%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN691-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n010.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 03:35:30 PM UTC 2026
% Result : Unsatisfiable 4.32s 13.06s
% Output : Proof 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 57 ( 37 unt; 0 def)
% Number of atoms : 89 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 70 ( 38 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 11 con; 0-4 aty)
% Number of variables : 133 ( 22 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f49,negated_conjecture,
( ~ p3(X119,X121)
| ~ p2(X118,X120)
| p4(f5(X118,X119),f5(X120,X121)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_50) ).
fof(f49_nnf,plain,
! [X118,X119,X120,X121] :
( ~ p3(X119,X121)
| ~ p2(X118,X120)
| p4(f5(X118,X119),f5(X120,X121)) ),
inference(nnf_transformation,[status(thm)],[f49]) ).
fof(f49_sk,plain,
! [X118,X119,X120,X121] :
( ~ p3(X119,X121)
| ~ p2(X118,X120)
| p4(f5(X118,X119),f5(X120,X121)) ),
inference(skolemisation,[status(esa)],[f49_nnf]) ).
cnf(c49,plain,
( ~ p3(X1,X3)
| ~ p2(X0,X2)
| p4(f5(X0,X1),f5(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f49_sk]) ).
cnf(hi48,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)],[c49]) ).
cnf(f16,negated_conjecture,
p2(X31,X31),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_17) ).
fof(f16_nnf,plain,
! [X31] : p2(X31,X31),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X31] : p2(X31,X31),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
p2(X0,X0),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,negated_conjecture,
p2(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(f66,negated_conjecture,
p3(f7(c41,f10(f13(f15(c42,X47),X48),X49)),f10(f13(f15(c42,f17(f19(f21(c47,X47),X48),X49)),f26(f28(f30(c48,X47),X48),X49)),f34(f36(f38(c49,X47),X48),X49))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_67) ).
fof(f66_nnf,plain,
! [X47,X48,X49] : p3(f7(c41,f10(f13(f15(c42,X47),X48),X49)),f10(f13(f15(c42,f17(f19(f21(c47,X47),X48),X49)),f26(f28(f30(c48,X47),X48),X49)),f34(f36(f38(c49,X47),X48),X49))),
inference(nnf_transformation,[status(thm)],[f66]) ).
fof(f66_sk,plain,
! [X47,X48,X49] : p3(f7(c41,f10(f13(f15(c42,X47),X48),X49)),f10(f13(f15(c42,f17(f19(f21(c47,X47),X48),X49)),f26(f28(f30(c48,X47),X48),X49)),f34(f36(f38(c49,X47),X48),X49))),
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c66,plain,
p3(f7(c41,f10(f13(f15(c42,X0),X1),X2)),f10(f13(f15(c42,f17(f19(f21(c47,X0),X1),X2)),f26(f28(f30(c48,X0),X1),X2)),f34(f36(f38(c49,X0),X1),X2))),
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(hi65,negated_conjecture,
p3(f7(c41,f10(f13(f15(c42,X0),X1),X2)),f10(f13(f15(c42,f17(f19(f21(c47,X0),X1),X2)),f26(f28(f30(c48,X0),X1),X2)),f34(f36(f38(c49,X0),X1),X2))) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(h4,plain,
p4(f5(V0,f7(c41,f10(f13(f15(c42,V1),V2),V3))),f5(V0,f10(f13(f15(c42,f17(f19(f21(c47,V1),V2),V3)),f26(f28(f30(c48,V1),V2),V3)),f34(f36(f38(c49,V1),V2),V3)))) = true,
inference(hyper_resolution,[status(thm)],[hi48,hi16,hi65]) ).
cnf(f44,negated_conjecture,
( ~ p22(X109,X108)
| ~ p4(X110,X107)
| ~ p39(X110,X109)
| p39(X107,X108) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p39_45) ).
fof(f44_nnf,plain,
! [X107,X108,X110,X109] :
( ~ p22(X109,X108)
| ~ p4(X110,X107)
| ~ p39(X110,X109)
| p39(X107,X108) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [X107,X108,X110,X109] :
( ~ p22(X109,X108)
| ~ p4(X110,X107)
| ~ p39(X110,X109)
| p39(X107,X108) ),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c44,plain,
( ~ p22(X3,X1)
| ~ p4(X2,X0)
| ~ p39(X2,X3)
| p39(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(hi43,negated_conjecture,
ifeq(p39(X0,X1),true,ifeq(p4(X0,X2),true,ifeq(p22(X1,X3),true,p39(X2,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
cnf(f45,negated_conjecture,
p39(f5(c40,f7(c41,f10(f13(f15(c42,c43),c44),c45))),c46),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p39_46) ).
fof(f45_nnf,plain,
p39(f5(c40,f7(c41,f10(f13(f15(c42,c43),c44),c45))),c46),
inference(nnf_transformation,[status(thm)],[f45]) ).
cnf(c45,plain,
p39(f5(c40,f7(c41,f10(f13(f15(c42,c43),c44),c45))),c46),
inference(cnf_transformation,[status(esa)],[f45_nnf]) ).
cnf(hi44,negated_conjecture,
p39(f5(c40,f7(c41,f10(f13(f15(c42,c43),c44),c45))),c46) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
cnf(f14,negated_conjecture,
p22(X37,X37),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22_15) ).
