%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN553-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 03:35:11 PM UTC 2026
% Result : Unsatisfiable 10.89s 2.11s
% Output : Proof 10.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 43 unt; 0 def)
% Number of atoms : 67 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 30 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 86 ( 2 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f8,negated_conjecture,
~ p2(f8(f8(f9(c4),c4),f9(c3)),f8(f9(c4),f8(f9(c3),c4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_9) ).
fof(f8_nnf,plain,
~ p2(f8(f8(f9(c4),c4),f9(c3)),f8(f9(c4),f8(f9(c3),c4))),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ p2(f8(f8(f9(c4),c4),f9(c3)),f8(f9(c4),f8(f9(c3),c4))),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ p2(f8(f8(f9(c4),c4),f9(c3)),f8(f9(c4),f8(f9(c3),c4))),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t142,plain,
ifeq(p2(f8(f8(f9(c4),c4),f9(c3)),f8(f9(c4),f8(f9(c3),c4))),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(f5,negated_conjecture,
( ~ p2(X3,X2)
| ~ p2(X1,X3)
| p2(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_6) ).
fof(f5_nnf,plain,
! [X1,X2,X3] :
( ~ p2(X3,X2)
| ~ p2(X1,X3)
| p2(X1,X2) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X1,X2,X3] :
( ~ p2(X3,X2)
| ~ p2(X1,X3)
| p2(X1,X2) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ p2(X2,X1)
| ~ p2(X0,X2)
| p2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi3,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p2(X1,X2),true,p2(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f6,negated_conjecture,
p2(f8(X8,f8(X9,X10)),f8(f8(X8,X9),X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_7) ).
fof(f6_nnf,plain,
! [X8,X9,X10] : p2(f8(X8,f8(X9,X10)),f8(f8(X8,X9),X10)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X8,X9,X10] : p2(f8(X8,f8(X9,X10)),f8(f8(X8,X9),X10)),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
p2(f8(X0,f8(X1,X2)),f8(f8(X0,X1),X2)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi4,negated_conjecture,
p2(f8(X0,f8(X1,X2)),f8(f8(X0,X1),X2)) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(f4,negated_conjecture,
p2(f8(X11,X12),f8(X12,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_5) ).
fof(f4_nnf,plain,
! [X11,X12] : p2(f8(X11,X12),f8(X12,X11)),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X11,X12] : p2(f8(X11,X12),f8(X12,X11)),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
p2(f8(X0,X1),f8(X1,X0)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi2,negated_conjecture,
p2(f8(X0,X1),f8(X1,X0)) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h34,plain,
p2(f8(V0,f8(V1,V2)),f8(V2,f8(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi4,hi2]) ).
cnf(f7,negated_conjecture,
( ~ p2(X5,X7)
| ~ p2(X4,X6)
| p2(f8(X4,X5),f8(X6,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_8) ).
fof(f7_nnf,plain,
! [X4,X5,X6,X7] :
( ~ p2(X5,X7)
| ~ p2(X4,X6)
| p2(f8(X4,X5),f8(X6,X7)) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X4,X5,X6,X7] :
( ~ p2(X5,X7)
| ~ p2(X4,X6)
| p2(f8(X4,X5),f8(X6,X7)) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ p2(X1,X3)
| ~ p2(X0,X2)
| p2(f8(X0,X1),f8(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi5,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p2(X2,X3),true,p2(f8(X0,X2),f8(X1,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(f0,negated_conjecture,
p2(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_1) ).
fof(f0_nnf,plain,
! [X0] : p2(X0,X0),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X0] : p2(X0,X0),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
p2(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
p2(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h4,plain,
p2(f8(V0,f8(V1,V2)),f8(V0,f8(V2,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi0,hi2]) ).
cnf(h38,plain,
p2(f8(f8(V0,V1),V2),f8(V2,f8(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi2,h4]) ).
cnf(t77,plain,
p2(f8(f8(X1,X2),X3),f8(X1,f8(X3,X2))) = true,
inference(hyper_resolution,[status(thm)],[hi3,h38,h34]) ).
cnf(t191,plain,
p2(f8(f8(X1,X2),X3),f8(X1,f8(X3,X2))) = true,
inference(orient,[status(thm)],[t77]) ).
cnf(t1070,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t142,t191]) ).
cnf(t3,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t143,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t3]) ).
cnf(t1071,plain,
false = true,
inference(step,[status(thm)],[t1070,t143]) ).
cnf(t1069,plain,
false = true,
inference(orient,[status(thm)],[t1071]) ).
cnf(f2,negated_conjecture,
~ p2(c4,f5(f6(c7))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_3) ).
fof(f2_nnf,plain,
~ p2(c4,f5(f6(c7))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ p2(c4,f5(f6(c7))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ p2(c4,f5(f6(c7))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(f3,negated_conjecture,
~ p2(c3,f5(f6(c7))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_4) ).
fof(f3_nnf,plain,
~ p2(c3,f5(f6(c7))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ p2(c3,f5(f6(c7))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
~ p2(c3,f5(f6(c7))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2,c3,c8]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1069]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN553-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.42 % Computer : n004.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 01:43:50 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.89/2.11 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.89/2.11 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------