%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN697-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 172.89s 22.77s
% Output : Proof 172.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 81 ( 65 unt; 0 def)
% Number of atoms : 109 ( 42 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 70 ( 42 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-4 aty)
% Number of variables : 96 ( 2 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f40,negated_conjecture,
( ~ p2(X43,X45)
| ~ p2(X43,X44)
| p2(X44,X45) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_41) ).
fof(f40_nnf,plain,
! [X44,X45,X43] :
( ~ p2(X43,X45)
| ~ p2(X43,X44)
| p2(X44,X45) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [X44,X45,X43] :
( ~ p2(X43,X45)
| ~ p2(X43,X44)
| p2(X44,X45) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
( ~ p2(X2,X1)
| ~ p2(X2,X0)
| p2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(t54,plain,
ifeq(p2(X1,X2),true,ifeq(p2(X1,X3),true,p2(X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t1044,plain,
ifeq(p2(X1,X2),true,ifeq(p2(X1,X3),true,p2(X2,X3),true),true) = true,
inference(orient,[status(thm)],[t54]) ).
cnf(f54,negated_conjecture,
~ p2(f11(f4(c45),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p2_55) ).
fof(f54_nnf,plain,
~ p2(f11(f4(c45),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)),
inference(nnf_transformation,[status(thm)],[f54]) ).
fof(f54_sk,plain,
~ p2(f11(f4(c45),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)),
inference(skolemisation,[status(esa)],[f54_nnf]) ).
cnf(c54,plain,
~ p2(f11(f4(c45),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)),
inference(cnf_transformation,[status(esa)],[f54_sk]) ).
cnf(t44,plain,
p2(f11(f4(c45),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)) = false,
inference(equality_encoding,[status(esa)],[c54]) ).
cnf(t608,plain,
p2(f11(f4(c45),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)) = false,
inference(orient,[status(thm)],[t44]) ).
cnf(t1275,plain,
true = ifeq(p2(X1,f11(f4(c45),c43)),true,ifeq(p2(X1,f11(f4(f23(c44,f9(f20(c37)))),c43)),true,false,true),true),
inference(cp,[status(thm)],[t1044,t608]) ).
cnf(t74670,plain,
ifeq(p2(X1,f11(f4(c45),c43)),true,ifeq(p2(X1,f11(f4(f23(c44,f9(f20(c37)))),c43)),true,false,true),true) = true,
inference(orient,[status(thm)],[t1275]) ).
cnf(f11,negated_conjecture,
p2(X43,X43),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_12) ).
fof(f11_nnf,plain,
! [X43] : p2(X43,X43),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X43] : p2(X43,X43),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
p2(X0,X0),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t12,plain,
p2(X1,X1) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t96,plain,
p2(X1,X1) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t1046,plain,
true = ifeq(p2(X1,X2),true,ifeq(true,true,p2(X2,X1),true),true),
inference(cp,[status(thm)],[t1044,t96]) ).
cnf(t26,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t110,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t26]) ).
cnf(t74887,plain,
true = ifeq(p2(X1,X2),true,p2(X2,X1),true),
inference(step,[status(thm)],[t1046,t110]) ).
cnf(t1462,plain,
ifeq(p2(X1,X2),true,p2(X2,X1),true) = true,
inference(orient,[status(thm)],[t74887]) ).
cnf(f53,negated_conjecture,
p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c44),c43)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_54) ).
fof(f53_nnf,plain,
p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c44),c43)),
inference(nnf_transformation,[status(thm)],[f53]) ).
cnf(c53,plain,
p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c44),c43)),
inference(cnf_transformation,[status(esa)],[f53_nnf]) ).
cnf(t46,plain,
p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c44),c43)) = true,
inference(equality_encoding,[status(esa)],[c53]) ).
cnf(t690,plain,
p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c44),c43)) = true,
inference(orient,[status(thm)],[t46]) ).
cnf(t1637,plain,
true = ifeq(true,true,p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)),true),
inference(cp,[status(thm)],[t1462,t690]) ).
cnf(t75911,plain,
true = p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)),
inference(step,[status(thm)],[t1637,t110]) ).
cnf(t19518,plain,
p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)) = true,
inference(orient,[status(thm)],[t75911]) ).
cnf(t74671,plain,
true = ifeq(p2(f11(f4(c44),c43),f11(f4(c45),c43)),true,ifeq(true,true,false,true),true),
inference(cp,[status(thm)],[t74670,t19518]) ).
cnf(f60,negated_conjecture,
( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_61) ).
fof(f60_nnf,plain,
! [X46,X47,X48,X49] :
( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) ),
inference(nnf_transformation,[status(thm)],[f60]) ).
fof(f60_sk,plain,
! [X46,X47,X48,X49] :
( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) ),
inference(skolemisation,[status(esa)],[f60_nnf]) ).
cnf(c60,plain,
( ~ p3(X0,X2)
| ~ p10(X1,X3)
| p2(f11(X0,X1),f11(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f60_sk]) ).
cnf(t67,plain,
ifeq(p10(X1,X2),true,ifeq(p3(X3,X4),true,p2(f11(X3,X1),f11(X4,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c60]) ).
cnf(t2846,plain,
ifeq(p10(X1,X2),true,ifeq(p3(X3,X4),true,p2(f11(X3,X1),f11(X4,X2)),true),true) = true,
inference(orient,[status(thm)],[t67]) ).
