%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN702-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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
% 0.10/0.12 % Problem : SYN702-1 : TPTP v9.0.0. Released v2.5.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:40:35 EDT 2025
% 0.11/0.33 % 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(c57_type, type, (
% 0.20/0.48 c57: $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(c56_type, type, (
% 0.20/0.48 c56: $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(c55_type, type, (
% 0.20/0.48 c55: $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(p7_type, type, (
% 0.20/0.48 p7: ( $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(c55, X65), X66), X67), X68)), f30(f32(f34(f36(c56, X65), X66), X67), X68)), f40(f42(f44(f46(c57, X65), X66), X67), X68))) <=> p3(f8(f10(c49, f13(f16(f18(c50, X65), X66), X67)), X68), f13(f16(f18(c50, f20(f22(f24(f26(c55, X65), X66), X67), X68)), f30(f32(f34(f36(c56, X65), X66), X67), X68)), f40(f42(f44(f46(c57, 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(c55, X65), X66), X67), X68)), f30(f32(f34(f36(c56, X65), X66), X67), X68)), f40(f42(f44(f46(c57, 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(c55, X65), X66), X67), X68)), f30(f32(f34(f36(c56, X65), X66), X67), X68)), f40(f42(f44(f46(c57, 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(c55, X65), X66), X67), X68)), f30(f32(f34(f36(c56, X65), X66), X67), X68)), f40(f42(f44(f46(c57, 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(c55, X65), X66), X67), X68)), f30(f32(f34(f36(c56, X65), X66), X67), X68)), f40(f42(f44(f46(c57, 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(c55, X65), X66), X67), X68)), f30(f32(f34(f36(c56, X65), X66), X67), X68)), f40(f42(f44(f46(c57, X65), X66), X67), X68)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_79')).
% 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(c55, X65), X66), X67), X68)), f30(f32(f34(f36(c56, X65), X66), X67), X68)), f40(f42(f44(f46(c57, 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(c55, X65), X66), X67), X68)), f30(f32(f34(f36(c56, X65), X66), X67), X68)), f40(f42(f44(f46(c57, 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(c55, X65), X66), X67), X68)), f30(f32(f34(f36(c56, X65), X66), X67), X68)), f40(f42(f44(f46(c57, 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(c55, X65), X66), X67), X68)), f30(f32(f34(f36(c56, X65), X66), X67), X68)), f40(f42(f44(f46(c57, X65), X66), X67), X68)))) | p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f13(f16(f18(c50, f20(f22(f24(f26(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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_57')).
% 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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[32])).
% 0.20/0.48 tff(34,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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[33, 31])).
% 0.20/0.48 tff(35,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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(36,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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.48 tff(37,plain,
% 0.20/0.48 (p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[36, 30, 20, 9])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 (^[X67: $i, X68: $i, X66: $i, X65: $i] : refl((~p47(f20(f22(f24(f26(c55, X65), X66), X67), X68), X68)) <=> (~p47(f20(f22(f24(f26(c55, X65), X66), X67), X68), X68)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 (![X67: $i, X68: $i, X66: $i, X65: $i] : (~p47(f20(f22(f24(f26(c55, X65), X66), X67), X68), X68)) <=> ![X67: $i, X68: $i, X66: $i, X65: $i] : (~p47(f20(f22(f24(f26(c55, X65), X66), X67), X68), X68))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 (![X67: $i, X68: $i, X66: $i, X65: $i] : (~p47(f20(f22(f24(f26(c55, X65), X66), X67), X68), X68)) <=> ![X67: $i, X68: $i, X66: $i, X65: $i] : (~p47(f20(f22(f24(f26(c55, X65), X66), X67), X68), X68))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(41,axiom,(![X67: $i, X68: $i, X66: $i, X65: $i] : (~p47(f20(f22(f24(f26(c55, X65), X66), X67), X68), X68))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p47_51')).
% 0.20/0.49 tff(42,plain,
% 0.20/0.49 (![X67: $i, X68: $i, X66: $i, X65: $i] : (~p47(f20(f22(f24(f26(c55, X65), X66), X67), X68), X68))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.49 tff(43,plain,(
% 0.20/0.49 ![X67: $i, X68: $i, X66: $i, X65: $i] : (~p47(f20(f22(f24(f26(c55, X65), X66), X67), X68), X68))),
% 0.20/0.49 inference(skolemize,[status(sab)],[42])).
% 0.20/0.49 tff(44,plain,
% 0.20/0.49 (![X67: $i, X68: $i, X66: $i, X65: $i] : (~p47(f20(f22(f24(f26(c55, X65), X66), X67), X68), X68))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.20/0.49 tff(45,plain,
% 0.20/0.49 ((~![X67: $i, X68: $i, X66: $i, X65: $i] : (~p47(f20(f22(f24(f26(c55, X65), X66), X67), X68), X68))) | (~p47(f20(f22(f24(f26(c55, c51), c52), c53), c54), c54))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(46,plain,
% 0.20/0.49 (~p47(f20(f22(f24(f26(c55, c51), c52), c53), c54), c54)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.49 tff(47,plain,
% 0.20/0.49 (^[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))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(48,plain,
% 0.20/0.49 (![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)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.49 tff(49,plain,
% 0.20/0.49 (![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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(50,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_73')).
