%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN038-1 : TPTP v9.3.1. Released v1.0.0.
% 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 03:33:32 PM UTC 2026
% Result : Unsatisfiable 4.30s 1.13s
% Output : Proof 4.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 5 unt; 0 def)
% Number of atoms : 109 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 104 ( 43 ~; 61 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 94 ( 3 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1,negated_conjecture,
( p(X,f(X,Y))
| ~ q(Y,f(X,Y))
| ~ p(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
fof(f1_nnf,plain,
! [X,Y] :
( p(X,f(X,Y))
| ~ q(Y,f(X,Y))
| ~ p(X,Y) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( p(X,f(X,Y))
| ~ q(Y,f(X,Y))
| ~ p(X,Y) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( p(X0,f(X0,X1))
| ~ q(X1,f(X0,X1))
| ~ p(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(f3,negated_conjecture,
( p(f(X,Y),f(X,Y))
| p(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
fof(f3_nnf,plain,
! [X,Y] :
( p(f(X,Y),f(X,Y))
| p(X,Y) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] :
( p(f(X,Y),f(X,Y))
| p(X,Y) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( p(f(X0,X1),f(X0,X1))
| p(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p9,plain,
( p(X0,X1)
| p(f(X0,X1),f(f(X0,X1),f(X0,X1)))
| ~ q(f(X0,X1),f(f(X0,X1),f(X0,X1))) ),
inference(resolution,[status(thm)],[c1,c3]) ).
cnf(f5,negated_conjecture,
( q(f(X,Y),f(X,Y))
| q(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
fof(f5_nnf,plain,
! [X,Y] :
( q(f(X,Y),f(X,Y))
| q(X,Y) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] :
( q(f(X,Y),f(X,Y))
| q(X,Y) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( q(f(X0,X1),f(X0,X1))
| q(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f4,negated_conjecture,
( ~ q(f(X,Y),f(X,Y))
| p(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
fof(f4_nnf,plain,
! [X,Y] :
( ~ q(f(X,Y),f(X,Y))
| p(X,Y) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] :
( ~ q(f(X,Y),f(X,Y))
| p(X,Y) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( ~ q(f(X0,X1),f(X0,X1))
| p(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p7,plain,
( p(X0,X1)
| q(X0,X1) ),
inference(resolution,[status(thm)],[c5,c4]) ).
cnf(p12,plain,
( p(f(X0,X1),f(f(X0,X1),f(X0,X1)))
| p(X0,X1)
| p(f(X0,X1),f(f(X0,X1),f(X0,X1))) ),
inference(resolution,[status(thm)],[p9,p7]) ).
cnf(p15,plain,
( p(X0,X1)
| p(f(X0,X1),f(f(X0,X1),f(X0,X1))) ),
inference(factoring,[status(thm)],[p12]) ).
cnf(f2,negated_conjecture,
( q(f(X,Y),f(X,Y))
| ~ p(f(X,Y),f(X,Y))
| ~ p(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
fof(f2_nnf,plain,
! [X,Y] :
( q(f(X,Y),f(X,Y))
| ~ p(f(X,Y),f(X,Y))
| ~ p(X,Y) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] :
( q(f(X,Y),f(X,Y))
| ~ p(f(X,Y),f(X,Y))
| ~ p(X,Y) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( q(f(X0,X1),f(X0,X1))
| ~ p(f(X0,X1),f(X0,X1))
| ~ p(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p18,plain,
( q(f(f(X0,X1),f(f(X0,X1),f(X0,X1))),f(f(X0,X1),f(f(X0,X1),f(X0,X1))))
| ~ p(f(f(X0,X1),f(f(X0,X1),f(X0,X1))),f(f(X0,X1),f(f(X0,X1),f(X0,X1))))
| p(X0,X1) ),
inference(resolution,[status(thm)],[p15,c2]) ).