cnf(f6,negated_conjecture,
p10(X5,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10_7) ).
fof(f6_nnf,plain,
! [X5] : p10(X5,X5),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X5] : p10(X5,X5),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
p10(X0,X0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t8,plain,
p10(X1,X1) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t92,plain,
p10(X1,X1) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t2847,plain,
true = ifeq(true,true,ifeq(p3(X1,X2),true,p2(f11(X1,X3),f11(X2,X3)),true),true),
inference(cp,[status(thm)],[t2846,t92]) ).
cnf(t76012,plain,
true = ifeq(p3(X1,X2),true,p2(f11(X1,X3),f11(X2,X3)),true),
inference(step,[status(thm)],[t2847,t110]) ).
cnf(t20766,plain,
ifeq(p3(X1,X2),true,p2(f11(X1,X3),f11(X2,X3)),true) = true,
inference(orient,[status(thm)],[t76012]) ).
cnf(f29,negated_conjecture,
( ~ p2(X91,X92)
| p3(f4(X91),f4(X92)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_30) ).
fof(f29_nnf,plain,
! [X91,X92] :
( ~ p2(X91,X92)
| p3(f4(X91),f4(X92)) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X91,X92] :
( ~ p2(X91,X92)
| p3(f4(X91),f4(X92)) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( ~ p2(X0,X1)
| p3(f4(X0),f4(X1)) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(t38,plain,
ifeq(p2(X1,X2),true,p3(f4(X1),f4(X2)),true) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(t258,plain,
ifeq(p2(X1,X2),true,p3(f4(X1),f4(X2)),true) = true,
inference(orient,[status(thm)],[t38]) ).
cnf(f15,negated_conjecture,
p2(c44,c45),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_16) ).
fof(f15_nnf,plain,
p2(c44,c45),
inference(nnf_transformation,[status(thm)],[f15]) ).
cnf(c15,plain,
p2(c44,c45),
inference(cnf_transformation,[status(esa)],[f15_nnf]) ).
cnf(t13,plain,
p2(c44,c45) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t97,plain,
p2(c44,c45) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t259,plain,
true = ifeq(true,true,p3(f4(c44),f4(c45)),true),
inference(cp,[status(thm)],[t258,t97]) ).
cnf(t74728,plain,
true = p3(f4(c44),f4(c45)),
inference(step,[status(thm)],[t259,t110]) ).
cnf(t286,plain,
p3(f4(c44),f4(c45)) = true,
inference(orient,[status(thm)],[t74728]) ).
cnf(t20767,plain,
true = ifeq(true,true,p2(f11(f4(c44),X1),f11(f4(c45),X1)),true),
inference(cp,[status(thm)],[t20766,t286]) ).
cnf(t76013,plain,
true = p2(f11(f4(c44),X1),f11(f4(c45),X1)),
inference(step,[status(thm)],[t20767,t110]) ).
cnf(t20987,plain,
p2(f11(f4(c44),X1),f11(f4(c45),X1)) = true,
inference(orient,[status(thm)],[t76013]) ).
cnf(t77749,plain,
true = ifeq(true,true,ifeq(true,true,false,true),true),
inference(step,[status(thm)],[t74671,t20987]) ).
cnf(t77750,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t77749,t110]) ).
cnf(t77751,plain,
true = false,
inference(step,[status(thm)],[t77750,t110]) ).
cnf(t74672,plain,
false = true,
inference(orient,[status(thm)],[t77751]) ).
cnf(f55,negated_conjecture,
~ p2(f11(f4(f23(c46,f9(f20(c37)))),c47),f11(f4(c46),c47)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p2_56) ).
fof(f55_nnf,plain,
~ p2(f11(f4(f23(c46,f9(f20(c37)))),c47),f11(f4(c46),c47)),
inference(nnf_transformation,[status(thm)],[f55]) ).
fof(f55_sk,plain,
~ p2(f11(f4(f23(c46,f9(f20(c37)))),c47),f11(f4(c46),c47)),
inference(skolemisation,[status(esa)],[f55_nnf]) ).
cnf(c55,plain,
~ p2(f11(f4(f23(c46,f9(f20(c37)))),c47),f11(f4(c46),c47)),
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(f68,negated_conjecture,
( ~ p2(f11(f4(f24(X95)),c43),f11(f4(X95),c43))
| ~ p31(X95,f5(c42))
| ~ p31(X95,c44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p31_69) ).
fof(f68_nnf,plain,
! [X95] :
( ~ p2(f11(f4(f24(X95)),c43),f11(f4(X95),c43))
| ~ p31(X95,f5(c42))
| ~ p31(X95,c44) ),
inference(nnf_transformation,[status(thm)],[f68]) ).
fof(f68_sk,plain,
! [X95] :
( ~ p2(f11(f4(f24(X95)),c43),f11(f4(X95),c43))
| ~ p31(X95,f5(c42))
| ~ p31(X95,c44) ),
inference(skolemisation,[status(esa)],[f68_nnf]) ).
cnf(c68,plain,
( ~ p2(f11(f4(f24(X0)),c43),f11(f4(X0),c43))
| ~ p31(X0,f5(c42))
| ~ p31(X0,c44) ),
inference(cnf_transformation,[status(esa)],[f68_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c54,c55,c68]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t74672]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN697-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Fri Sep 25 02:06:50 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 172.89/22.77 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 172.89/22.77 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------