fof(f14_nnf,plain,
! [X37] : p22(X37,X37),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X37] : p22(X37,X37),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
p22(X0,X0),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,negated_conjecture,
p22(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h7,plain,
p39(f5(c40,f10(f13(f15(c42,f17(f19(f21(c47,c43),c44),c45)),f26(f28(f30(c48,c43),c44),c45)),f34(f36(f38(c49,c43),c44),c45))),c46) = true,
inference(hyper_resolution,[status(thm)],[hi43,hi44,h4,hi14]) ).
cnf(f62,negated_conjecture,
( ~ p39(f5(c40,f10(f13(f15(c42,X103),X105),X106)),X104)
| p39(X103,X104) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p39_63) ).
fof(f62_nnf,plain,
! [X103,X104,X105,X106] :
( ~ p39(f5(c40,f10(f13(f15(c42,X103),X105),X106)),X104)
| p39(X103,X104) ),
inference(nnf_transformation,[status(thm)],[f62]) ).
fof(f62_sk,plain,
! [X103,X104,X105,X106] :
( ~ p39(f5(c40,f10(f13(f15(c42,X103),X105),X106)),X104)
| p39(X103,X104) ),
inference(skolemisation,[status(esa)],[f62_nnf]) ).
cnf(c62,plain,
( ~ p39(f5(c40,f10(f13(f15(c42,X0),X2),X3)),X1)
| p39(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f62_sk]) ).
cnf(hi61,negated_conjecture,
ifeq(p39(f5(c40,f10(f13(f15(c42,X0),X1),X2)),X3),true,p39(X0,X3),true) = true,
inference(equality_encoding,[status(esa)],[c62]) ).
cnf(h9,plain,
p39(f17(f19(f21(c47,c43),c44),c45),c46) = true,
inference(hyper_resolution,[status(thm)],[hi61,h7]) ).
cnf(f43,negated_conjecture,
( ~ p39(f17(f19(f21(c47,X47),X48),X49),X50)
| p39(X47,X50) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p39_44) ).
fof(f43_nnf,plain,
! [X47,X50,X48,X49] :
( ~ p39(f17(f19(f21(c47,X47),X48),X49),X50)
| p39(X47,X50) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [X47,X50,X48,X49] :
( ~ p39(f17(f19(f21(c47,X47),X48),X49),X50)
| p39(X47,X50) ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c43,plain,
( ~ p39(f17(f19(f21(c47,X0),X2),X3),X1)
| p39(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(hi42,negated_conjecture,
ifeq(p39(f17(f19(f21(c47,X0),X1),X2),X3),true,p39(X0,X3),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(h14,plain,
p39(c43,c46) = true,
inference(hyper_resolution,[status(thm)],[hi42,h9]) ).
cnf(f63,negated_conjecture,
( ~ p39(X103,X104)
| p39(f5(c40,f10(f13(f15(c42,X103),X105),X106)),X104) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p39_64) ).
fof(f63_nnf,plain,
! [X103,X105,X106,X104] :
( ~ p39(X103,X104)
| p39(f5(c40,f10(f13(f15(c42,X103),X105),X106)),X104) ),
inference(nnf_transformation,[status(thm)],[f63]) ).
fof(f63_sk,plain,
! [X103,X105,X106,X104] :
( ~ p39(X103,X104)
| p39(f5(c40,f10(f13(f15(c42,X103),X105),X106)),X104) ),
inference(skolemisation,[status(esa)],[f63_nnf]) ).
cnf(c63,plain,
( ~ p39(X0,X3)
| p39(f5(c40,f10(f13(f15(c42,X0),X1),X2)),X3) ),
inference(cnf_transformation,[status(esa)],[f63_sk]) ).
cnf(hi62,negated_conjecture,
ifeq(p39(X0,X1),true,p39(f5(c40,f10(f13(f15(c42,X0),X2),X3)),X1),true) = true,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(t24,plain,
p39(f5(c40,f10(f13(f15(c42,c43),X1),X2)),c46) = true,
inference(hyper_resolution,[status(thm)],[hi62,h14]) ).
cnf(t158,plain,
p39(f5(c40,f10(f13(f15(c42,c43),X1),X2)),c46) = true,
inference(orient,[status(thm)],[t24]) ).
cnf(f42,negated_conjecture,
~ p39(f5(c40,f10(f13(f15(c42,c43),c44),c45)),c46),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p39_43) ).
fof(f42_nnf,plain,
~ p39(f5(c40,f10(f13(f15(c42,c43),c44),c45)),c46),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
~ p39(f5(c40,f10(f13(f15(c42,c43),c44),c45)),c46),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c42,plain,
~ p39(f5(c40,f10(f13(f15(c42,c43),c44),c45)),c46),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(goal_0,negated_conjecture,
p39(f5(c40,f10(f13(f15(c42,c43),c44),c45)),c46) != true,
inference(equality_encoding,[status(esa)],[c42]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t158]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN691-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/12.49 % Computer : n010.cluster.edu
% 0.10/12.49 % Model : x86_64 x86_64
% 0.10/12.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/12.49 % Memory : 8046.5625MB
% 0.10/12.49 % OS : Linux 6.8.0-71-generic
% 0.10/12.49 % CPULimit : 300
% 0.10/12.49 % WCLimit : 300
% 0.10/12.49 % DateTime : Fri Sep 25 02:06:15 UTC 2026
% 0.14/12.50 % CPUTime :
% 0.14/12.50 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.32/13.06 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.32/13.06 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------