%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN705-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:35:31 PM UTC 2026
% Result : Unsatisfiable 4.25s 1.30s
% Output : Proof 4.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 65 ( 45 unt; 0 def)
% Number of atoms : 97 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 76 ( 44 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 13 con; 0-4 aty)
% Number of variables : 166 ( 33 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f57,negated_conjecture,
( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_58) ).
fof(f57_nnf,plain,
! [X126,X127,X128,X129] :
( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) ),
inference(nnf_transformation,[status(thm)],[f57]) ).
fof(f57_sk,plain,
! [X126,X127,X128,X129] :
( ~ p3(X127,X129)
| ~ p2(X126,X128)
| p4(f5(X126,X127),f5(X128,X129)) ),
inference(skolemisation,[status(esa)],[f57_nnf]) ).
cnf(c57,plain,
( ~ p3(X1,X3)
| ~ p2(X0,X2)
| p4(f5(X0,X1),f5(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f57_sk]) ).
cnf(hi55,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p3(X2,X3),true,p4(f5(X0,X2),f5(X1,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c57]) ).
cnf(f19,negated_conjecture,
p2(X38,X38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_20) ).
fof(f19_nnf,plain,
! [X38] : p2(X38,X38),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X38] : p2(X38,X38),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
p2(X0,X0),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi19,negated_conjecture,
p2(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(f79,negated_conjecture,
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/sandbox/benchmark/theBenchmark.p',p3_80) ).
fof(f79_nnf,plain,
! [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))),
inference(nnf_transformation,[status(thm)],[f79]) ).
fof(f79_sk,plain,
! [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))),
inference(skolemisation,[status(esa)],[f79_nnf]) ).
cnf(c79,plain,
p3(f8(f10(c49,f13(f16(f18(c50,X0),X1),X2)),X3),f13(f16(f18(c50,f20(f22(f24(f26(c56,X0),X1),X2),X3)),f30(f32(f34(f36(c57,X0),X1),X2),X3)),f40(f42(f44(f46(c58,X0),X1),X2),X3))),
inference(cnf_transformation,[status(esa)],[f79_sk]) ).
cnf(hi77,negated_conjecture,
p3(f8(f10(c49,f13(f16(f18(c50,X0),X1),X2)),X3),f13(f16(f18(c50,f20(f22(f24(f26(c56,X0),X1),X2),X3)),f30(f32(f34(f36(c57,X0),X1),X2),X3)),f40(f42(f44(f46(c58,X0),X1),X2),X3))) = true,
inference(equality_encoding,[status(esa)],[c79]) ).
cnf(h21,plain,
p4(f5(V0,f8(f10(c49,f13(f16(f18(c50,V1),V2),V3)),V4)),f5(V0,f13(f16(f18(c50,f20(f22(f24(f26(c56,V1),V2),V3),V4)),f30(f32(f34(f36(c57,V1),V2),V3),V4)),f40(f42(f44(f46(c58,V1),V2),V3),V4)))) = true,
inference(hyper_resolution,[status(thm)],[hi55,hi19,hi77]) ).
cnf(f52,negated_conjecture,
( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p47_53) ).
fof(f52_nnf,plain,
! [X151,X152,X153,X154] :
( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) ),
inference(nnf_transformation,[status(thm)],[f52]) ).
fof(f52_sk,plain,
! [X151,X152,X153,X154] :
( ~ p4(X153,X151)
| ~ p7(X154,X152)
| ~ p47(X153,X154)
| p47(X151,X152) ),
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c52,plain,
( ~ p4(X2,X0)
| ~ p7(X3,X1)
| ~ p47(X2,X3)
| p47(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi50,negated_conjecture,
ifeq(p47(X0,X1),true,ifeq(p7(X1,X2),true,ifeq(p4(X0,X3),true,p47(X3,X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c52]) ).
cnf(f76,negated_conjecture,
p47(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),c55),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p47_77) ).
fof(f76_nnf,plain,
p47(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),c55),
inference(nnf_transformation,[status(thm)],[f76]) ).
cnf(c76,plain,
p47(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),c55),
inference(cnf_transformation,[status(esa)],[f76_nnf]) ).
cnf(hi74,negated_conjecture,
p47(f5(c48,f8(f10(c49,f13(f16(f18(c50,c51),c52),c53)),c54)),c55) = true,
inference(equality_encoding,[status(esa)],[c76]) ).
cnf(f2,negated_conjecture,
p7(X162,X162),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_3) ).
fof(f2_nnf,plain,
! [X162] : p7(X162,X162),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X162] : p7(X162,X162),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
p7(X0,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,negated_conjecture,
p7(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h76,plain,
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) = true,
inference(hyper_resolution,[status(thm)],[hi50,hi74,hi2,h21]) ).
cnf(f73,negated_conjecture,
( ~ p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148)
| p47(X147,X148) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p47_74) ).
