%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET944+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 02:44:20 PM UTC 2026
% Result : Theorem 26.60s 3.86s
% Output : Proof 26.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 9
% Syntax : Number of formulae : 114 ( 93 unt; 0 def)
% Number of atoms : 204 ( 99 equ)
% Maximal formula atoms : 14 ( 1 avg)
% Number of connectives : 156 ( 66 ~; 53 |; 30 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-4 aty)
% Number of variables : 200 ( 12 sgn 49 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f2_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)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk0(A,B),B)
& in(sk0(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c4,plain,
( ~ in(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t19,plain,
ifeq(in(sk0(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t60,plain,
ifeq(in(sk0(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(orient,[status(thm)],[t19]) ).
fof(f3,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f3_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_intersection2(A,B) )
& ( ! [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [C,A,B,D] :
( ( ( in(sk1(A,B,C),B)
& in(sk1(A,B,C),A)
& ~ in(sk1(A,B,C),C) )
| ( ( ~ in(sk1(A,B,C),B)
| ~ in(sk1(A,B,C),A) )
& in(sk1(A,B,C),C) )
| C = set_intersection2(A,B) )
& ( ( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f3_nnf]) ).
cnf(c7,plain,
( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2)
| X2 != set_intersection2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t32,plain,
ifeq(X1,set_intersection2(X2,X3),ifeq(in(X4,X2),true,ifeq(in(X4,X3),true,in(X4,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t48,plain,
ifeq(X1,set_intersection2(X2,X3),ifeq(in(X4,X2),true,ifeq(in(X4,X3),true,in(X4,X1),true),true),true) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t37,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t49,plain,
true = ifeq(in(X1,X2),true,ifeq(in(X1,X3),true,in(X1,set_intersection2(X2,X3)),true),true),
inference(cp,[status(thm)],[t48,t37]) ).
cnf(t258,plain,
ifeq(in(X1,X2),true,ifeq(in(X1,X3),true,in(X1,set_intersection2(X2,X3)),true),true) = true,
inference(orient,[status(thm)],[t49]) ).
fof(f1,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f1_nnf,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t12,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t88,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(orient,[status(thm)],[t12]) ).
cnf(t263,plain,
true = ifeq(in(X1,X2),true,ifeq(in(X1,X3),true,in(X1,set_intersection2(X3,X2)),true),true),
inference(cp,[status(thm)],[t258,t88]) ).
cnf(t269,plain,
ifeq(in(X1,X2),true,ifeq(in(X1,X3),true,in(X1,set_intersection2(X3,X2)),true),true) = true,
inference(orient,[status(thm)],[t263]) ).
fof(f4,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(f4_nnf,plain,
! [A,B] :
( ( ? [C] :
( ( ? [D] :
( in(D,A)
& in(C,D) )
& ~ in(C,B) )
| ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
& in(C,B) ) )
| B = union(A) )
& ( ! [C] :
( ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [B,A,C,D] :
( ( ( in(sk4(A,B),A)
& in(sk3(A,B),sk4(A,B))
& ~ in(sk3(A,B),B) )
| ( ( ~ in(D,A)
| ~ in(sk3(A,B),D) )
& in(sk3(A,B),B) )
| B = union(A) )
& ( ( ( ~ in(D,A)
| ~ in(C,D)
| in(C,B) )
& ( ( in(sk2(A,B,C),A)
& in(C,sk2(A,B,C)) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f4_nnf]) ).
cnf(c16,plain,
( ~ in(X3,X0)
| ~ in(X2,X3)
| in(X2,X1)
| X1 != union(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t31,plain,
ifeq(X1,union(X2),ifeq(in(X3,X4),true,ifeq(in(X4,X2),true,in(X3,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t42,plain,
ifeq(X1,union(X2),ifeq(in(X3,X4),true,ifeq(in(X4,X2),true,in(X3,X1),true),true),true) = true,
inference(orient,[status(thm)],[t31]) ).
cnf(t43,plain,
true = ifeq(in(X1,X2),true,ifeq(in(X2,X3),true,in(X1,union(X3)),true),true),
inference(cp,[status(thm)],[t42,t37]) ).
