%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU126+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 : n018.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 02:51:00 PM UTC 2026
% Result : Theorem 10.23s 2.07s
% Output : Proof 10.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 73 ( 36 unt; 0 def)
% Number of atoms : 151 ( 39 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 153 ( 75 ~; 45 |; 26 &)
% ( 2 <=>; 5 =>; 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 : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 136 ( 8 sgn 81 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
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(c4,plain,
( subset(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(X0,X1,subset(X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
fof(f1,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f1_nnf,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi0,axiom,
set_union2(X0,X1) = set_union2(X1,X0),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h163,plain,
subset(set_union2(V0,V1),set_union2(V1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi0]) ).
fof(f23,lemma,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f23_nnf,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c46,plain,
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(hi33,axiom,
ifeq(subset(X0,X1),true,ifeq(subset(X1,X2),true,subset(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
fof(f30,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f30_nnf,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c56,plain,
subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(hi40,axiom,
subset(X0,set_union2(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(h19689,plain,
subset(V0,set_union2(V1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi33,hi40,h163]) ).
fof(f32,lemma,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(f32_nnf,plain,
! [A,B,C] :
( subset(set_union2(A,C),B)
| ~ subset(C,B)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [A,B,C] :
( subset(set_union2(A,C),B)
| ~ subset(C,B)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c58,plain,
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(hi42,axiom,
ifeq(subset(X0,X1),true,ifeq(subset(X2,X1),true,subset(set_union2(X0,X2),X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c58]) ).
fof(f21,conjecture,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f21_neg,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f21_nnf,plain,
? [A,B] :
( set_union2(A,B) != B
& subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f21_neg]) ).
fof(f21_sk,plain,
( set_union2(sk6,sk7) != sk7
& subset(sk6,sk7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk6,sk7])],[f21_nnf]) ).
cnf(c43,plain,
subset(sk6,sk7),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi31,negated_conjecture,
subset(sk6,sk7) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
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]) ).
cnf(h20,plain,
subset(set_union2(sk6,sk7),sk7) = true,
inference(hyper_resolution,[status(thm)],[hi42,hi31,hi29]) ).
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]) ).
cnf(h20083,plain,
set_union2(sk6,sk7) = sk7,
inference(hyper_resolution,[status(thm)],[hi4,h20,h19689]) ).
cnf(c44,plain,
set_union2(sk6,sk7) != sk7,
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi46,negated_conjecture,
ifeq(set_union2(sk6,sk7),sk7,false,true) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
cnf(t1,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi46,h20083]) ).
cnf(t266,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(f25,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(f25_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)],[f25]) ).
fof(f25_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])],[f25_nnf]) ).
cnf(c50,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
fof(f27,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(f27_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)],[f27]) ).
fof(f27_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])],[f27_nnf]) ).
cnf(c53,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
fof(f29,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f29_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c55,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c6,c40,c44,c50,c53,c55]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t266]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU126+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.58 % Computer : n018.cluster.edu
% 0.09/0.58 % Model : x86_64 x86_64
% 0.09/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.58 % Memory : 8046.5625MB
% 0.09/0.58 % OS : Linux 6.8.0-71-generic
% 0.09/0.58 % CPULimit : 300
% 0.09/0.58 % WCLimit : 300
% 0.09/0.58 % DateTime : Thu Sep 24 12:52:50 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.58 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.23/2.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.23/2.07 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------