%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN015-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 03:33:20 PM UTC 2026
% Result : Unsatisfiable 8.13s 1.57s
% Output : Proof 8.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 14
% Syntax : Number of formulae : 92 ( 18 unt; 0 def)
% Number of atoms : 290 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 277 ( 79 ~; 198 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 71 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f9,negated_conjecture,
( equalish(A,m)
| ~ element(A,m)
| element(A,f(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_7) ).
fof(f9_nnf,plain,
! [A] :
( equalish(A,m)
| ~ element(A,m)
| element(A,f(A)) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A] :
( equalish(A,m)
| ~ element(A,m)
| element(A,f(A)) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( equalish(X0,m)
| ~ element(X0,m)
| element(X0,f(X0)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(f3,axiom,
( element(C,B)
| ~ element(C,A)
| ~ equalish(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_substitutionish1) ).
fof(f3_nnf,plain,
! [A,B,C] :
( element(C,B)
| ~ element(C,A)
| ~ equalish(A,B) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C] :
( element(C,B)
| ~ element(C,A)
| ~ equalish(A,B) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( element(X2,X1)
| ~ element(X2,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(f1,axiom,
( equalish(Y,X)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetryish) ).
fof(f1_nnf,plain,
! [X,Y] :
( equalish(Y,X)
| ~ equalish(X,Y) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( equalish(Y,X)
| ~ equalish(X,Y) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(f25,negated_conjecture,
equalish(m,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_23) ).
fof(f25_nnf,plain,
equalish(m,k),
inference(nnf_transformation,[status(thm)],[f25]) ).
cnf(c25,plain,
equalish(m,k),
inference(cnf_transformation,[status(esa)],[f25_nnf]) ).
cnf(p28,plain,
equalish(k,m),
inference(resolution,[status(thm)],[c1,c25]) ).
cnf(p33,plain,
( element(X0,m)
| ~ element(X0,k) ),
inference(resolution,[status(thm)],[c3,p28]) ).
cnf(f18,negated_conjecture,
( equalish(A,k)
| element(A,k)
| ~ equalish(A,n) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_16) ).
fof(f18_nnf,plain,
! [A] :
( equalish(A,k)
| element(A,k)
| ~ equalish(A,n) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A] :
( equalish(A,k)
| element(A,k)
| ~ equalish(A,n) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( equalish(X0,k)
| element(X0,k)
| ~ equalish(X0,n) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(f0,axiom,
equalish(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivityish) ).
fof(f0_nnf,plain,
! [X] : equalish(X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : equalish(X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
equalish(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p31,plain,
( equalish(n,k)
| element(n,k) ),
inference(resolution,[status(thm)],[c18,c0]) ).
cnf(p34,plain,
( equalish(n,k)
| element(n,m) ),
inference(resolution,[status(thm)],[p33,p31]) ).
cnf(p43,plain,
( equalish(n,k)
| equalish(n,m)
| element(n,f(n)) ),
inference(resolution,[status(thm)],[c9,p34]) ).
cnf(f11,negated_conjecture,
( equalish(B,m)
| element(B,m)
| equalish(A,m)
| equalish(A,B)
| ~ element(B,A)
| ~ element(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_9) ).
fof(f11_nnf,plain,
! [A,B] :
( equalish(B,m)
| element(B,m)
| equalish(A,m)
| equalish(A,B)
| ~ element(B,A)
| ~ element(A,B) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B] :
( equalish(B,m)
| element(B,m)
| equalish(A,m)
| equalish(A,B)
| ~ element(B,A)
| ~ element(A,B) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( equalish(X1,m)
| element(X1,m)
| equalish(X0,m)
| equalish(X0,X1)
| ~ element(X1,X0)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p55,plain,
( equalish(f(n),m)
| element(f(n),m)
| equalish(n,m)
| equalish(n,f(n))
| ~ element(f(n),n)
| equalish(n,k)
| equalish(n,m) ),
inference(resolution,[status(thm)],[p43,c11]) ).
cnf(p131,plain,
( equalish(f(n),m)
| element(f(n),m)
| equalish(n,f(n))
| ~ element(f(n),n)
| equalish(n,k)
| equalish(n,m) ),
inference(factoring,[status(thm)],[p55]) ).
cnf(f10,negated_conjecture,
( equalish(A,m)
| ~ element(A,m)
| element(f(A),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_8) ).