cnf(t136,plain,
ifeq(in(X1,X2),true,ifeq(in(X2,X3),true,in(X1,union(X3)),true),true) = true,
inference(orient,[status(thm)],[t43]) ).
cnf(c6,plain,
( in(X3,X1)
| ~ in(X3,X2)
| X2 != set_intersection2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t23,plain,
ifeq(X1,set_intersection2(X2,X3),ifeq(in(X4,X1),true,in(X4,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t51,plain,
ifeq(X1,set_intersection2(X2,X3),ifeq(in(X4,X1),true,in(X4,X3),true),true) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(t52,plain,
true = ifeq(in(X1,set_intersection2(X2,X3)),true,in(X1,X3),true),
inference(cp,[status(thm)],[t51,t37]) ).
cnf(t115,plain,
ifeq(in(X1,set_intersection2(X2,X3)),true,in(X1,X3),true) = true,
inference(orient,[status(thm)],[t52]) ).
cnf(c15,plain,
( in(sk2(X0,X1,X2),X0)
| ~ in(X2,X1)
| X1 != union(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t27,plain,
ifeq(X1,union(X2),ifeq(in(X3,X1),true,in(sk2(X2,X1,X3),X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t46,plain,
ifeq(X1,union(X2),ifeq(in(X3,X1),true,in(sk2(X2,X1,X3),X2),true),true) = true,
inference(orient,[status(thm)],[t27]) ).
cnf(t47,plain,
true = ifeq(in(X1,union(X2)),true,in(sk2(X2,union(X2),X1),X2),true),
inference(cp,[status(thm)],[t46,t37]) ).
cnf(t177,plain,
ifeq(in(X1,union(X2)),true,in(sk2(X2,union(X2),X1),X2),true) = true,
inference(orient,[status(thm)],[t47]) ).
cnf(c3,plain,
( in(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t17,plain,
or(subset(X1,X2),in(sk0(X1,X2),X1)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t72,plain,
or(subset(X1,X2),in(sk0(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t17]) ).
fof(f9,conjecture,
! [A,B] : subset(union(set_intersection2(A,B)),set_intersection2(union(A),union(B))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_zfmisc_1) ).
fof(f9_neg,negated_conjecture,
~ ! [A,B] : subset(union(set_intersection2(A,B)),set_intersection2(union(A),union(B))),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f9_nnf,plain,
? [A,B] : ~ subset(union(set_intersection2(A,B)),set_intersection2(union(A),union(B))),
inference(nnf_transformation,[status(thm)],[f9_neg]) ).
fof(f9_sk,plain,
~ subset(union(set_intersection2(sk7,sk8)),set_intersection2(union(sk7),union(sk8))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7,sk8])],[f9_nnf]) ).
cnf(c27,plain,
~ subset(union(set_intersection2(sk7,sk8)),set_intersection2(union(sk7),union(sk8))),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t18,plain,
subset(union(set_intersection2(sk7,sk8)),set_intersection2(union(sk7),union(sk8))) = false,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(t3180,plain,
subset(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk7),union(sk8))) = false,
inference(step,[status(thm)],[t18,t88]) ).
cnf(t3181,plain,
subset(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))) = false,
inference(step,[status(thm)],[t3180,t88]) ).
cnf(t96,plain,
subset(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))) = false,
inference(orient,[status(thm)],[t3181]) ).
cnf(t97,plain,
true = or(false,in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),union(set_intersection2(sk8,sk7)))),
inference(cp,[status(thm)],[t72,t96]) ).
cnf(t7,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t40,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t3190,plain,
true = in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),union(set_intersection2(sk8,sk7))),
inference(step,[status(thm)],[t97,t40]) ).
cnf(t183,plain,
in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),union(set_intersection2(sk8,sk7))) = true,
inference(orient,[status(thm)],[t3190]) ).
cnf(t199,plain,
true = ifeq(true,true,in(sk2(set_intersection2(sk8,sk7),union(set_intersection2(sk8,sk7)),sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7)))),set_intersection2(sk8,sk7)),true),
inference(cp,[status(thm)],[t177,t183]) ).