% 0.20/0.49 tff(51,plain,
% 0.20/0.49 (![X148: $i, X150: $i, X147: $i, X149: $i] : (p47(X147, X148) | (~p47(f5(c48, f13(f16(f18(c50, X147), X149), X150)), X148)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.49 tff(52,plain,(
% 0.20/0.49 ![X148: $i, X150: $i, X147: $i, X149: $i] : (p47(X147, X148) | (~p47(f5(c48, f13(f16(f18(c50, X147), X149), X150)), X148)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[51])).
% 0.20/0.49 tff(53,plain,
% 0.20/0.49 (![X148: $i, X150: $i, X147: $i, X149: $i] : (p47(X147, X148) | (~p47(f5(c48, f13(f16(f18(c50, X147), X149), X150)), X148)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.20/0.49 tff(54,plain,
% 0.20/0.49 (((~![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(c55, c51), c52), c53), c54), c54) | (~p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))), c54)))) <=> ((~![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(c55, c51), c52), c53), c54), c54) | (~p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))), c54)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(55,plain,
% 0.20/0.49 ((~![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(c55, c51), c52), c53), c54), c54) | (~p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))), c54)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(56,plain,
% 0.20/0.49 ((~![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(c55, c51), c52), c53), c54), c54) | (~p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))), c54))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.49 tff(57,plain,
% 0.20/0.49 (~p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))), c54)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[56, 53, 46])).
% 0.20/0.49 tff(58,assumption,(~p7(c54, c54)), introduced(assumption)).
% 0.20/0.49 tff(59,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(60,plain,
% 0.20/0.49 (![X162: $i] : p7(X162, X162) <=> ![X162: $i] : p7(X162, X162)),
% 0.20/0.49 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.49 tff(61,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(62,axiom,(![X162: $i] : p7(X162, X162)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_3')).
% 0.20/0.49 tff(63,plain,
% 0.20/0.49 (![X162: $i] : p7(X162, X162)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.49 tff(64,plain,(
% 0.20/0.49 ![X162: $i] : p7(X162, X162)),
% 0.20/0.49 inference(skolemize,[status(sab)],[63])).
% 0.20/0.49 tff(65,plain,
% 0.20/0.49 (![X162: $i] : p7(X162, X162)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.20/0.49 tff(66,plain,
% 0.20/0.49 ((~![X162: $i] : p7(X162, X162)) | p7(c54, c54)),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(67,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[66, 65, 58])).
% 0.20/0.49 tff(68,plain,(p7(c54, c54)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(69,plain,
% 0.20/0.49 (p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54) <=> p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(70,axiom,(p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p47_76')).
% 0.20/0.49 tff(71,plain,
% 0.20/0.49 (p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.49 tff(72,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(73,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)],[72])).
% 0.20/0.49 tff(74,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(75,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(76,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)],[75])).
% 0.20/0.49 tff(77,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_52')).
% 0.20/0.49 tff(78,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))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.49 tff(79,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))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.20/0.49 tff(80,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))),
% 0.20/0.49 inference(skolemize,[status(sab)],[79])).
% 0.20/0.49 tff(81,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))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.20/0.49 tff(82,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))) | ((~p7(c54, c54)) | (~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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))))) | p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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))) | (~p7(c54, c54)) | (~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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))))) | p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))), c54))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(83,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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))))) | (~p7(c54, c54)) | (~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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))), c54)) <=> ((~p7(c54, c54)) | (~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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))))) | p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))), c54))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(84,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))) | ((~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))))) | (~p7(c54, c54)) | (~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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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))) | ((~p7(c54, c54)) | (~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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))))) | p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))), c54)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[83])).
% 0.20/0.49 tff(85,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))) | ((~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))))) | (~p7(c54, c54)) | (~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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, 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))) | (~p7(c54, c54)) | (~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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))))) | p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))), c54))),
% 0.20/0.49 inference(transitivity,[status(thm)],[84, 82])).
% 0.20/0.49 tff(86,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))) | ((~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))))) | (~p7(c54, c54)) | (~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(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))), c54))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(87,plain,
% 0.20/0.49 ((~![X152: $i, X154: $i, X151: $i, X153: $i] : ((~p4(X153, X151)) | (~p7(X154, X152)) | (~p47(X153, X154)) | p47(X151, X152))) | (~p7(c54, c54)) | (~p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c54)) | (~p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))))) | p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c55, c51), c52), c53), c54)), f30(f32(f34(f36(c56, c51), c52), c53), c54)), f40(f42(f44(f46(c57, c51), c52), c53), c54))), c54)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[87, 81, 71, 68, 57, 37])).
% 0.20/0.50 % SZS output end Proof
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------