fof(f10_nnf,plain,
! [A] :
( equalish(A,m)
| ~ element(A,m)
| element(f(A),A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A] :
( equalish(A,m)
| ~ element(A,m)
| element(f(A),A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( equalish(X0,m)
| ~ element(X0,m)
| element(f(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p44,plain,
( equalish(n,k)
| equalish(n,m)
| element(f(n),n) ),
inference(resolution,[status(thm)],[c10,p34]) ).
cnf(p300,plain,
( equalish(n,k)
| equalish(n,m)
| equalish(f(n),m)
| element(f(n),m)
| equalish(n,f(n))
| equalish(n,k)
| equalish(n,m) ),
inference(resolution,[status(thm)],[p131,p44]) ).
cnf(p486,plain,
( equalish(n,k)
| equalish(f(n),m)
| element(f(n),m)
| equalish(n,f(n))
| equalish(n,k)
| equalish(n,m) ),
inference(factoring,[status(thm)],[p300]) ).
cnf(p528,plain,
( equalish(f(n),m)
| element(f(n),m)
| equalish(n,f(n))
| equalish(n,k)
| equalish(n,m) ),
inference(factoring,[status(thm)],[p486]) ).
cnf(p32,plain,
( element(X0,k)
| ~ element(X0,m) ),
inference(resolution,[status(thm)],[c3,c25]) ).
cnf(p534,plain,
( element(f(n),k)
| equalish(f(n),m)
| equalish(n,f(n))
| equalish(n,k)
| equalish(n,m) ),
inference(resolution,[status(thm)],[p528,p32]) ).
cnf(f19,negated_conjecture,
( equalish(A,k)
| equalish(A,m)
| equalish(A,n)
| ~ element(A,k) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_17) ).
fof(f19_nnf,plain,
! [A] :
( equalish(A,k)
| equalish(A,m)
| equalish(A,n)
| ~ element(A,k) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A] :
( equalish(A,k)
| equalish(A,m)
| equalish(A,n)
| ~ element(A,k) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( equalish(X0,k)
| equalish(X0,m)
| equalish(X0,n)
| ~ element(X0,k) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p542,plain,
( equalish(f(n),k)
| equalish(f(n),m)
| equalish(f(n),n)
| equalish(f(n),m)
| equalish(n,f(n))
| equalish(n,k)
| equalish(n,m) ),
inference(resolution,[status(thm)],[p534,c19]) ).
cnf(p693,plain,
( equalish(f(n),k)
| equalish(f(n),n)
| equalish(f(n),m)
| equalish(n,f(n))
| equalish(n,k)
| equalish(n,m) ),
inference(factoring,[status(thm)],[p542]) ).
cnf(p828,plain,
( equalish(n,f(n))
| equalish(f(n),k)
| equalish(f(n),m)
| equalish(n,f(n))
| equalish(n,k)
| equalish(n,m) ),
inference(resolution,[status(thm)],[p693,c1]) ).
cnf(p859,plain,
( equalish(f(n),k)
| equalish(f(n),m)
| equalish(n,f(n))
| equalish(n,k)
| equalish(n,m) ),
inference(factoring,[status(thm)],[p828]) ).
cnf(f7,negated_conjecture,
( equalish(A,m)
| ~ element(A,m)
| ~ equalish(f(A),m) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_5) ).
fof(f7_nnf,plain,
! [A] :
( equalish(A,m)
| ~ element(A,m)
| ~ equalish(f(A),m) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A] :
( equalish(A,m)
| ~ element(A,m)
| ~ equalish(f(A),m) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( equalish(X0,m)
| ~ element(X0,m)
| ~ equalish(f(X0),m) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p865,plain,
( equalish(n,m)
| ~ element(n,m)
| equalish(f(n),k)
| equalish(n,f(n))
| equalish(n,k)
| equalish(n,m) ),
inference(resolution,[status(thm)],[p859,c7]) ).
cnf(p892,plain,
( ~ element(n,m)
| equalish(f(n),k)
| equalish(n,f(n))
| equalish(n,k)
| equalish(n,m) ),
inference(factoring,[status(thm)],[p865]) ).
cnf(p893,plain,
( equalish(n,k)
| equalish(f(n),k)
| equalish(n,f(n))
| equalish(n,k)
| equalish(n,m) ),
inference(resolution,[status(thm)],[p892,p34]) ).
