%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU200+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 : n008.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 02:51:19 PM UTC 2026
% Result : Theorem 68.74s 9.24s
% Output : Proof 68.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 28
% Syntax : Number of formulae : 146 ( 71 unt; 0 def)
% Number of atoms : 307 ( 67 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 339 ( 178 ~; 94 |; 51 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 7 con; 0-4 aty)
% Number of variables : 251 ( 36 sgn 155 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f114,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_relat_1) ).
fof(f114_neg,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ),
inference(negated_conjecture,[status(cth)],[f114]) ).
fof(f114_nnf,plain,
? [A,B] :
( ~ subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
& relation(B) ),
inference(nnf_transformation,[status(thm)],[f114_neg]) ).
fof(f114_sk,plain,
( ~ subset(relation_rng(relation_rng_restriction(sk53,sk54)),relation_rng(sk54))
& relation(sk54) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk53,sk54])],[f114_nnf]) ).
cnf(c279,plain,
~ subset(relation_rng(relation_rng_restriction(sk53,sk54)),relation_rng(sk54)),
inference(cnf_transformation,[status(esa)],[f114_sk]) ).
cnf(t155,plain,
subset(relation_rng(relation_rng_restriction(sk53,sk54)),relation_rng(sk54)) = false,
inference(equality_encoding,[status(esa)],[c279]) ).
cnf(t2155,plain,
subset(relation_rng(relation_rng_restriction(sk53,sk54)),relation_rng(sk54)) = false,
inference(orient,[status(thm)],[t155]) ).
fof(f127,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
=> ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
fof(f127_nnf,plain,
! [A] :
( ! [B] :
( ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) )
| ~ subset(A,B)
| ~ relation(B) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f127]) ).
fof(f127_sk,plain,
! [A,B] :
( ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) )
| ~ subset(A,B)
| ~ relation(B)
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f127_nnf]) ).
cnf(c298,plain,
( subset(relation_rng(X0),relation_rng(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f127_sk]) ).
cnf(t232,plain,
ifeq(relation(X1),true,ifeq(relation(X2),true,ifeq(subset(X1,X2),true,subset(relation_rng(X1),relation_rng(X2)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c298]) ).
cnf(t323,plain,
ifeq(relation(X1),true,ifeq(relation(X2),true,ifeq(subset(X1,X2),true,subset(relation_rng(X1),relation_rng(X2)),true),true),true) = true,
inference(orient,[status(thm)],[t232]) ).
fof(f113,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng_restriction(A,B),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_relat_1) ).
fof(f113_nnf,plain,
! [A,B] :
( subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f113]) ).
fof(f113_sk,plain,
! [B,A] :
( subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f113_nnf]) ).
cnf(c277,plain,
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f113_sk]) ).
cnf(t184,plain,
ifeq(relation(X1),true,subset(relation_rng_restriction(X2,X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c277]) ).
cnf(t368,plain,
ifeq(relation(X1),true,subset(relation_rng_restriction(X2,X1),X1),true) = true,
inference(orient,[status(thm)],[t184]) ).
fof(f68,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_union2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
fof(f68_nnf,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f68]) ).
fof(f68_sk,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f68_nnf]) ).
cnf(c213,plain,
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f68_sk]) ).
cnf(hi156,axiom,
ifeq(relation(X0),true,ifeq(relation(X1),true,relation(set_union2(X0,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c213]) ).
cnf(c278,plain,
relation(sk54),
inference(cnf_transformation,[status(esa)],[f114_sk]) ).
cnf(hi214,negated_conjecture,
relation(sk54) = true,
inference(equality_encoding,[status(esa)],[c278]) ).
cnf(t87,plain,
relation(set_union2(sk54,sk54)) = true,
inference(hyper_resolution,[status(thm)],[hi156,hi214,hi214]) ).
fof(f80,axiom,
! [A,B] : set_union2(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f80_nnf,plain,
! [A,B] : set_union2(A,A) = A,
inference(nnf_transformation,[status(thm)],[f80]) ).
fof(f80_sk,plain,
! [A] : set_union2(A,A) = A,
inference(skolemisation,[status(esa)],[f80_nnf]) ).
cnf(c229,plain,
set_union2(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f80_sk]) ).
cnf(t66,plain,
set_union2(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c229]) ).
cnf(t263,plain,
set_union2(X1,X1) = X1,
inference(orient,[status(thm)],[t66]) ).
cnf(t7517,plain,
relation(sk54) = true,
inference(step,[status(thm)],[t87,t263]) ).
cnf(t1321,plain,
relation(sk54) = true,
inference(orient,[status(thm)],[t7517]) ).
cnf(t1324,plain,
true = ifeq(true,true,subset(relation_rng_restriction(X1,sk54),sk54),true),
inference(cp,[status(thm)],[t368,t1321]) ).
cnf(t107,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t251,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t107]) ).
cnf(t7699,plain,
true = subset(relation_rng_restriction(X1,sk54),sk54),
inference(step,[status(thm)],[t1324,t251]) ).
