%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN074-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 03:33:43 PM UTC 2026
% Result : Unsatisfiable 6.10s 16.88s
% Output : Proof 6.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 65 ( 10 unt; 0 def)
% Number of atoms : 143 ( 93 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 129 ( 51 ~; 78 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 71 ( 4 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f9,negated_conjecture,
( h(X,Z) = Z
| big_f(f(X),h(X,Z))
| f(X) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_10) ).
fof(f9_nnf,plain,
! [X,Z] :
( h(X,Z) = Z
| big_f(f(X),h(X,Z))
| f(X) != X ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Z] :
( h(X,Z) = Z
| big_f(f(X),h(X,Z))
| f(X) != X ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( h(X0,X1) = X1
| big_f(f(X0),h(X0,X1))
| f(X0) != X0 ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(f0,axiom,
( X = a
| ~ big_f(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
fof(f0_nnf,plain,
! [X,Y] :
( X = a
| ~ big_f(X,Y) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( X = a
| ~ big_f(X,Y) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( X0 = a
| ~ big_f(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(f7,negated_conjecture,
( f(X) = X
| big_f(f(X),Y)
| Y != g(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8) ).
fof(f7_nnf,plain,
! [Y,X] :
( f(X) = X
| big_f(f(X),Y)
| Y != g(X) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [Y,X] :
( f(X) = X
| big_f(f(X),Y)
| Y != g(X) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( f(X1) = X1
| big_f(f(X1),X0)
| X0 != g(X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p13,plain,
( f(X0) = X0
| big_f(f(X0),g(X0)) ),
inference(equality_resolution,[status(thm)],[c7]) ).
cnf(p14,plain,
( f(X0) = X0
| f(X0) = a ),
inference(resolution,[status(thm)],[c0,p13]) ).
cnf(p15,plain,
f(a) = a,
inference(factoring,[status(thm)],[p14]) ).
cnf(p195,plain,
( h(a,X0) = X0
| big_f(a,h(a,X0)) ),
inference(resolution,[status(thm)],[c9,p15]) ).
cnf(f1,axiom,
( Y = b
| ~ big_f(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
fof(f1_nnf,plain,
! [X,Y] :
( Y = b
| ~ big_f(X,Y) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( Y = b
| ~ big_f(X,Y) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( X1 = b
| ~ big_f(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p215,plain,
( h(a,X0) = b
| h(a,X0) = X0 ),
inference(resolution,[status(thm)],[p195,c1]) ).
cnf(p222,plain,
( X0 != b
| h(a,X0) = X0 ),
inference(equality_factoring,[status(thm)],[p215]) ).
cnf(p232,plain,
( f(b) = a
| h(a,f(b)) = f(b) ),
inference(resolution,[status(thm)],[p222,p14]) ).
cnf(f10,negated_conjecture,
( ~ big_f(f(X),h(X,Z))
| h(X,Z) != Z
| f(X) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_11) ).
fof(f10_nnf,plain,
! [X,Z] :
( ~ big_f(f(X),h(X,Z))
| h(X,Z) != Z
| f(X) != X ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Z] :
( ~ big_f(f(X),h(X,Z))
| h(X,Z) != Z
| f(X) != X ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( ~ big_f(f(X0),h(X0,X1))
| h(X0,X1) != X1
| f(X0) != X0 ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p246,plain,
( ~ big_f(a,h(a,X0))
| h(a,X0) != X0 ),
inference(resolution,[status(thm)],[c10,p15]) ).
cnf(p348,plain,
( ~ big_f(a,h(a,f(b)))
| f(b) = a ),
inference(resolution,[status(thm)],[p232,p246]) ).
cnf(p352,plain,
( ~ big_f(a,f(b))
| f(b) = a
| f(b) = a ),
inference(superposition,[status(thm)],[p232,p348]) ).
cnf(p1075,plain,
( ~ big_f(a,f(b))
| f(b) = a ),
inference(factoring,[status(thm)],[p352]) ).
cnf(f2,axiom,
( big_f(X,Y)
| Y != b
| X != a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
fof(f2_nnf,plain,
! [X,Y] :
( big_f(X,Y)
| Y != b
| X != a ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] :
( big_f(X,Y)
| Y != b
| X != a ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( big_f(X0,X1)
| X1 != b
| X0 != a ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p34,plain,
( big_f(a,X0)
| X0 != b ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p543,plain,
( f(b) = a
| big_f(a,f(b)) ),
inference(resolution,[status(thm)],[p34,p14]) ).
