14(f16(f18(c40, X106), X107), X108)))))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(48,axiom,(![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | (~p4(f5(X106, f14(f16(f18(c40, X106), X107), X108)), f5(X107, f14(f16(f18(c40, X106), X107), X108)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_56')).
% 0.50/0.68 tff(49,plain,
% 0.50/0.68 (![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | (~p4(f5(X106, f14(f16(f18(c40, X106), X107), X108)), f5(X107, f14(f16(f18(c40, X106), X107), X108)))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.50/0.68 tff(50,plain,(
% 0.50/0.68 ![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | (~p4(f5(X106, f14(f16(f18(c40, X106), X107), X108)), f5(X107, f14(f16(f18(c40, X106), X107), X108)))))),
% 0.50/0.68 inference(skolemize,[status(sab)],[49])).
% 0.50/0.68 tff(51,plain,
% 0.50/0.68 (![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | (~p4(f5(X106, f14(f16(f18(c40, X106), X107), X108)), f5(X107, f14(f16(f18(c40, X106), X107), X108)))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.50/0.68 tff(52,plain,
% 0.50/0.68 (((~![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | (~p4(f5(X106, f14(f16(f18(c40, X106), X107), X108)), f5(X107, f14(f16(f18(c40, X106), X107), X108)))))) | (p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))) | (~p4(f5(f26(f28(c46, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f5(f26(f28(c47, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))))))) <=> ((~![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | (~p4(f5(X106, f14(f16(f18(c40, X106), X107), X108)), f5(X107, f14(f16(f18(c40, X106), X107), X108)))))) | p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))) | (~p4(f5(f26(f28(c46, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f5(f26(f28(c47, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))))))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(53,plain,
% 0.50/0.68 ((~![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | (~p4(f5(X106, f14(f16(f18(c40, X106), X107), X108)), f5(X107, f14(f16(f18(c40, X106), X107), X108)))))) | (p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))) | (~p4(f5(f26(f28(c46, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f5(f26(f28(c47, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))))))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(54,plain,
% 0.50/0.68 ((~![X107: $i, X106: $i, X108: $i] : (p4(f5(f9(c39, X106), X108), f5(f9(c39, X107), X108)) | (~p4(f5(X106, f14(f16(f18(c40, X106), X107), X108)), f5(X107, f14(f16(f18(c40, X106), X107), X108)))))) | p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))) | (~p4(f5(f26(f28(c46, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))), f5(f26(f28(c47, c37), c39), f14(f16(f18(c40, f26(f28(c46, c37), c39)), f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.50/0.68 tff(55,plain,
% 0.50/0.68 ($false),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[54, 51, 10, 44])).
% 0.50/0.68 tff(56,plain,(p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.68 tff(57,plain,
% 0.50/0.68 (^[X119: $i, X116: $i, X117: $i] : refl(((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117))))) <=> ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117))))))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(58,plain,
% 0.50/0.68 (![X119: $i, X116: $i, X117: $i] : ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117))))) <=> ![X119: $i, X116: $i, X117: $i] : ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117)))))),
% 0.50/0.68 inference(quant_intro,[status(thm)],[57])).
% 0.50/0.68 tff(59,plain,
% 0.50/0.68 (![X119: $i, X116: $i, X117: $i] : ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117))))) <=> ![X119: $i, X116: $i, X117: $i] : ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117)))))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(60,plain,
% 0.50/0.68 (^[X119: $i, X116: $i, X117: $i] : trans(monotonicity(rewrite((p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p34(c36, X116))) <=> ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)))), (((p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p34(c36, X116))) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117))))) <=> (((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119))) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117))))))), rewrite((((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119))) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117))))) <=> ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117)))))), (((p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p34(c36, X116))) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117))))) <=> ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117)))))))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(61,plain,
% 0.50/0.68 (![X119: $i, X116: $i, X117: $i] : ((p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p34(c36, X116))) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117))))) <=> ![X119: $i, X116: $i, X117: $i] : ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117)))))),
% 0.50/0.68 inference(quant_intro,[status(thm)],[60])).
% 0.50/0.68 tff(62,axiom,(![X119: $i, X116: $i, X117: $i] : ((p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p34(c36, X116))) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_58')).
% 0.50/0.68 tff(63,plain,
% 0.50/0.68 (![X119: $i, X116: $i, X117: $i] : ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117)))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.50/0.68 tff(64,plain,
% 0.50/0.68 (![X119: $i, X116: $i, X117: $i] : ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117)))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.50/0.68 tff(65,plain,(
% 0.50/0.68 ![X119: $i, X116: $i, X117: $i] : ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117)))))),
% 0.50/0.68 inference(skolemize,[status(sab)],[64])).
% 0.50/0.68 tff(66,plain,
% 0.50/0.68 (![X119: $i, X116: $i, X117: $i] : ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117)))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.50/0.68 tff(67,plain,
% 0.50/0.68 (((~![X119: $i, X116: $i, X117: $i] : ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117)))))) | ((~p34(c36, c37)) | (~p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))) | p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39)))))) <=> ((~![X119: $i, X116: $i, X117: $i] : ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117)))))) | (~p34(c36, c37)) | (~p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))) | p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39)))))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(68,plain,
% 0.50/0.68 (((~p34(c36, c37)) | p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39)))) | (~p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39))))) <=> ((~p34(c36, c37)) | (~p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))) | p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39)))))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(69,plain,
% 0.50/0.68 (((~![X119: $i, X116: $i, X117: $i] : ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117)))))) | ((~p34(c36, c37)) | p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39)))) | (~p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))))) <=> ((~![X119: $i, X116: $i, X117: $i] : ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117)))))) | ((~p34(c36, c37)) | (~p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))) | p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39))))))),
% 0.50/0.68 inference(monotonicity,[status(thm)],[68])).
% 0.50/0.68 tff(70,plain,
% 0.50/0.68 (((~![X119: $i, X116: $i, X117: $i] : ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117)))))) | ((~p34(c36, c37)) | p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39)))) | (~p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))))) <=> ((~![X119: $i, X116: $i, X117: $i] : ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117)))))) | (~p34(c36, c37)) | (~p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))) | p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39)))))),
% 0.50/0.68 inference(transitivity,[status(thm)],[69, 67])).
% 0.50/0.68 tff(71,plain,
% 0.50/0.68 ((~![X119: $i, X116: $i, X117: $i] : ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117)))))) | ((~p34(c36, c37)) | p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39)))) | (~p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(72,plain,
% 0.50/0.68 ((~![X119: $i, X116: $i, X117: $i] : ((~p34(c36, X116)) | p4(f5(f26(f28(c46, X116), X117), X119), f5(f9(X117, f26(f28(c46, X116), X117)), X119)) | (~p4(f5(f9(X117, f26(f28(c46, X116), X117)), f30(f32(c45, X116), X117)), f5(f9(X117, f26(f28(c47, X116), X117)), f30(f32(c45, X116), X117)))))) | (~p34(c36, c37)) | (~p4(f5(f9(c39, f26(f28(c46, c37), c39)), f30(f32(c45, c37), c39)), f5(f9(c39, f26(f28(c47, c37), c39)), f30(f32(c45, c37), c39)))) | p4(f5(f26(f28(c46, c37), c39), f7(c38, f26(f28(c46, c37), c39))), f5(f9(c39, f26(f28(c46, c37), c39)), f7(c38, f26(f28(c46, c37), c39))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.50/0.68 tff(73,plain,
% 0.50/0.68 ($false),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[72, 35, 66, 56, 9])).
% 0.50/0.68 % SZS output end Proof
% 0.50/0.69 % E exiting
%------------------------------------------------------------------------------