cnf(t3215,plain,
true = in(sk2(set_intersection2(sk8,sk7),union(set_intersection2(sk8,sk7)),sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7)))),set_intersection2(sk8,sk7)),
inference(step,[status(thm)],[t199,t37]) ).
cnf(t303,plain,
in(sk2(set_intersection2(sk8,sk7),union(set_intersection2(sk8,sk7)),sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7)))),set_intersection2(sk8,sk7)) = true,
inference(orient,[status(thm)],[t3215]) ).
cnf(t309,plain,
true = ifeq(true,true,in(sk2(set_intersection2(sk8,sk7),union(set_intersection2(sk8,sk7)),sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7)))),sk7),true),
inference(cp,[status(thm)],[t115,t303]) ).
cnf(t3229,plain,
true = in(sk2(set_intersection2(sk8,sk7),union(set_intersection2(sk8,sk7)),sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7)))),sk7),
inference(step,[status(thm)],[t309,t37]) ).
cnf(t389,plain,
in(sk2(set_intersection2(sk8,sk7),union(set_intersection2(sk8,sk7)),sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7)))),sk7) = true,
inference(orient,[status(thm)],[t3229]) ).
cnf(t416,plain,
true = ifeq(in(X1,sk2(set_intersection2(sk8,sk7),union(set_intersection2(sk8,sk7)),sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))))),true,ifeq(true,true,in(X1,union(sk7)),true),true),
inference(cp,[status(thm)],[t136,t389]) ).
cnf(t3272,plain,
true = ifeq(in(X1,sk2(set_intersection2(sk8,sk7),union(set_intersection2(sk8,sk7)),sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))))),true,in(X1,union(sk7)),true),
inference(step,[status(thm)],[t416,t37]) ).
cnf(t639,plain,
ifeq(in(X1,sk2(set_intersection2(sk8,sk7),union(set_intersection2(sk8,sk7)),sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))))),true,in(X1,union(sk7)),true) = true,
inference(orient,[status(thm)],[t3272]) ).
cnf(c14,plain,
( in(X2,sk2(X0,X1,X2))
| ~ in(X2,X1)
| X1 != union(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t26,plain,
ifeq(X1,union(X2),ifeq(in(X3,X1),true,in(X3,sk2(X2,X1,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t44,plain,
ifeq(X1,union(X2),ifeq(in(X3,X1),true,in(X3,sk2(X2,X1,X3)),true),true) = true,
inference(orient,[status(thm)],[t26]) ).
cnf(t45,plain,
true = ifeq(in(X1,union(X2)),true,in(X1,sk2(X2,union(X2),X1)),true),
inference(cp,[status(thm)],[t44,t37]) ).
cnf(t159,plain,
ifeq(in(X1,union(X2)),true,in(X1,sk2(X2,union(X2),X1)),true) = true,
inference(orient,[status(thm)],[t45]) ).
cnf(t200,plain,
true = ifeq(true,true,in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),sk2(set_intersection2(sk8,sk7),union(set_intersection2(sk8,sk7)),sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))))),true),
inference(cp,[status(thm)],[t159,t183]) ).
cnf(t3282,plain,
true = in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),sk2(set_intersection2(sk8,sk7),union(set_intersection2(sk8,sk7)),sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))))),
inference(step,[status(thm)],[t200,t37]) ).
cnf(t680,plain,
in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),sk2(set_intersection2(sk8,sk7),union(set_intersection2(sk8,sk7)),sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))))) = true,
inference(orient,[status(thm)],[t3282]) ).
cnf(t716,plain,
true = ifeq(true,true,in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),union(sk7)),true),
inference(cp,[status(thm)],[t639,t680]) ).
cnf(t3283,plain,
true = in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),union(sk7)),
inference(step,[status(thm)],[t716,t37]) ).
cnf(t721,plain,
in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),union(sk7)) = true,
inference(orient,[status(thm)],[t3283]) ).
cnf(t743,plain,
true = ifeq(true,true,ifeq(in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),X1),true,in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),set_intersection2(X1,union(sk7))),true),true),
inference(cp,[status(thm)],[t269,t721]) ).
cnf(t3545,plain,
true = ifeq(in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),X1),true,in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),set_intersection2(X1,union(sk7))),true),
inference(step,[status(thm)],[t743,t37]) ).