cnf(p894,plain,
( equalish(f(n),k)
| equalish(n,f(n))
| equalish(n,k)
| equalish(n,m) ),
inference(factoring,[status(thm)],[p893]) ).
cnf(p896,plain,
( equalish(k,f(n))
| equalish(n,f(n))
| equalish(n,k)
| equalish(n,m) ),
inference(resolution,[status(thm)],[p894,c1]) ).
cnf(p906,plain,
( equalish(f(n),n)
| equalish(k,f(n))
| equalish(n,k)
| equalish(n,m) ),
inference(resolution,[status(thm)],[p896,c1]) ).
cnf(f8,negated_conjecture,
( equalish(A,m)
| ~ element(A,m)
| ~ equalish(f(A),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_6) ).
fof(f8_nnf,plain,
! [A] :
( equalish(A,m)
| ~ element(A,m)
| ~ equalish(f(A),A) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A] :
( equalish(A,m)
| ~ element(A,m)
| ~ equalish(f(A),A) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( equalish(X0,m)
| ~ element(X0,m)
| ~ equalish(f(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p917,plain,
( equalish(n,m)
| ~ element(n,m)
| equalish(k,f(n))
| equalish(n,k)
| equalish(n,m) ),
inference(resolution,[status(thm)],[p906,c8]) ).
cnf(p919,plain,
( ~ element(n,m)
| equalish(k,f(n))
| equalish(n,k)
| equalish(n,m) ),
inference(factoring,[status(thm)],[p917]) ).
cnf(p920,plain,
( equalish(n,k)
| equalish(k,f(n))
| equalish(n,k)
| equalish(n,m) ),
inference(resolution,[status(thm)],[p919,p34]) ).
cnf(p922,plain,
( equalish(k,f(n))
| equalish(n,k)
| equalish(n,m) ),
inference(factoring,[status(thm)],[p920]) ).
cnf(f2,axiom,
( equalish(X,Z)
| ~ equalish(Y,Z)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivityish) ).
fof(f2_nnf,plain,
! [X,Y,Z] :
( equalish(X,Z)
| ~ equalish(Y,Z)
| ~ equalish(X,Y) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z] :
( equalish(X,Z)
| ~ equalish(Y,Z)
| ~ equalish(X,Y) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p29,plain,
( equalish(m,X0)
| ~ equalish(k,X0) ),
inference(resolution,[status(thm)],[c2,c25]) ).
cnf(p925,plain,
( equalish(m,f(n))
| equalish(n,k)
| equalish(n,m) ),
inference(resolution,[status(thm)],[p922,p29]) ).
cnf(p945,plain,
( equalish(f(n),m)
| equalish(n,k)
| equalish(n,m) ),
inference(resolution,[status(thm)],[p925,c1]) ).
cnf(p956,plain,
( equalish(n,m)
| ~ element(n,m)
| equalish(n,k)
| equalish(n,m) ),
inference(resolution,[status(thm)],[p945,c7]) ).
cnf(p958,plain,
( ~ element(n,m)
| equalish(n,k)
| equalish(n,m) ),
inference(factoring,[status(thm)],[p956]) ).
cnf(p959,plain,
( equalish(n,k)
| equalish(n,k)
| equalish(n,m) ),
inference(resolution,[status(thm)],[p958,p34]) ).
cnf(p960,plain,
( equalish(n,k)
| equalish(n,m) ),
inference(factoring,[status(thm)],[p959]) ).
cnf(p966,plain,
( equalish(m,n)
| equalish(n,k) ),
inference(resolution,[status(thm)],[p960,c1]) ).
cnf(f22,negated_conjecture,
~ equalish(n,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_20) ).
fof(f22_nnf,plain,
~ equalish(n,k),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
~ equalish(n,k),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
~ equalish(n,k),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p973,plain,
equalish(m,n),
inference(resolution,[status(thm)],[p966,c22]) ).
cnf(f21,negated_conjecture,
~ equalish(m,n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_19) ).
fof(f21_nnf,plain,
~ equalish(m,n),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
~ equalish(m,n),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
~ equalish(m,n),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p974,plain,
$false,
inference(resolution,[status(thm)],[p973,c21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN015-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.06/0.33 % Computer : n008.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Thu Sep 24 23:52:09 UTC 2026
% 0.06/0.34 % CPUTime :
% 0.06/0.34 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.13/1.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.13/1.57 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------