%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU107+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 02:50:57 PM UTC 2026
% Result : Theorem 27.66s 4.35s
% Output : Proof 27.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 14 unt; 0 def)
% Number of atoms : 120 ( 14 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 118 ( 43 ~; 55 |; 14 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 62 ( 2 sgn 40 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f24_nnf,plain,
! [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c48,plain,
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
fof(f20,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f20_nnf,plain,
! [A,B] : subset(A,A),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A] : subset(A,A),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c41,plain,
subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p462,plain,
set_difference(X0,X0) = empty_set,
inference(resolution,[status(thm)],[c48,c41]) ).
fof(f23,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f23_nnf,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c46,plain,
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
fof(f19,axiom,
! [A,B,C] :
( ( element(C,A)
& element(B,A)
& preboolean(A)
& ~ empty(A) )
=> prebool_difference(A,B,C) = set_difference(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_finsub_1) ).
fof(f19_nnf,plain,
! [A,B,C] :
( prebool_difference(A,B,C) = set_difference(B,C)
| ~ element(C,A)
| ~ element(B,A)
| ~ preboolean(A)
| empty(A) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,B,C] :
( prebool_difference(A,B,C) = set_difference(B,C)
| ~ element(C,A)
| ~ element(B,A)
| ~ preboolean(A)
| empty(A) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c40,plain,
( prebool_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
fof(f21,conjecture,
! [A] :
( ( preboolean(A)
& ~ empty(A) )
=> in(empty_set,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_finsub_1) ).
fof(f21_neg,negated_conjecture,
~ ! [A] :
( ( preboolean(A)
& ~ empty(A) )
=> in(empty_set,A) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f21_nnf,plain,
? [A] :
( ~ in(empty_set,A)
& preboolean(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f21_neg]) ).
fof(f21_sk,plain,
( ~ in(empty_set,sk10)
& preboolean(sk10)
& ~ empty(sk10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f21_nnf]) ).
cnf(c43,plain,
preboolean(sk10),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p303,plain,
( prebool_difference(sk10,X0,X1) = set_difference(X0,X1)
| ~ element(X1,sk10)
| ~ element(X0,sk10)
| empty(sk10) ),
inference(resolution,[status(thm)],[c40,c43]) ).
cnf(p305,plain,
( prebool_difference(sk10,X0,X0) = set_difference(X0,X0)
| ~ element(X0,sk10)
| empty(sk10) ),
inference(factoring,[status(thm)],[p303]) ).
fof(f6,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f6_nnf,plain,
! [A] :
? [B] : element(B,A),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A] : element(sk0(A),A),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f6_nnf]) ).
cnf(c7,plain,
element(sk0(X0),X0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p327,plain,
( prebool_difference(sk10,sk0(sk10),sk0(sk10)) = set_difference(sk0(sk10),sk0(sk10))
| empty(sk10) ),
inference(resolution,[status(thm)],[p305,c7]) ).
fof(f5,axiom,
! [A,B,C] :
( ( element(C,A)
& element(B,A)
& preboolean(A)
& ~ empty(A) )
=> element(prebool_difference(A,B,C),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_finsub_1) ).
fof(f5_nnf,plain,
! [A,B,C] :
( element(prebool_difference(A,B,C),A)
| ~ element(C,A)
| ~ element(B,A)
| ~ preboolean(A)
| empty(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C] :
( element(prebool_difference(A,B,C),A)
| ~ element(C,A)
| ~ element(B,A)
| ~ preboolean(A)
| empty(A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c6,plain,
( element(prebool_difference(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p69,plain,
( element(prebool_difference(sk10,X0,X1),sk10)
| ~ element(X1,sk10)
| ~ element(X0,sk10)
| empty(sk10) ),
inference(resolution,[status(thm)],[c6,c43]) ).
cnf(p71,plain,
( element(prebool_difference(sk10,X0,X0),sk10)
| ~ element(X0,sk10)
| empty(sk10) ),
inference(factoring,[status(thm)],[p69]) ).
cnf(p73,plain,
( element(prebool_difference(sk10,sk0(sk10),sk0(sk10)),sk10)
| empty(sk10) ),
inference(resolution,[status(thm)],[c7,p71]) ).
cnf(p348,plain,
( element(set_difference(sk0(sk10),sk0(sk10)),sk10)
| empty(sk10)
| empty(sk10) ),
inference(superposition,[status(thm)],[p327,p73]) ).
cnf(p375,plain,
( element(set_difference(sk0(sk10),sk0(sk10)),sk10)
| empty(sk10) ),
inference(factoring,[status(thm)],[p348]) ).
cnf(p443,plain,
( empty(sk10)
| in(set_difference(sk0(sk10),sk0(sk10)),sk10)
| empty(sk10) ),
inference(resolution,[status(thm)],[c46,p375]) ).
cnf(p445,plain,
( in(set_difference(sk0(sk10),sk0(sk10)),sk10)
| empty(sk10) ),
inference(factoring,[status(thm)],[p443]) ).
cnf(p533,plain,
( in(empty_set,sk10)
| empty(sk10) ),
inference(demodulation,[status(thm)],[p462,p445]) ).
cnf(c44,plain,
~ in(empty_set,sk10),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p548,plain,
empty(sk10),
inference(resolution,[status(thm)],[p533,c44]) ).
cnf(c42,plain,
~ empty(sk10),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p549,plain,
$false,
inference(resolution,[status(thm)],[p548,c42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU107+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.34 % Computer : n003.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 12:48:06 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 27.66/4.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.66/4.35 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------