cnf(t2800,plain,
ifeq(in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),X1),true,in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),set_intersection2(X1,union(sk7))),true) = true,
inference(orient,[status(thm)],[t3545]) ).
cnf(c5,plain,
( in(X3,X0)
| ~ in(X3,X2)
| X2 != set_intersection2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t22,plain,
ifeq(X1,set_intersection2(X2,X3),ifeq(in(X4,X1),true,in(X4,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t54,plain,
ifeq(X1,set_intersection2(X2,X3),ifeq(in(X4,X1),true,in(X4,X2),true),true) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t55,plain,
true = ifeq(in(X1,set_intersection2(X2,X3)),true,in(X1,X2),true),
inference(cp,[status(thm)],[t54,t37]) ).
cnf(t144,plain,
ifeq(in(X1,set_intersection2(X2,X3)),true,in(X1,X2),true) = true,
inference(orient,[status(thm)],[t55]) ).
cnf(t308,plain,
true = ifeq(true,true,in(sk2(set_intersection2(sk8,sk7),union(set_intersection2(sk8,sk7)),sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7)))),sk8),true),
inference(cp,[status(thm)],[t144,t303]) ).
cnf(t3222,plain,
true = in(sk2(set_intersection2(sk8,sk7),union(set_intersection2(sk8,sk7)),sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7)))),sk8),
inference(step,[status(thm)],[t308,t37]) ).
cnf(t347,plain,
in(sk2(set_intersection2(sk8,sk7),union(set_intersection2(sk8,sk7)),sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7)))),sk8) = true,
inference(orient,[status(thm)],[t3222]) ).
cnf(t374,plain,
true = ifeq(in(X1,sk2(set_intersection2(sk8,sk7),union(set_intersection2(sk8,sk7)),sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))))),true,ifeq(true,true,in(X1,union(sk8)),true),true),
inference(cp,[status(thm)],[t136,t347]) ).
cnf(t3266,plain,
true = ifeq(in(X1,sk2(set_intersection2(sk8,sk7),union(set_intersection2(sk8,sk7)),sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))))),true,in(X1,union(sk8)),true),
inference(step,[status(thm)],[t374,t37]) ).
cnf(t612,plain,
ifeq(in(X1,sk2(set_intersection2(sk8,sk7),union(set_intersection2(sk8,sk7)),sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))))),true,in(X1,union(sk8)),true) = true,
inference(orient,[status(thm)],[t3266]) ).
cnf(t717,plain,
true = ifeq(true,true,in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),union(sk8)),true),
inference(cp,[status(thm)],[t612,t680]) ).
cnf(t3291,plain,
true = in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),union(sk8)),
inference(step,[status(thm)],[t717,t37]) ).
cnf(t777,plain,
in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),union(sk8)) = true,
inference(orient,[status(thm)],[t3291]) ).
cnf(t2806,plain,
true = ifeq(true,true,in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),set_intersection2(union(sk8),union(sk7))),true),
inference(cp,[status(thm)],[t2800,t777]) ).
cnf(t3546,plain,
true = in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),set_intersection2(union(sk8),union(sk7))),
inference(step,[status(thm)],[t2806,t37]) ).
cnf(t2823,plain,
in(sk0(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),set_intersection2(union(sk8),union(sk7))) = true,
inference(orient,[status(thm)],[t3546]) ).
cnf(t2831,plain,
true = ifeq(true,true,subset(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),true),
inference(cp,[status(thm)],[t60,t2823]) ).
cnf(t3549,plain,
true = subset(union(set_intersection2(sk8,sk7)),set_intersection2(union(sk8),union(sk7))),
inference(step,[status(thm)],[t2831,t37]) ).
cnf(t3550,plain,
true = false,
inference(step,[status(thm)],[t3549,t96]) ).
cnf(t2884,plain,
false = true,
inference(orient,[status(thm)],[t3550]) ).
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(f7,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f7_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
~ empty(sk6),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk6])],[f7_nnf]) ).
cnf(c25,plain,
~ empty(sk6),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c25,c27]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2884]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET944+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 12:25:50 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 26.60/3.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.60/3.86 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------