cnf(t3555,plain,
subset(relation_rng_restriction(X1,sk54),sk54) = true,
inference(orient,[status(thm)],[t7699]) ).
cnf(t3568,plain,
true = ifeq(relation(relation_rng_restriction(X1,sk54)),true,ifeq(relation(sk54),true,ifeq(true,true,subset(relation_rng(relation_rng_restriction(X1,sk54)),relation_rng(sk54)),true),true),true),
inference(cp,[status(thm)],[t323,t3555]) ).
fof(f60,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f60_nnf,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f60]) ).
fof(f60_sk,plain,
! [B,A] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f60_nnf]) ).
cnf(c204,plain,
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f60_sk]) ).
cnf(t173,plain,
ifeq(relation(X1),true,relation(relation_rng_restriction(X2,X1)),true) = true,
inference(equality_encoding,[status(esa)],[c204]) ).
cnf(t363,plain,
ifeq(relation(X1),true,relation(relation_rng_restriction(X2,X1)),true) = true,
inference(orient,[status(thm)],[t173]) ).
cnf(t1326,plain,
true = ifeq(true,true,relation(relation_rng_restriction(X1,sk54)),true),
inference(cp,[status(thm)],[t363,t1321]) ).
cnf(t7642,plain,
true = relation(relation_rng_restriction(X1,sk54)),
inference(step,[status(thm)],[t1326,t251]) ).
cnf(t2848,plain,
relation(relation_rng_restriction(X1,sk54)) = true,
inference(orient,[status(thm)],[t7642]) ).
cnf(t7955,plain,
true = ifeq(true,true,ifeq(relation(sk54),true,ifeq(true,true,subset(relation_rng(relation_rng_restriction(X1,sk54)),relation_rng(sk54)),true),true),true),
inference(step,[status(thm)],[t3568,t2848]) ).
cnf(t7956,plain,
true = ifeq(relation(sk54),true,ifeq(true,true,subset(relation_rng(relation_rng_restriction(X1,sk54)),relation_rng(sk54)),true),true),
inference(step,[status(thm)],[t7955,t251]) ).
cnf(t7957,plain,
true = ifeq(true,true,ifeq(true,true,subset(relation_rng(relation_rng_restriction(X1,sk54)),relation_rng(sk54)),true),true),
inference(step,[status(thm)],[t7956,t1321]) ).
cnf(t7958,plain,
true = ifeq(true,true,subset(relation_rng(relation_rng_restriction(X1,sk54)),relation_rng(sk54)),true),
inference(step,[status(thm)],[t7957,t251]) ).
cnf(t7959,plain,
true = subset(relation_rng(relation_rng_restriction(X1,sk54)),relation_rng(sk54)),
inference(step,[status(thm)],[t7958,t251]) ).
cnf(t7490,plain,
subset(relation_rng(relation_rng_restriction(X1,sk54)),relation_rng(sk54)) = true,
inference(orient,[status(thm)],[t7959]) ).
cnf(t7960,plain,
true = false,
inference(step,[status(thm)],[t2155,t7490]) ).
cnf(t7501,plain,
true = false,
inference(rw,[status(thm)],[t7960]) ).
cnf(t7502,plain,
false = true,
inference(orient,[status(thm)],[t7501]) ).
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(f1,axiom,
! [A,B] :
( proper_subset(A,B)
=> ~ proper_subset(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(f1_nnf,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f13,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f13_nnf,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A,B] :
( ( in(sk13(A),A)
| A = empty_set )
& ( ~ in(B,A)
| A != empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13])],[f13_nnf]) ).
cnf(c56,plain,
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
fof(f26,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f26_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_difference(A,B) )
& ( ! [D] :
( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [C,A,B,D] :
( ( ( ~ in(sk34(A,B,C),B)
& in(sk34(A,B,C),A)
& ~ in(sk34(A,B,C),C) )
| ( ( in(sk34(A,B,C),B)
| ~ in(sk34(A,B,C),A) )
& in(sk34(A,B,C),C) )
| C = set_difference(A,B) )
& ( ( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk34])],[f26_nnf]) ).
cnf(c136,plain,
( ~ in(X3,X1)
| ~ in(X3,X2)
| X2 != set_difference(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
fof(f35,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f35_nnf,plain,
! [A,B] :
( ( A = B
| ~ subset(A,B)
| proper_subset(A,B) )
& ( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
! [A,B] :
( ( A = B
| ~ subset(A,B)
| proper_subset(A,B) )
& ( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c178,plain,
( X0 != X1
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
fof(f65,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f65_nnf,plain,
! [A] : ~ empty(powerset(A)),
inference(nnf_transformation,[status(thm)],[f65]) ).
fof(f65_sk,plain,
! [A] : ~ empty(powerset(A)),
inference(skolemisation,[status(esa)],[f65_nnf]) ).
cnf(c210,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
fof(f67,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(f67_nnf,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(nnf_transformation,[status(thm)],[f67]) ).
fof(f67_sk,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(skolemisation,[status(esa)],[f67_nnf]) ).
