%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN557-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 8.86s 1.81s
% Output : Proof 8.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 34 unt; 0 def)
% Number of atoms : 54 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 18 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 60 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,negated_conjecture,
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_6) ).
fof(f5_nnf,plain,
! [X4,X5,X3] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X4,X5,X3] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ p2(X2,X1)
| ~ p2(X2,X0)
| p2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi4,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p2(X0,X2),true,p2(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f9,negated_conjecture,
p2(f3(X12,f3(X13,X14)),f3(X13,f3(X12,X14))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_10) ).
fof(f9_nnf,plain,
! [X12,X13,X14] : p2(f3(X12,f3(X13,X14)),f3(X13,f3(X12,X14))),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X12,X13,X14] : p2(f3(X12,f3(X13,X14)),f3(X13,f3(X12,X14))),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
p2(f3(X0,f3(X1,X2)),f3(X1,f3(X0,X2))),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi8,negated_conjecture,
p2(f3(X0,f3(X1,X2)),f3(X1,f3(X0,X2))) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(f3,negated_conjecture,
p2(f3(X10,X11),f3(X11,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_4) ).
fof(f3_nnf,plain,
! [X10,X11] : p2(f3(X10,X11),f3(X11,X10)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X10,X11] : p2(f3(X10,X11),f3(X11,X10)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
p2(f3(X0,X1),f3(X1,X0)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi2,negated_conjecture,
p2(f3(X0,X1),f3(X1,X0)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h2,plain,
p2(f3(c8,f3(f5(c7),f5(c9))),f3(f3(c8,f5(c9)),f5(c7))) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi8,hi2]) ).
cnf(f0,negated_conjecture,
p2(X3,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_1) ).
fof(f0_nnf,plain,
! [X3] : p2(X3,X3),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X3] : p2(X3,X3),
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(h0,plain,
p2(f3(c6,f5(c7)),f3(c6,f5(c7))) = true,
inference(hyper_resolution,[status(thm)],[hi0]) ).
cnf(f11,negated_conjecture,
p2(f3(c6,f5(c7)),f3(c8,f3(f5(c7),f5(c9)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_12) ).
fof(f11_nnf,plain,
p2(f3(c6,f5(c7)),f3(c8,f3(f5(c7),f5(c9)))),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
p2(f3(c6,f5(c7)),f3(c8,f3(f5(c7),f5(c9)))),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(hi10,negated_conjecture,
p2(f3(c6,f5(c7)),f3(c8,f3(f5(c7),f5(c9)))) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h1,plain,
p2(f3(c8,f3(f5(c7),f5(c9))),f3(c6,f5(c7))) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi10,h0]) ).
cnf(h3,plain,
p2(f3(c6,f5(c7)),f3(f3(c8,f5(c9)),f5(c7))) = true,
inference(hyper_resolution,[status(thm)],[hi4,h1,h2]) ).
cnf(f7,negated_conjecture,
( ~ p2(f3(X0,X2),f3(X1,X2))
| p2(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_8) ).
fof(f7_nnf,plain,
! [X0,X1,X2] :
( ~ p2(f3(X0,X2),f3(X1,X2))
| p2(X0,X1) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X0,X1,X2] :
( ~ p2(f3(X0,X2),f3(X1,X2))
| p2(X0,X1) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ p2(f3(X0,X2),f3(X1,X2))
| p2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi6,negated_conjecture,
ifeq(p2(f3(X0,X1),f3(X2,X1)),true,p2(X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t3,plain,
p2(c6,f3(c8,f5(c9))) = true,
inference(hyper_resolution,[status(thm)],[hi6,h3]) ).
cnf(t20,plain,
p2(c6,f3(c8,f5(c9))) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(f2,negated_conjecture,
~ p2(c6,f3(c8,f5(c9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_3) ).
fof(f2_nnf,plain,
~ p2(c6,f3(c8,f5(c9))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ p2(c6,f3(c8,f5(c9))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ p2(c6,f3(c8,f5(c9))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
p2(c6,f3(c8,f5(c9))) != true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t20]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN557-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.44 % Computer : n007.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 01:41:38 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.86/1.81 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.86/1.81 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------