%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN638-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 03:35:22 PM UTC 2026
% Result : Unsatisfiable 10.70s 1.97s
% Output : Proof 10.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 43 unt; 0 def)
% Number of atoms : 79 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 65 ( 41 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-4 aty)
% Number of variables : 70 ( 2 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f39,negated_conjecture,
p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(c25,c26,c27)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22_40) ).
fof(f39_nnf,plain,
p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(c25,c26,c27)))),
inference(nnf_transformation,[status(thm)],[f39]) ).
cnf(c39,plain,
p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(c25,c26,c27)))),
inference(cnf_transformation,[status(esa)],[f39_nnf]) ).
cnf(t35,plain,
p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(c25,c26,c27)))) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t433,plain,
p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(c25,c26,c27)))) = true,
inference(orient,[status(thm)],[t35]) ).
cnf(f31,negated_conjecture,
( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_32) ).
fof(f31_nnf,plain,
! [X41,X42,X43,X44] :
( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [X41,X42,X43,X44] :
( ~ p4(X42,X44)
| ~ p4(X41,X43)
| p4(f17(X41,X42),f17(X43,X44)) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c31,plain,
( ~ p4(X1,X3)
| ~ p4(X0,X2)
| p4(f17(X0,X1),f17(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(hi30,negated_conjecture,
ifeq(p4(X0,X1),true,ifeq(p4(X2,X3),true,p4(f17(X0,X2),f17(X1,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(f3,negated_conjecture,
p4(X36,X36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_4) ).
fof(f3_nnf,plain,
! [X36] : p4(X36,X36),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X36] : p4(X36,X36),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
p4(X0,X0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,negated_conjecture,
p4(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f38,negated_conjecture,
p4(f5(f8(f11(c25),f9(f10(c25),c28)),X51,c27),f5(f8(f11(c25),f9(f10(c25),c28)),X51,c29)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_39) ).
fof(f38_nnf,plain,
! [X51] : p4(f5(f8(f11(c25),f9(f10(c25),c28)),X51,c27),f5(f8(f11(c25),f9(f10(c25),c28)),X51,c29)),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [X51] : p4(f5(f8(f11(c25),f9(f10(c25),c28)),X51,c27),f5(f8(f11(c25),f9(f10(c25),c28)),X51,c29)),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
p4(f5(f8(f11(c25),f9(f10(c25),c28)),X0,c27),f5(f8(f11(c25),f9(f10(c25),c28)),X0,c29)),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(hi36,negated_conjecture,
p4(f5(f8(f11(c25),f9(f10(c25),c28)),X0,c27),f5(f8(f11(c25),f9(f10(c25),c28)),X0,c29)) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(h4,plain,
p4(f17(V0,f5(f8(f11(c25),f9(f10(c25),c28)),V1,c27)),f17(V0,f5(f8(f11(c25),f9(f10(c25),c28)),V1,c29))) = true,
inference(hyper_resolution,[status(thm)],[hi30,hi3,hi36]) ).
cnf(f11,negated_conjecture,
( ~ p4(X39,X40)
| p4(f16(X39),f16(X40)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_12) ).
fof(f11_nnf,plain,
! [X39,X40] :
( ~ p4(X39,X40)
| p4(f16(X39),f16(X40)) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X39,X40] :
( ~ p4(X39,X40)
| p4(f16(X39),f16(X40)) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( ~ p4(X0,X1)
| p4(f16(X0),f16(X1)) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi10,negated_conjecture,
ifeq(p4(X0,X1),true,p4(f16(X0),f16(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h15,plain,
p4(f16(f17(V0,f5(f8(f11(c25),f9(f10(c25),c28)),V1,c27))),f16(f17(V0,f5(f8(f11(c25),f9(f10(c25),c28)),V1,c29)))) = true,
inference(hyper_resolution,[status(thm)],[hi10,h4]) ).
cnf(f27,negated_conjecture,
( ~ p22(X22,X23)
| ~ p4(X23,X21)
| ~ p4(X22,X20)
| p22(X20,X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22_28) ).
fof(f27_nnf,plain,
! [X20,X21,X22,X23] :
( ~ p22(X22,X23)
| ~ p4(X23,X21)
| ~ p4(X22,X20)
| p22(X20,X21) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [X20,X21,X22,X23] :
( ~ p22(X22,X23)
| ~ p4(X23,X21)
| ~ p4(X22,X20)
| p22(X20,X21) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
( ~ p22(X2,X3)
| ~ p4(X3,X1)
| ~ p4(X2,X0)
| p22(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(hi26,negated_conjecture,
ifeq(p4(X0,X1),true,ifeq(p4(X2,X3),true,ifeq(p22(X0,X2),true,p22(X1,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(hi37,negated_conjecture,
p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(c25,c26,c27)))) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t36,plain,
p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))),f16(f17(c27,f5(c25,c26,c27)))) = true,
inference(hyper_resolution,[status(thm)],[hi26,h15,hi3,hi37]) ).
cnf(t436,plain,
p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))),f16(f17(c27,f5(c25,c26,c27)))) = true,
inference(orient,[status(thm)],[t36]) ).
cnf(t8,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t65,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t8]) ).
cnf(f7,negated_conjecture,
~ p6(f10(c25),f13(c30)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p6_8) ).
fof(f7_nnf,plain,
~ p6(f10(c25),f13(c30)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
~ p6(f10(c25),f13(c30)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
~ p6(f10(c25),f13(c30)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(f32,negated_conjecture,
~ p4(f5(c25,c26,c27),f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p4_33) ).
fof(f32_nnf,plain,
~ p4(f5(c25,c26,c27),f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27)),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
~ p4(f5(c25,c26,c27),f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27)),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c32,plain,
~ p4(f5(c25,c26,c27),f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27)),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(f40,negated_conjecture,
~ p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))),f16(f17(c27,f5(c25,c26,c27)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p22_41) ).
fof(f40_nnf,plain,
~ p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))),f16(f17(c27,f5(c25,c26,c27)))),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
~ p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))),f16(f17(c27,f5(c25,c26,c27)))),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
~ p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))),f16(f17(c27,f5(c25,c26,c27)))),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c7,c32,c40]) ).
cnf(g0_0,plain,
true != ifeq(p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))),f16(f17(c27,f5(c25,c26,c27)))),true,false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))),f16(f17(c27,f5(c25,c26,c27)))),true,false,p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(c25,c26,c27))))),
inference(rw,[status(thm)],[g0_0,t433]) ).
cnf(g0_2,plain,
true != ifeq(p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))),f16(f17(c27,f5(c25,c26,c27)))),p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c29))),f16(f17(c27,f5(c25,c26,c27)))),false,p22(f16(f17(c27,f5(f8(f11(c25),f9(f10(c25),c28)),c26,c27))),f16(f17(c27,f5(c25,c26,c27))))),
inference(rw,[status(thm)],[g0_1,t436]) ).
cnf(g0_3,plain,
true != false,
inference(rw,[status(thm)],[g0_2,t65]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN638-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 01:57:32 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.70/1.97 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.70/1.97 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------