fof(f73_nnf,plain,
! [X147,X148,X149,X150] :
( ~ p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148)
| p47(X147,X148) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
fof(f73_sk,plain,
! [X147,X148,X149,X150] :
( ~ p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148)
| p47(X147,X148) ),
inference(skolemisation,[status(esa)],[f73_nnf]) ).
cnf(c73,plain,
( ~ p47(f5(c48,f13(f16(f18(c50,X0),X2),X3)),X1)
| p47(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f73_sk]) ).
cnf(hi71,negated_conjecture,
ifeq(p47(f5(c48,f13(f16(f18(c50,X0),X1),X2)),X3),true,p47(X0,X3),true) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(h225,plain,
p47(f20(f22(f24(f26(c56,c51),c52),c53),c54),c55) = true,
inference(hyper_resolution,[status(thm)],[hi71,h76]) ).
cnf(f74,negated_conjecture,
( ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69)
| p47(X65,X69) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p47_75) ).
fof(f74_nnf,plain,
! [X65,X69,X66,X67,X68] :
( ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69)
| p47(X65,X69) ),
inference(nnf_transformation,[status(thm)],[f74]) ).
fof(f74_sk,plain,
! [X65,X69,X66,X67,X68] :
( ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X69)
| p47(X65,X69) ),
inference(skolemisation,[status(esa)],[f74_nnf]) ).
cnf(c74,plain,
( ~ p47(f20(f22(f24(f26(c56,X0),X2),X3),X4),X1)
| p47(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f74_sk]) ).
cnf(hi72,negated_conjecture,
ifeq(p47(f20(f22(f24(f26(c56,X0),X1),X2),X3),X4),true,p47(X0,X4),true) = true,
inference(equality_encoding,[status(esa)],[c74]) ).
cnf(h230,plain,
p47(c51,c55) = true,
inference(hyper_resolution,[status(thm)],[hi72,h225]) ).
cnf(f75,negated_conjecture,
( ~ p47(X147,X148)
| p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p47_76) ).
fof(f75_nnf,plain,
! [X147,X149,X150,X148] :
( ~ p47(X147,X148)
| p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148) ),
inference(nnf_transformation,[status(thm)],[f75]) ).
fof(f75_sk,plain,
! [X147,X149,X150,X148] :
( ~ p47(X147,X148)
| p47(f5(c48,f13(f16(f18(c50,X147),X149),X150)),X148) ),
inference(skolemisation,[status(esa)],[f75_nnf]) ).
cnf(c75,plain,
( ~ p47(X0,X3)
| p47(f5(c48,f13(f16(f18(c50,X0),X1),X2)),X3) ),
inference(cnf_transformation,[status(esa)],[f75_sk]) ).
cnf(hi73,negated_conjecture,
ifeq(p47(X0,X1),true,p47(f5(c48,f13(f16(f18(c50,X0),X2),X3)),X1),true) = true,
inference(equality_encoding,[status(esa)],[c75]) ).
cnf(t81,plain,
p47(f5(c48,f13(f16(f18(c50,c51),X1),X2)),c55) = true,
inference(hyper_resolution,[status(thm)],[hi73,h230]) ).
cnf(t357,plain,
p47(f5(c48,f13(f16(f18(c50,c51),X1),X2)),c55) = true,
inference(orient,[status(thm)],[t81]) ).
cnf(t27,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t27]) ).
cnf(f50,negated_conjecture,
~ p47(f5(c48,f13(f16(f18(c50,c51),c52),c53)),c55),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p47_51) ).
fof(f50_nnf,plain,
~ p47(f5(c48,f13(f16(f18(c50,c51),c52),c53)),c55),
inference(nnf_transformation,[status(thm)],[f50]) ).
fof(f50_sk,plain,
~ p47(f5(c48,f13(f16(f18(c50,c51),c52),c53)),c55),
inference(skolemisation,[status(esa)],[f50_nnf]) ).
cnf(c50,plain,
~ p47(f5(c48,f13(f16(f18(c50,c51),c52),c53)),c55),
inference(cnf_transformation,[status(esa)],[f50_sk]) ).
cnf(f51,negated_conjecture,
~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X68),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p47_52) ).
fof(f51_nnf,plain,
! [X65,X66,X67,X68] : ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X68),
inference(nnf_transformation,[status(thm)],[f51]) ).
fof(f51_sk,plain,
! [X65,X66,X67,X68] : ~ p47(f20(f22(f24(f26(c56,X65),X66),X67),X68),X68),
inference(skolemisation,[status(esa)],[f51_nnf]) ).
cnf(c51,plain,
~ p47(f20(f22(f24(f26(c56,X0),X1),X2),X3),X3),
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c50,c51]) ).
cnf(g0_0,plain,
true != ifeq(p47(f5(c48,f13(f16(f18(c50,c51),c52),c53)),c55),true,false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(true,true,false,true),
inference(rw,[status(thm)],[g0_0,t357]) ).
cnf(g0_2,plain,
true != false,
inference(rw,[status(thm)],[g0_1,t256]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN705-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 02:03:31 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.25/1.30 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.25/1.30 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------