%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU355+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 02:51:49 PM UTC 2026
% Result : Theorem 4.05s 1.09s
% Output : Proof 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 109 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 124 ( 47 ~; 44 |; 19 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 54 ( 1 sgn 34 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f20_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c29,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f3,axiom,
! [A] :
( rel_str(A)
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( relstr_set_smaller(A,B,C)
<=> ! [D] :
( element(D,the_carrier(A))
=> ( in(D,B)
=> related(A,D,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lattice3) ).
fof(f3_nnf,plain,
! [A] :
( ! [B,C] :
( ( ( ? [D] :
( ~ related(A,D,C)
& in(D,B)
& element(D,the_carrier(A)) )
| relstr_set_smaller(A,B,C) )
& ( ! [D] :
( related(A,D,C)
| ~ in(D,B)
| ~ element(D,the_carrier(A)) )
| ~ relstr_set_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,C,B,D] :
( ( ( ( ~ related(A,sk1(A,B,C),C)
& in(sk1(A,B,C),B)
& element(sk1(A,B,C),the_carrier(A)) )
| relstr_set_smaller(A,B,C) )
& ( related(A,D,C)
| ~ in(D,B)
| ~ element(D,the_carrier(A))
| ~ relstr_set_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A))
| ~ rel_str(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f3_nnf]) ).
cnf(c8,plain,
( in(sk1(X0,X1,X2),X1)
| relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f19,conjecture,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ( relstr_element_smaller(A,empty_set,B)
& relstr_set_smaller(A,empty_set,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_yellow_0) ).
fof(f19_neg,negated_conjecture,
~ ! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ( relstr_element_smaller(A,empty_set,B)
& relstr_set_smaller(A,empty_set,B) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f19_nnf,plain,
? [A] :
( ? [B] :
( ( ~ relstr_element_smaller(A,empty_set,B)
| ~ relstr_set_smaller(A,empty_set,B) )
& element(B,the_carrier(A)) )
& rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f19_neg]) ).
fof(f19_sk,plain,
( ( ~ relstr_element_smaller(sk8,empty_set,sk9)
| ~ relstr_set_smaller(sk8,empty_set,sk9) )
& element(sk9,the_carrier(sk8))
& rel_str(sk8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9])],[f19_nnf]) ).
cnf(c26,plain,
rel_str(sk8),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p84,plain,
( in(sk1(sk8,X1,X0),X1)
| relstr_set_smaller(sk8,X1,X0)
| ~ element(X0,the_carrier(sk8)) ),
inference(resolution,[status(thm)],[c8,c26]) ).
cnf(c27,plain,
element(sk9,the_carrier(sk8)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p86,plain,
( in(sk1(sk8,X0,sk9),X0)
| relstr_set_smaller(sk8,X0,sk9) ),
inference(resolution,[status(thm)],[p84,c27]) ).
cnf(p180,plain,
( relstr_set_smaller(sk8,X0,sk9)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[c29,p86]) ).
fof(f12,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f12_nnf,plain,
empty(empty_set),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c18,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(p188,plain,
relstr_set_smaller(sk8,empty_set,sk9),
inference(resolution,[status(thm)],[p180,c18]) ).
cnf(c28,plain,
( ~ relstr_element_smaller(sk8,empty_set,sk9)
| ~ relstr_set_smaller(sk8,empty_set,sk9) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p189,plain,
~ relstr_element_smaller(sk8,empty_set,sk9),
inference(resolution,[status(thm)],[p188,c28]) ).
fof(f2,axiom,
! [A] :
( rel_str(A)
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( relstr_element_smaller(A,B,C)
<=> ! [D] :
( element(D,the_carrier(A))
=> ( in(D,B)
=> related(A,C,D) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattice3) ).
fof(f2_nnf,plain,
! [A] :
( ! [B,C] :
( ( ( ? [D] :
( ~ related(A,C,D)
& in(D,B)
& element(D,the_carrier(A)) )
| relstr_element_smaller(A,B,C) )
& ( ! [D] :
( related(A,C,D)
| ~ in(D,B)
| ~ element(D,the_carrier(A)) )
| ~ relstr_element_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,C,B,D] :
( ( ( ( ~ related(A,C,sk0(A,B,C))
& in(sk0(A,B,C),B)
& element(sk0(A,B,C),the_carrier(A)) )
| relstr_element_smaller(A,B,C) )
& ( related(A,C,D)
| ~ in(D,B)
| ~ element(D,the_carrier(A))
| ~ relstr_element_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A))
| ~ rel_str(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c4,plain,
( in(sk0(X0,X1,X2),X1)
| relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p48,plain,
( in(sk0(sk8,X1,X0),X1)
| relstr_element_smaller(sk8,X1,X0)
| ~ element(X0,the_carrier(sk8)) ),
inference(resolution,[status(thm)],[c4,c26]) ).
cnf(p50,plain,
( in(sk0(sk8,X0,sk9),X0)
| relstr_element_smaller(sk8,X0,sk9) ),
inference(resolution,[status(thm)],[p48,c27]) ).
cnf(p177,plain,
( relstr_element_smaller(sk8,X0,sk9)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[c29,p50]) ).
cnf(p185,plain,
relstr_element_smaller(sk8,empty_set,sk9),
inference(resolution,[status(thm)],[p177,c18]) ).
cnf(p192,plain,
$false,
inference(resolution,[status(thm)],[p189,p185]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU355+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.37 % Computer : n017.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 13:44:31 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.05/1.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.05/1.09 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------