%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN706-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 5.94s 1.30s
% Output : Proof 5.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 73 ( 53 unt; 0 def)
% Number of atoms : 113 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 93 ( 53 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 13 con; 0-4 aty)
% Number of variables : 124 ( 7 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f26,negated_conjecture,
p45(f20(c52,c50),c58),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p45_27) ).
fof(f26_nnf,plain,
p45(f20(c52,c50),c58),
inference(nnf_transformation,[status(thm)],[f26]) ).
cnf(c26,plain,
p45(f20(c52,c50),c58),
inference(cnf_transformation,[status(esa)],[f26_nnf]) ).
cnf(t28,plain,
p45(f20(c52,c50),c58) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t518,plain,
p45(f20(c52,c50),c58) = true,
inference(orient,[status(thm)],[t28]) ).
cnf(f67,negated_conjecture,
( ~ p39(X91,X93)
| ~ p3(X92,X94)
| p36(f40(X91,X92),f40(X93,X94)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p36_68) ).
fof(f67_nnf,plain,
! [X91,X92,X93,X94] :
( ~ p39(X91,X93)
| ~ p3(X92,X94)
| p36(f40(X91,X92),f40(X93,X94)) ),
inference(nnf_transformation,[status(thm)],[f67]) ).
fof(f67_sk,plain,
! [X91,X92,X93,X94] :
( ~ p39(X91,X93)
| ~ p3(X92,X94)
| p36(f40(X91,X92),f40(X93,X94)) ),
inference(skolemisation,[status(esa)],[f67_nnf]) ).
cnf(c67,plain,
( ~ p39(X0,X2)
| ~ p3(X1,X3)
| p36(f40(X0,X1),f40(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
cnf(hi65,negated_conjecture,
ifeq(p3(X0,X1),true,ifeq(p39(X2,X3),true,p36(f40(X2,X0),f40(X3,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(f12,negated_conjecture,
p3(X78,X78),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_13) ).
fof(f12_nnf,plain,
! [X78] : p3(X78,X78),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X78] : p3(X78,X78),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
p3(X0,X0),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi12,negated_conjecture,
p3(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(f8,negated_conjecture,
p39(X102,X102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p39_9) ).
fof(f8_nnf,plain,
! [X102] : p39(X102,X102),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X102] : p39(X102,X102),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
p39(X0,X0),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,negated_conjecture,
p39(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h5,plain,
p36(f40(V0,V1),f40(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi65,hi12,hi8]) ).
cnf(f66,negated_conjecture,
( ~ p7(X99,X101)
| ~ p36(X98,X100)
| p37(f38(X98,X99),f38(X100,X101)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p37_67) ).
fof(f66_nnf,plain,
! [X98,X99,X100,X101] :
( ~ p7(X99,X101)
| ~ p36(X98,X100)
| p37(f38(X98,X99),f38(X100,X101)) ),
inference(nnf_transformation,[status(thm)],[f66]) ).
fof(f66_sk,plain,
! [X98,X99,X100,X101] :
( ~ p7(X99,X101)
| ~ p36(X98,X100)
| p37(f38(X98,X99),f38(X100,X101)) ),
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c66,plain,
( ~ p7(X1,X3)
| ~ p36(X0,X2)
| p37(f38(X0,X1),f38(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(hi64,negated_conjecture,
ifeq(p36(X0,X1),true,ifeq(p7(X2,X3),true,p37(f38(X0,X2),f38(X1,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(f58,negated_conjecture,
p7(f8(f11(c54,f14(f17(c55,X166),f35(X167,X166))),X167),X167),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_59) ).
fof(f58_nnf,plain,
! [X166,X167] : p7(f8(f11(c54,f14(f17(c55,X166),f35(X167,X166))),X167),X167),
inference(nnf_transformation,[status(thm)],[f58]) ).
fof(f58_sk,plain,
! [X166,X167] : p7(f8(f11(c54,f14(f17(c55,X166),f35(X167,X166))),X167),X167),
inference(skolemisation,[status(esa)],[f58_nnf]) ).
cnf(c58,plain,
p7(f8(f11(c54,f14(f17(c55,X0),f35(X1,X0))),X1),X1),
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
cnf(hi56,negated_conjecture,
p7(f8(f11(c54,f14(f17(c55,X0),f35(X1,X0))),X1),X1) = true,
inference(equality_encoding,[status(esa)],[c58]) ).
cnf(h38,plain,
p37(f38(f40(V0,V1),f8(f11(c54,f14(f17(c55,V2),f35(V3,V2))),V3)),f38(f40(V0,V1),V3)) = true,
inference(hyper_resolution,[status(thm)],[hi64,h5,hi56]) ).
cnf(f77,negated_conjecture,
( ~ p45(f20(c52,X136),X137)
| p46(f23(c53,f35(X137,X142)),f5(c49,X136)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p46_78) ).
fof(f77_nnf,plain,
! [X137,X142,X136] :
( ~ p45(f20(c52,X136),X137)
| p46(f23(c53,f35(X137,X142)),f5(c49,X136)) ),
inference(nnf_transformation,[status(thm)],[f77]) ).
fof(f77_sk,plain,
! [X137,X142,X136] :
( ~ p45(f20(c52,X136),X137)
| p46(f23(c53,f35(X137,X142)),f5(c49,X136)) ),
inference(skolemisation,[status(esa)],[f77_nnf]) ).
