%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU180+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 02:51:15 PM UTC 2026
% Result : Theorem 29.94s 4.74s
% Output : Proof 29.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 19 unt; 0 def)
% Number of atoms : 175 ( 31 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 199 ( 75 ~; 71 |; 38 &)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 3 con; 0-3 aty)
% Number of variables : 113 ( 8 sgn 66 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
fof(f24_nnf,plain,
! [A] :
( relation_field(A) = set_union2(relation_dom(A),relation_rng(A))
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A] :
( relation_field(A) = set_union2(relation_dom(A),relation_rng(A))
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c115,plain,
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
fof(f107,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f107_neg,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
inference(negated_conjecture,[status(cth)],[f107]) ).
fof(f107_nnf,plain,
? [A,B,C] :
( ( ~ in(B,relation_field(C))
| ~ in(A,relation_field(C)) )
& in(ordered_pair(A,B),C)
& relation(C) ),
inference(nnf_transformation,[status(thm)],[f107_neg]) ).
fof(f107_sk,plain,
( ( ~ in(sk39,relation_field(sk40))
| ~ in(sk38,relation_field(sk40)) )
& in(ordered_pair(sk38,sk39),sk40)
& relation(sk40) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk38,sk39,sk40])],[f107_nnf]) ).
cnf(c228,plain,
relation(sk40),
inference(cnf_transformation,[status(esa)],[f107_sk]) ).
cnf(p2533,plain,
relation_field(sk40) = set_union2(relation_dom(sk40),relation_rng(sk40)),
inference(resolution,[status(thm)],[c115,c228]) ).
fof(f3,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f3_nnf,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p2536,plain,
set_union2(relation_dom(sk40),relation_rng(sk40)) = relation_field(sk40),
inference(superposition,[status(thm)],[p2533,c3]) ).
fof(f13,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f13_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( in(D,B)
| in(D,A) )
& ~ in(D,C) )
| ( ~ in(D,B)
& ~ in(D,A)
& in(D,C) ) )
| C = set_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [C,A,B,D] :
( ( ( ( in(sk10(A,B,C),B)
| in(sk10(A,B,C),A) )
& ~ in(sk10(A,B,C),C) )
| ( ~ in(sk10(A,B,C),B)
& ~ in(sk10(A,B,C),A)
& in(sk10(A,B,C),C) )
| C = set_union2(A,B) )
& ( ( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f13_nnf]) ).
cnf(c51,plain,
( ~ in(X3,X1)
| in(X3,X2)
| X2 != set_union2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p2540,plain,
( ~ in(X1,relation_rng(sk40))
| in(X1,X0)
| X0 != relation_field(sk40) ),
inference(superposition,[status(thm)],[p2536,c51]) ).
cnf(p2723,plain,
( ~ in(X0,relation_rng(sk40))
| in(X0,relation_field(sk40)) ),
inference(equality_resolution,[status(thm)],[p2540]) ).
fof(f21,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f21_nnf,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
& ~ in(C,B) )
| ( ! [D] : ~ in(ordered_pair(D,C),A)
& in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B,C,D] :
( ( ( ( in(ordered_pair(sk27(A,B),sk26(A,B)),A)
& ~ in(sk26(A,B),B) )
| ( ~ in(ordered_pair(D,sk26(A,B)),A)
& in(sk26(A,B),B) )
| B = relation_rng(A) )
& ( ( ( ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ( in(ordered_pair(sk25(A,B,C),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk25,sk26,sk27])],[f21_nnf]) ).
cnf(c108,plain,
( ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p2331,plain,
( ~ in(ordered_pair(X2,X1),sk40)
| in(X1,X0)
| X0 != relation_rng(sk40) ),
inference(resolution,[status(thm)],[c108,c228]) ).
cnf(p2334,plain,
( ~ in(ordered_pair(X1,X0),sk40)
| in(X0,relation_rng(sk40)) ),
inference(equality_resolution,[status(thm)],[p2331]) ).
cnf(c229,plain,
in(ordered_pair(sk38,sk39),sk40),
inference(cnf_transformation,[status(esa)],[f107_sk]) ).
cnf(p2338,plain,
in(sk39,relation_rng(sk40)),
inference(resolution,[status(thm)],[p2334,c229]) ).
cnf(p2763,plain,
in(sk39,relation_field(sk40)),
inference(resolution,[status(thm)],[p2723,p2338]) ).
fof(f141,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f141_nnf,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(nnf_transformation,[status(thm)],[f141]) ).
fof(f141_sk,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(skolemisation,[status(esa)],[f141_nnf]) ).
cnf(c277,plain,
subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[status(esa)],[f141_sk]) ).
cnf(p2537,plain,
subset(relation_dom(sk40),relation_field(sk40)),
inference(superposition,[status(thm)],[p2536,c277]) ).
fof(f15,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f15_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)],[f15]) ).
fof(f15_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk16(A,B),B)
& in(sk16(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16])],[f15_nnf]) ).
cnf(c70,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p2542,plain,
( in(X0,relation_field(sk40))
| ~ in(X0,relation_dom(sk40)) ),
inference(resolution,[status(thm)],[p2537,c70]) ).
fof(f17,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f17_nnf,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
& ~ in(C,B) )
| ( ! [D] : ~ in(ordered_pair(C,D),A)
& in(C,B) ) )
| B = relation_dom(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A,B,C,D] :
( ( ( ( in(ordered_pair(sk19(A,B),sk20(A,B)),A)
& ~ in(sk19(A,B),B) )
| ( ~ in(ordered_pair(sk19(A,B),D),A)
& in(sk19(A,B),B) )
| B = relation_dom(A) )
& ( ( ( ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( in(ordered_pair(C,sk18(A,B,C)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk18,sk19,sk20])],[f17_nnf]) ).
cnf(c83,plain,
( ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p1597,plain,
( ~ in(ordered_pair(X1,X2),sk40)
| in(X1,X0)
| X0 != relation_dom(sk40) ),
inference(resolution,[status(thm)],[c83,c228]) ).
cnf(p1600,plain,
( ~ in(ordered_pair(X0,X1),sk40)
| in(X0,relation_dom(sk40)) ),
inference(equality_resolution,[status(thm)],[p1597]) ).
cnf(p1604,plain,
in(sk38,relation_dom(sk40)),
inference(resolution,[status(thm)],[p1600,c229]) ).
cnf(p2566,plain,
in(sk38,relation_field(sk40)),
inference(resolution,[status(thm)],[p2542,p1604]) ).
cnf(c230,plain,
( ~ in(sk39,relation_field(sk40))
| ~ in(sk38,relation_field(sk40)) ),
inference(cnf_transformation,[status(esa)],[f107_sk]) ).
cnf(p2586,plain,
~ in(sk39,relation_field(sk40)),
inference(resolution,[status(thm)],[p2566,c230]) ).
cnf(p2794,plain,
$false,
inference(resolution,[status(thm)],[p2763,p2586]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU180+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 13:07:25 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 29.94/4.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.94/4.74 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------