%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU130+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 : n019.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 02:51:01 PM UTC 2026
% Result : Theorem 4.99s 6.80s
% Output : Proof 4.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 27 unt; 0 def)
% Number of atoms : 128 ( 29 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 137 ( 68 ~; 38 |; 25 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 103 ( 7 sgn 66 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f23,lemma,
! [A,B,C] :
( ( subset(A,C)
& subset(A,B) )
=> subset(A,set_intersection2(B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(f23_nnf,plain,
! [A,B,C] :
( subset(A,set_intersection2(B,C))
| ~ subset(A,C)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A,B,C] :
( subset(A,set_intersection2(B,C))
| ~ subset(A,C)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c45,plain,
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(hi33,axiom,
ifeq(subset(X0,X1),true,ifeq(subset(X0,X2),true,subset(X0,set_intersection2(X1,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
fof(f19,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f19_nnf,plain,
! [A,B] : subset(A,A),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A] : subset(A,A),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c41,plain,
subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi29,axiom,
subset(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c41]) ).
fof(f27,conjecture,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f27_neg,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f27_nnf,plain,
? [A,B] :
( set_intersection2(A,B) != A
& subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f27_neg]) ).
fof(f27_sk,plain,
( set_intersection2(sk6,sk7) != sk6
& subset(sk6,sk7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk6,sk7])],[f27_nnf]) ).
cnf(c49,plain,
subset(sk6,sk7),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(hi37,negated_conjecture,
subset(sk6,sk7) = true,
inference(equality_encoding,[status(esa)],[c49]) ).
cnf(h23,plain,
subset(sk6,set_intersection2(sk6,sk7)) = true,
inference(hyper_resolution,[status(thm)],[hi33,hi29,hi37]) ).
fof(f3,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f3_nnf,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c5,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi4,axiom,
ifeq(subset(X0,X1),true,ifeq(subset(X1,X0),true,X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
fof(f22,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f22_nnf,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c44,plain,
subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi32,axiom,
subset(set_intersection2(X0,X1),X0) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
cnf(h709,plain,
set_intersection2(sk6,sk7) = sk6,
inference(hyper_resolution,[status(thm)],[hi4,hi32,h23]) ).
cnf(c50,plain,
set_intersection2(sk6,sk7) != sk6,
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(hi51,negated_conjecture,
ifeq(set_intersection2(sk6,sk7),sk6,false,true) = true,
inference(equality_encoding,[status(esa)],[c50]) ).
cnf(t1,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi51,h709]) ).
cnf(t277,plain,
false = true,
inference(orient,[status(thm)],[t1]) ).
fof(f0,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f0_nnf,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f4,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f4_nnf,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( ( in(sk0(A),A)
| A = empty_set )
& ( ~ in(B,A)
| A != empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f4_nnf]) ).
cnf(c6,plain,
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f18,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f18_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
~ empty(sk5),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f18_nnf]) ).
cnf(c40,plain,
~ empty(sk5),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f30,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f30_nnf,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,B)
| ~ in(C,A) )
& ( ( in(sk8(A,B),B)
& in(sk8(A,B),A) )
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8])],[f30_nnf]) ).
cnf(c55,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f32,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f32_nnf,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,set_intersection2(A,B)) )
& ( in(sk9(A,B),set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9])],[f32_nnf]) ).
cnf(c58,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
fof(f34,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f34_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c60,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c6,c40,c50,c55,c58,c60]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t277]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU130+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/5.35 % Computer : n019.cluster.edu
% 0.11/5.35 % Model : x86_64 x86_64
% 0.11/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.35 % Memory : 8046.5625MB
% 0.11/5.35 % OS : Linux 6.8.0-71-generic
% 0.11/5.35 % CPULimit : 300
% 0.11/5.35 % WCLimit : 300
% 0.11/5.35 % DateTime : Thu Sep 24 12:51:55 UTC 2026
% 0.11/5.35 % CPUTime :
% 0.11/5.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.99/6.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.99/6.80 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------