cnf(c77,plain,
( ~ p45(f20(c52,X2),X0)
| p46(f23(c53,f35(X0,X1)),f5(c49,X2)) ),
inference(cnf_transformation,[status(esa)],[f77_sk]) ).
cnf(hi75,negated_conjecture,
ifeq(p45(f20(c52,X0),X1),true,p46(f23(c53,f35(X1,X2)),f5(c49,X0)),true) = true,
inference(equality_encoding,[status(esa)],[c77]) ).
cnf(hi26,negated_conjecture,
p45(f20(c52,c50),c58) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(h16,plain,
p46(f23(c53,f35(c58,V0)),f5(c49,c50)) = true,
inference(hyper_resolution,[status(thm)],[hi75,hi26]) ).
cnf(f80,negated_conjecture,
( ~ p46(f23(c53,X150),f5(c49,c50))
| ~ p45(f20(c52,c50),X151)
| p48(f38(f40(c59,c50),f8(f11(c54,f14(f17(c55,c61),X150)),X151)),c60) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p48_81) ).
fof(f80_nnf,plain,
! [X150,X151] :
( ~ p46(f23(c53,X150),f5(c49,c50))
| ~ p45(f20(c52,c50),X151)
| p48(f38(f40(c59,c50),f8(f11(c54,f14(f17(c55,c61),X150)),X151)),c60) ),
inference(nnf_transformation,[status(thm)],[f80]) ).
fof(f80_sk,plain,
! [X150,X151] :
( ~ p46(f23(c53,X150),f5(c49,c50))
| ~ p45(f20(c52,c50),X151)
| p48(f38(f40(c59,c50),f8(f11(c54,f14(f17(c55,c61),X150)),X151)),c60) ),
inference(skolemisation,[status(esa)],[f80_nnf]) ).
cnf(c80,plain,
( ~ p46(f23(c53,X0),f5(c49,c50))
| ~ p45(f20(c52,c50),X1)
| p48(f38(f40(c59,c50),f8(f11(c54,f14(f17(c55,c61),X0)),X1)),c60) ),
inference(cnf_transformation,[status(esa)],[f80_sk]) ).
cnf(hi78,negated_conjecture,
ifeq(p45(f20(c52,c50),X0),true,ifeq(p46(f23(c53,X1),f5(c49,c50)),true,p48(f38(f40(c59,c50),f8(f11(c54,f14(f17(c55,c61),X1)),X0)),c60),true),true) = true,
inference(equality_encoding,[status(esa)],[c80]) ).
cnf(h60,plain,
p48(f38(f40(c59,c50),f8(f11(c54,f14(f17(c55,c61),f35(c58,V0))),c58)),c60) = true,
inference(hyper_resolution,[status(thm)],[hi78,hi26,h16]) ).
cnf(f56,negated_conjecture,
( ~ p37(X148,X146)
| ~ p48(X148,X149)
| ~ p47(X149,X147)
| p48(X146,X147) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p48_57) ).
fof(f56_nnf,plain,
! [X146,X147,X149,X148] :
( ~ p37(X148,X146)
| ~ p48(X148,X149)
| ~ p47(X149,X147)
| p48(X146,X147) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [X146,X147,X149,X148] :
( ~ p37(X148,X146)
| ~ p48(X148,X149)
| ~ p47(X149,X147)
| p48(X146,X147) ),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c56,plain,
( ~ p37(X3,X0)
| ~ p48(X3,X2)
| ~ p47(X2,X1)
| p48(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(hi54,negated_conjecture,
ifeq(p47(X0,X1),true,ifeq(p48(X2,X0),true,ifeq(p37(X2,X3),true,p48(X3,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(f4,negated_conjecture,
p47(X143,X143),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p47_5) ).
fof(f4_nnf,plain,
! [X143] : p47(X143,X143),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X143] : p47(X143,X143),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
p47(X0,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,negated_conjecture,
p47(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t43,plain,
p48(f38(f40(c59,c50),c58),c60) = true,
inference(hyper_resolution,[status(thm)],[hi54,hi4,h60,h38]) ).
cnf(t596,plain,
p48(f38(f40(c59,c50),c58),c60) = true,
inference(orient,[status(thm)],[t43]) ).
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(f27,negated_conjecture,
~ p4(f5(c49,c50),c51),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p4_28) ).
fof(f27_nnf,plain,
~ p4(f5(c49,c50),c51),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
~ p4(f5(c49,c50),c51),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
~ p4(f5(c49,c50),c51),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(f28,negated_conjecture,
~ p48(f38(f40(c59,c50),c58),c60),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p48_29) ).
fof(f28_nnf,plain,
~ p48(f38(f40(c59,c50),c58),c60),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
~ p48(f38(f40(c59,c50),c58),c60),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
~ p48(f38(f40(c59,c50),c58),c60),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c27,c28]) ).
cnf(g0_0,plain,
true != ifeq(p48(f38(f40(c59,c50),c58),c60),true,false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(p48(f38(f40(c59,c50),c58),c60),true,false,p45(f20(c52,c50),c58)),
inference(rw,[status(thm)],[g0_0,t518]) ).
cnf(g0_2,plain,
true != ifeq(p48(f38(f40(c59,c50),c58),c60),p48(f38(f40(c59,c50),c58),c60),false,p45(f20(c52,c50),c58)),
inference(rw,[status(thm)],[g0_1,t596]) ).
cnf(g0_3,plain,
true != false,
inference(rw,[status(thm)],[g0_2,t256]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN706-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 02:10:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.94/1.30 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.94/1.30 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------