cnf(f0,negated_conjecture,
( q(Y,f(X,Y))
| ~ p(X,Y)
| ~ p(X,f(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
fof(f0_nnf,plain,
! [X,Y] :
( q(Y,f(X,Y))
| ~ p(X,Y)
| ~ p(X,f(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( q(Y,f(X,Y))
| ~ p(X,Y)
| ~ p(X,f(X,Y)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( q(X1,f(X0,X1))
| ~ p(X0,X1)
| ~ p(X0,f(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p16,plain,
( q(f(X0,X1),f(f(X0,X1),f(X0,X1)))
| ~ p(f(X0,X1),f(X0,X1))
| p(X0,X1) ),
inference(resolution,[status(thm)],[p15,c0]) ).
cnf(p19,plain,
( p(X0,X1)
| q(f(X0,X1),f(f(X0,X1),f(X0,X1)))
| p(X0,X1) ),
inference(resolution,[status(thm)],[p16,c3]) ).
cnf(p21,plain,
( q(f(X0,X1),f(f(X0,X1),f(X0,X1)))
| p(X0,X1) ),
inference(factoring,[status(thm)],[p19]) ).
cnf(f6,negated_conjecture,
( ~ q(f(X,Y),f(X,Y))
| ~ q(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
fof(f6_nnf,plain,
! [X,Y] :
( ~ q(f(X,Y),f(X,Y))
| ~ q(X,Y) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( ~ q(f(X,Y),f(X,Y))
| ~ q(X,Y) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ q(f(X0,X1),f(X0,X1))
| ~ q(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p22,plain,
( ~ q(f(f(X0,X1),f(f(X0,X1),f(X0,X1))),f(f(X0,X1),f(f(X0,X1),f(X0,X1))))
| p(X0,X1) ),
inference(resolution,[status(thm)],[p21,c6]) ).
cnf(p23,plain,
( p(f(f(X0,X1),f(f(X0,X1),f(X0,X1))),f(f(X0,X1),f(f(X0,X1),f(X0,X1))))
| p(X0,X1) ),
inference(resolution,[status(thm)],[p22,p7]) ).
cnf(p30,plain,
( p(X0,X1)
| q(f(f(X0,X1),f(f(X0,X1),f(X0,X1))),f(f(X0,X1),f(f(X0,X1),f(X0,X1))))
| p(X0,X1) ),
inference(resolution,[status(thm)],[p18,p23]) ).
cnf(p31,plain,
( q(f(f(X0,X1),f(f(X0,X1),f(X0,X1))),f(f(X0,X1),f(f(X0,X1),f(X0,X1))))
| p(X0,X1) ),
inference(factoring,[status(thm)],[p30]) ).
cnf(p33,plain,
( p(X0,X1)
| p(X0,X1) ),
inference(resolution,[status(thm)],[p31,p22]) ).
cnf(p34,plain,
p(X0,X1),
inference(factoring,[status(thm)],[p33]) ).
cnf(p35,plain,
( q(X1,f(X0,X1))
| ~ p(X0,X1) ),
inference(resolution,[status(thm)],[p34,c0]) ).
cnf(p37,plain,
q(X0,f(X1,X0)),
inference(resolution,[status(thm)],[p35,p34]) ).
cnf(p39,plain,
~ q(f(X0,f(X1,X0)),f(X0,f(X1,X0))),
inference(resolution,[status(thm)],[p37,c6]) ).
cnf(p36,plain,
( q(f(X0,X1),f(X0,X1))
| ~ p(f(X0,X1),f(X0,X1)) ),
inference(resolution,[status(thm)],[p34,c2]) ).
cnf(p38,plain,
q(f(X0,X1),f(X0,X1)),
inference(resolution,[status(thm)],[p36,p34]) ).
cnf(p41,plain,
$false,
inference(resolution,[status(thm)],[p39,p38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN038-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n004.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 : Thu Sep 24 23:55:22 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.30/1.13 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.30/1.13 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------