%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN584-1 : 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 03:35:15 PM UTC 2026
% Result : Unsatisfiable 7.34s 6.46s
% Output : Proof 7.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 35 unt; 0 def)
% Number of atoms : 75 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 69 ( 41 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-4 aty)
% Number of variables : 55 ( 2 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f8,negated_conjecture,
( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_9) ).
fof(f8_nnf,plain,
! [X1,X2,X0] :
( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X1,X2,X0] :
( ~ p12(X0,X2)
| ~ p12(X0,X1)
| p12(X1,X2) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ~ p12(X2,X1)
| ~ p12(X2,X0)
| p12(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,negated_conjecture,
ifeq(p12(X0,X1),true,ifeq(p12(X0,X2),true,p12(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(f22,negated_conjecture,
p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),c22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_23) ).
fof(f22_nnf,plain,
p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),c22),
inference(nnf_transformation,[status(thm)],[f22]) ).
cnf(c22,plain,
p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),c22),
inference(cnf_transformation,[status(esa)],[f22_nnf]) ).
cnf(hi22,negated_conjecture,
p12(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),c22) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(f0,negated_conjecture,
p12(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_1) ).
fof(f0_nnf,plain,
! [X0] : p12(X0,X0),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X0] : p12(X0,X0),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
p12(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
p12(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h0,plain,
p12(c22,f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17))) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi22,hi0]) ).
cnf(f14,negated_conjecture,
( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15_15) ).
fof(f14_nnf,plain,
! [X11,X12,X13,X14] :
( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X11,X12,X13,X14] :
( ~ p12(X13,X11)
| ~ p3(X14,X12)
| ~ p15(X13,X14)
| p15(X11,X12) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( ~ p12(X2,X0)
| ~ p3(X3,X1)
| ~ p15(X2,X3)
| p15(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,negated_conjecture,
ifeq(p15(X0,X1),true,ifeq(p3(X1,X2),true,ifeq(p12(X0,X3),true,p15(X3,X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(f20,negated_conjecture,
p15(c22,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15_21) ).
fof(f20_nnf,plain,
p15(c22,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))),
inference(nnf_transformation,[status(thm)],[f20]) ).
cnf(c20,plain,
p15(c22,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))),
inference(cnf_transformation,[status(esa)],[f20_nnf]) ).
cnf(hi20,negated_conjecture,
p15(c22,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(f3,negated_conjecture,
p3(X26,X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_4) ).
fof(f3_nnf,plain,
! [X26] : p3(X26,X26),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X26] : p3(X26,X26),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
p3(X0,X0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,negated_conjecture,
p3(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t105,plain,
p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi20,hi3,h0]) ).
cnf(t979,plain,
p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))) = true,
inference(orient,[status(thm)],[t105]) ).
cnf(t6,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t107,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(f23,negated_conjecture,
( ~ p15(X49,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p16(c22,X49)
| ~ p16(X49,c17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p16_24) ).
fof(f23_nnf,plain,
! [X49] :
( ~ p15(X49,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p16(c22,X49)
| ~ p16(X49,c17) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [X49] :
( ~ p15(X49,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p16(c22,X49)
| ~ p16(X49,c17) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( ~ p15(X0,f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))
| ~ p16(c22,X0)
| ~ p16(X0,c17) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(f24,negated_conjecture,
~ p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p15_25) ).
fof(f24_nnf,plain,
~ p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
~ p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
~ p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c24]) ).
cnf(g0_0,plain,
true != ifeq(p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))),true,false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))))),true,false,p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))),
inference(rw,[status(thm)],[g0_0,t979]) ).
cnf(g0_2,plain,
true != ifeq(true,true,false,p15(f13(c17,f14(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20))))),c17)),f4(f7(c18,f8(f9(c19,f10(f11(c20))),f9(c21,f10(f11(c20)))))))),
inference(rw,[status(thm)],[g0_1,t979]) ).
cnf(g0_3,plain,
true != false,
inference(rw,[status(thm)],[g0_2,t107]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN584-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.38 % Computer : n018.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Fri Sep 25 01:50:10 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.34/6.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.34/6.46 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------