cnf(p1076,plain,
( f(b) = a
| f(b) = a ),
inference(resolution,[status(thm)],[p1075,p543]) ).
cnf(p1080,plain,
f(b) = a,
inference(factoring,[status(thm)],[p1076]) ).
cnf(p24,plain,
( f(X0) = X0
| g(X0) = b ),
inference(resolution,[status(thm)],[c1,p13]) ).
cnf(p27,plain,
( f(X0) = X0
| big_f(f(X0),b)
| f(X0) = X0 ),
inference(superposition,[status(thm)],[p24,p13]) ).
cnf(p30,plain,
( big_f(f(X0),b)
| f(X0) = X0 ),
inference(factoring,[status(thm)],[p27]) ).
cnf(f3,negated_conjecture,
( f(X) = X
| Y = g(X)
| ~ big_f(f(X),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
fof(f3_nnf,plain,
! [X,Y] :
( f(X) = X
| Y = g(X)
| ~ big_f(f(X),Y) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] :
( f(X) = X
| Y = g(X)
| ~ big_f(f(X),Y) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( f(X0) = X0
| X1 = g(X0)
| ~ big_f(f(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p31,plain,
( f(X0) = X0
| b = g(X0)
| f(X0) = X0 ),
inference(resolution,[status(thm)],[p30,c3]) ).
cnf(p58,plain,
( b = g(X0)
| f(X0) = X0 ),
inference(factoring,[status(thm)],[p31]) ).
cnf(p548,plain,
( b = g(b)
| big_f(a,f(b)) ),
inference(resolution,[status(thm)],[p34,p58]) ).
cnf(p1168,plain,
( b = g(b)
| big_f(a,a) ),
inference(demodulation,[status(thm)],[p1080,p548]) ).
cnf(p223,plain,
( b != X0
| h(a,X0) = b ),
inference(equality_factoring,[status(thm)],[p215]) ).
cnf(p1443,plain,
( h(a,g(b)) = b
| big_f(a,a) ),
inference(resolution,[status(thm)],[p1168,p223]) ).
cnf(p1693,plain,
( big_f(a,h(a,g(b)))
| big_f(a,a) ),
inference(resolution,[status(thm)],[p1443,p34]) ).
cnf(p233,plain,
( f(X0) = X0
| h(a,g(X0)) = g(X0) ),
inference(resolution,[status(thm)],[p222,p24]) ).
cnf(p357,plain,
( ~ big_f(a,h(a,g(X0)))
| f(X0) = X0 ),
inference(resolution,[status(thm)],[p233,p246]) ).
cnf(p1737,plain,
( a = b
| big_f(a,a) ),
inference(resolution,[status(thm)],[p1693,p357]) ).
cnf(p1739,plain,
( a = b
| a = b ),
inference(resolution,[status(thm)],[p1737,c1]) ).
cnf(p1784,plain,
a = b,
inference(factoring,[status(thm)],[p1739]) ).
cnf(p221,plain,
h(a,b) = b,
inference(factoring,[status(thm)],[p215]) ).
cnf(p1807,plain,
b = a,
inference(superposition,[status(thm)],[p1784,p221]) ).
cnf(p542,plain,
big_f(a,b),
inference(equality_resolution,[status(thm)],[p34]) ).
cnf(p1856,plain,
big_f(a,a),
inference(demodulation,[status(thm)],[p1807,p542]) ).
cnf(p283,plain,
~ big_f(a,b),
inference(resolution,[status(thm)],[p246,p221]) ).
cnf(p1840,plain,
~ big_f(a,a),
inference(demodulation,[status(thm)],[p1807,p283]) ).
cnf(p2059,plain,
$false,
inference(resolution,[status(thm)],[p1856,p1840]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN074-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/15.43 % CPULimit : 300
% 0.08/15.44 % WCLimit : 300
% 0.08/15.44 % DateTime : Fri Sep 25 00:05:46 UTC 2026
% 0.08/15.44 % CPUTime :
% 0.08/15.44 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.10/16.88 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.10/16.88 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------