%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU046+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 : n012.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 9.16s 1.52s
% Output : Proof 9.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 8 unt; 0 def)
% Number of atoms : 163 ( 12 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 196 ( 75 ~; 73 |; 36 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 84 ( 13 sgn 45 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f35,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(f35_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)],[f35]) ).
fof(f35_sk,plain,
! [B,C,A,D] :
( ( ( ( apply(B,sk13(A,B,C)) != apply(C,sk13(A,B,C))
& in(sk13(A,B,C),relation_dom(B)) )
| ( in(apply(C,sk12(A,B,C)),A)
& in(sk12(A,B,C),relation_dom(C))
& ~ in(sk12(A,B,C),relation_dom(B)) )
| ( ( ~ in(apply(C,sk12(A,B,C)),A)
| ~ in(sk12(A,B,C),relation_dom(C)) )
& in(sk12(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,[sk12,sk13])],[f35_nnf]) ).
cnf(c56,plain,
( in(X3,relation_dom(X2))
| ~ in(X3,relation_dom(X1))
| X1 != relation_rng_restriction(X0,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
fof(f5,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f5_nnf,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [B,A] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c9,plain,
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f36,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
& subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_funct_1) ).
fof(f36_neg,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
& subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f36_nnf,plain,
? [A,B] :
( ( ~ subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
| ~ subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)) )
& function(B)
& relation(B) ),
inference(nnf_transformation,[status(thm)],[f36_neg]) ).
fof(f36_sk,plain,
( ( ~ subset(relation_rng(relation_rng_restriction(sk14,sk15)),relation_rng(sk15))
| ~ subset(relation_dom(relation_rng_restriction(sk14,sk15)),relation_dom(sk15)) )
& function(sk15)
& relation(sk15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk14,sk15])],[f36_nnf]) ).
cnf(c72,plain,
relation(sk15),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p100,plain,
relation(relation_rng_restriction(X0,sk15)),
inference(resolution,[status(thm)],[c9,c72]) ).
cnf(p312,plain,
( in(X3,relation_dom(X1))
| ~ in(X3,relation_dom(relation_rng_restriction(X0,sk15)))
| relation_rng_restriction(X0,sk15) != relation_rng_restriction(X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_rng_restriction(X0,sk15)) ),
inference(resolution,[status(thm)],[c56,p100]) ).
cnf(p751,plain,
( in(X1,relation_dom(sk15))
| ~ in(X1,relation_dom(relation_rng_restriction(X0,sk15)))
| ~ function(sk15)
| ~ relation(sk15)
| ~ function(relation_rng_restriction(X0,sk15)) ),
inference(equality_resolution,[status(thm)],[p312]) ).
fof(f11,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(f11_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)],[f11]) ).
fof(f11_sk,plain,
! [B,A] :
( ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) )
| ~ function(B)
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c19,plain,
( function(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p124,plain,
( function(relation_rng_restriction(X0,sk15))
| ~ function(sk15) ),
inference(resolution,[status(thm)],[c19,c72]) ).
cnf(c73,plain,
function(sk15),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p141,plain,
function(relation_rng_restriction(X0,sk15)),
inference(resolution,[status(thm)],[p124,c73]) ).
cnf(p753,plain,
( in(X0,relation_dom(sk15))
| ~ in(X0,relation_dom(relation_rng_restriction(X1,sk15)))
| ~ function(sk15)
| ~ relation(sk15) ),
inference(resolution,[status(thm)],[p751,p141]) ).
cnf(p754,plain,
( in(X0,relation_dom(sk15))
| ~ in(X0,relation_dom(relation_rng_restriction(X1,sk15)))
| ~ function(sk15) ),
inference(resolution,[status(thm)],[p753,c72]) ).
cnf(p755,plain,
( in(X0,relation_dom(sk15))
| ~ in(X0,relation_dom(relation_rng_restriction(X1,sk15))) ),
inference(resolution,[status(thm)],[p754,c73]) ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f4_nnf,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk0(A,B),B)
& in(sk0(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f4_nnf]) ).
cnf(c7,plain,
( in(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p756,plain,
( subset(relation_dom(relation_rng_restriction(X0,sk15)),X1)
| in(sk0(relation_dom(relation_rng_restriction(X0,sk15)),X1),relation_dom(sk15)) ),
inference(resolution,[status(thm)],[p755,c7]) ).
cnf(c8,plain,
( ~ in(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p758,plain,
( subset(relation_dom(relation_rng_restriction(X0,sk15)),relation_dom(sk15))
| subset(relation_dom(relation_rng_restriction(X0,sk15)),relation_dom(sk15)) ),
inference(resolution,[status(thm)],[p756,c8]) ).
cnf(p763,plain,
subset(relation_dom(relation_rng_restriction(X0,sk15)),relation_dom(sk15)),
inference(factoring,[status(thm)],[p758]) ).
cnf(c74,plain,
( ~ subset(relation_rng(relation_rng_restriction(sk14,sk15)),relation_rng(sk15))
| ~ subset(relation_dom(relation_rng_restriction(sk14,sk15)),relation_dom(sk15)) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p764,plain,
~ subset(relation_rng(relation_rng_restriction(sk14,sk15)),relation_rng(sk15)),
inference(resolution,[status(thm)],[p763,c74]) ).
fof(f27,axiom,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_relat_1) ).
fof(f27_nnf,plain,
! [A,B] :
( subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [B,A] :
( subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c47,plain,
( subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p218,plain,
subset(relation_rng(relation_rng_restriction(X0,sk15)),relation_rng(sk15)),
inference(resolution,[status(thm)],[c47,c72]) ).
cnf(p766,plain,
$false,
inference(resolution,[status(thm)],[p764,p218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU046+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Thu Sep 24 12:38:05 UTC 2026
% 0.05/0.30 % CPUTime :
% 0.05/0.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.16/1.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.16/1.52 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------