cnf(c212,plain,
~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
fof(f69,axiom,
! [A] : ~ empty(singleton(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(f69_nnf,plain,
! [A] : ~ empty(singleton(A)),
inference(nnf_transformation,[status(thm)],[f69]) ).
fof(f69_sk,plain,
! [A] : ~ empty(singleton(A)),
inference(skolemisation,[status(esa)],[f69_nnf]) ).
cnf(c214,plain,
~ empty(singleton(X0)),
inference(cnf_transformation,[status(esa)],[f69_sk]) ).
fof(f71,axiom,
! [A,B] : ~ empty(unordered_pair(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(f71_nnf,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(nnf_transformation,[status(thm)],[f71]) ).
fof(f71_sk,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(skolemisation,[status(esa)],[f71_nnf]) ).
cnf(c216,plain,
~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[status(esa)],[f71_sk]) ).
fof(f85,axiom,
! [A,B] : ~ proper_subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(f85_nnf,plain,
! [A,B] : ~ proper_subset(A,A),
inference(nnf_transformation,[status(thm)],[f85]) ).
fof(f85_sk,plain,
! [A] : ~ proper_subset(A,A),
inference(skolemisation,[status(esa)],[f85_nnf]) ).
cnf(c234,plain,
~ proper_subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f85_sk]) ).
fof(f86,lemma,
! [A] : singleton(A) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f86_nnf,plain,
! [A] : singleton(A) != empty_set,
inference(nnf_transformation,[status(thm)],[f86]) ).
fof(f86_sk,plain,
! [A] : singleton(A) != empty_set,
inference(skolemisation,[status(esa)],[f86_nnf]) ).
cnf(c235,plain,
singleton(X0) != empty_set,
inference(cnf_transformation,[status(esa)],[f86_sk]) ).
fof(f88,lemma,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f88_nnf,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(nnf_transformation,[status(thm)],[f88]) ).
fof(f88_sk,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(skolemisation,[status(esa)],[f88_nnf]) ).
cnf(c237,plain,
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f88_sk]) ).
fof(f101,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f101_nnf,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f101]) ).
fof(f101_sk,plain,
( relation(sk50)
& ~ empty(sk50) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk50])],[f101_nnf]) ).
cnf(c259,plain,
~ empty(sk50),
inference(cnf_transformation,[status(esa)],[f101_sk]) ).
fof(f103,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f103_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f103]) ).
fof(f103_sk,plain,
~ empty(sk52),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk52])],[f103_nnf]) ).
cnf(c263,plain,
~ empty(sk52),
inference(cnf_transformation,[status(esa)],[f103_sk]) ).
fof(f146,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(f146_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)],[f146]) ).
fof(f146_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,B)
| ~ in(C,A) )
& ( ( in(sk57(A,B),B)
& in(sk57(A,B),A) )
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk57])],[f146_nnf]) ).
cnf(c332,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f146_sk]) ).
fof(f162,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(f162_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)],[f162]) ).
fof(f162_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,set_intersection2(A,B)) )
& ( in(sk58(A,B),set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk58])],[f162_nnf]) ).
cnf(c350,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f162_sk]) ).
fof(f164,lemma,
! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
fof(f164_nnf,plain,
! [A,B,C] :
( ~ in(B,C)
| ~ in(B,subset_complement(A,C))
| ~ element(C,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f164]) ).
fof(f164_sk,plain,
! [C,A,B] :
( ~ in(B,C)
| ~ in(B,subset_complement(A,C))
| ~ element(C,powerset(A)) ),
inference(skolemisation,[status(esa)],[f164_nnf]) ).
cnf(c352,plain,
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[status(esa)],[f164_sk]) ).
fof(f166,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f166_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f166]) ).
fof(f166_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f166_nnf]) ).
cnf(c354,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f166_sk]) ).
fof(f168,lemma,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(f168_nnf,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f168]) ).
fof(f168_sk,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f168_nnf]) ).
cnf(c357,plain,
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f168_sk]) ).
fof(f172,lemma,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f172_nnf,plain,
! [A,B] :
( ( in(B,A)
| set_difference(A,singleton(B)) = A )
& ( ~ in(B,A)
| set_difference(A,singleton(B)) != A ) ),
inference(nnf_transformation,[status(thm)],[f172]) ).
fof(f172_sk,plain,
! [A,B] :
( ( in(B,A)
| set_difference(A,singleton(B)) = A )
& ( ~ in(B,A)
| set_difference(A,singleton(B)) != A ) ),
inference(skolemisation,[status(esa)],[f172_nnf]) ).
cnf(c363,plain,
( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 ),
inference(cnf_transformation,[status(esa)],[f172_sk]) ).
fof(f178,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f178_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f178]) ).
fof(f178_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f178_nnf]) ).
cnf(c373,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f178_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c56,c136,c178,c210,c212,c214,c216,c234,c235,c237,c259,c263,c279,c332,c350,c352,c354,c357,c363,c373]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t7502]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU200+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 13:09:53 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 68.74/9.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 68.74/9.24 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------