%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU045+1 : TPTP v9.3.1. Released v3.2.0.
% 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 02:50:52 PM UTC 2026
% Result : Theorem 67.00s 9.05s
% Output : Proof 67.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 9 unt; 0 def)
% Number of atoms : 131 ( 24 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 162 ( 62 ~; 57 |; 32 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 59 ( 6 sgn 32 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f33,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_rng_restriction(A,C)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& ! [D] :
( in(D,relation_dom(B))
<=> ( in(apply(C,D),A)
& in(D,relation_dom(C)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_1) ).
fof(f33_nnf,plain,
! [A,B] :
( ! [C] :
( ( ( ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| ? [D] :
( ( in(apply(C,D),A)
& in(D,relation_dom(C))
& ~ in(D,relation_dom(B)) )
| ( ( ~ in(apply(C,D),A)
| ~ in(D,relation_dom(C)) )
& in(D,relation_dom(B)) ) )
| B = relation_rng_restriction(A,C) )
& ( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& ! [D] :
( ( ~ in(apply(C,D),A)
| ~ in(D,relation_dom(C))
| in(D,relation_dom(B)) )
& ( ( in(apply(C,D),A)
& in(D,relation_dom(C)) )
| ~ in(D,relation_dom(B)) ) ) )
| B != relation_rng_restriction(A,C) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [B,C,A,D] :
( ( ( ( apply(B,sk15(A,B,C)) != apply(C,sk15(A,B,C))
& in(sk15(A,B,C),relation_dom(B)) )
| ( in(apply(C,sk14(A,B,C)),A)
& in(sk14(A,B,C),relation_dom(C))
& ~ in(sk14(A,B,C),relation_dom(B)) )
| ( ( ~ in(apply(C,sk14(A,B,C)),A)
| ~ in(sk14(A,B,C),relation_dom(C)) )
& in(sk14(A,B,C),relation_dom(B)) )
| B = relation_rng_restriction(A,C) )
& ( ( ( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& ( ~ in(apply(C,D),A)
| ~ in(D,relation_dom(C))
| in(D,relation_dom(B)) )
& ( ( in(apply(C,D),A)
& in(D,relation_dom(C)) )
| ~ in(D,relation_dom(B)) ) )
| B != relation_rng_restriction(A,C) ) )
| ~ function(C)
| ~ relation(C)
| ~ function(B)
| ~ relation(B) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk14,sk15])],[f33_nnf]) ).
cnf(c57,plain,
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1))
| X1 != relation_rng_restriction(X0,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(p305,plain,
( apply(relation_rng_restriction(X0,X1),X2) = apply(X1,X2)
| ~ in(X2,relation_dom(relation_rng_restriction(X0,X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1)) ),
inference(equality_resolution,[status(thm)],[c57]) ).
fof(f18,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f18_nnf,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [B,A] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c25,plain,
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f32,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_rng_restriction(A,C)))
=> apply(relation_rng_restriction(A,C),B) = apply(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_funct_1) ).
fof(f32_neg,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_rng_restriction(A,C)))
=> apply(relation_rng_restriction(A,C),B) = apply(C,B) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f32_nnf,plain,
? [A,B,C] :
( apply(relation_rng_restriction(A,C),B) != apply(C,B)
& in(B,relation_dom(relation_rng_restriction(A,C)))
& function(C)
& relation(C) ),
inference(nnf_transformation,[status(thm)],[f32_neg]) ).
fof(f32_sk,plain,
( apply(relation_rng_restriction(sk11,sk13),sk12) != apply(sk13,sk12)
& in(sk12,relation_dom(relation_rng_restriction(sk11,sk13)))
& function(sk13)
& relation(sk13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11,sk12,sk13])],[f32_nnf]) ).
cnf(c50,plain,
relation(sk13),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p159,plain,
relation(relation_rng_restriction(X0,sk13)),
inference(resolution,[status(thm)],[c25,c50]) ).
cnf(p5035,plain,
( apply(relation_rng_restriction(X0,sk13),X1) = apply(sk13,X1)
| ~ in(X1,relation_dom(relation_rng_restriction(X0,sk13)))
| ~ function(sk13)
| ~ relation(sk13)
| ~ function(relation_rng_restriction(X0,sk13)) ),
inference(resolution,[status(thm)],[p305,p159]) ).
fof(f19,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(f19_nnf,plain,
! [A,B] :
( ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) )
| ~ function(B)
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [B,A] :
( ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) )
| ~ function(B)
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c27,plain,
( function(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p181,plain,
( function(relation_rng_restriction(X0,sk13))
| ~ function(sk13) ),
inference(resolution,[status(thm)],[c27,c50]) ).
cnf(c51,plain,
function(sk13),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p193,plain,
function(relation_rng_restriction(X0,sk13)),
inference(resolution,[status(thm)],[p181,c51]) ).
cnf(p12696,plain,
( apply(relation_rng_restriction(X1,sk13),X0) = apply(sk13,X0)
| ~ in(X0,relation_dom(relation_rng_restriction(X1,sk13)))
| ~ function(sk13)
| ~ relation(sk13) ),
inference(resolution,[status(thm)],[p5035,p193]) ).
cnf(p12697,plain,
( apply(relation_rng_restriction(X1,sk13),X0) = apply(sk13,X0)
| ~ in(X0,relation_dom(relation_rng_restriction(X1,sk13)))
| ~ function(sk13) ),
inference(resolution,[status(thm)],[p12696,c50]) ).
cnf(p12698,plain,
( apply(relation_rng_restriction(X1,sk13),X0) = apply(sk13,X0)
| ~ in(X0,relation_dom(relation_rng_restriction(X1,sk13))) ),
inference(resolution,[status(thm)],[p12697,c51]) ).
cnf(c52,plain,
in(sk12,relation_dom(relation_rng_restriction(sk11,sk13))),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p12699,plain,
apply(relation_rng_restriction(sk11,sk13),sk12) = apply(sk13,sk12),
inference(resolution,[status(thm)],[p12698,c52]) ).
cnf(c53,plain,
apply(relation_rng_restriction(sk11,sk13),sk12) != apply(sk13,sk12),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p12700,plain,
apply(sk13,sk12) != apply(sk13,sk12),
inference(demodulation,[status(thm)],[p12699,c53]) ).
cnf(p12740,plain,
$false,
inference(equality_resolution,[status(thm)],[p12700]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU045+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 12:37:50 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 67.00/9.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 67.00/9.05 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------