%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU152+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 02:51:07 PM UTC 2026
% Result : Theorem 17.32s 2.67s
% Output : Proof 17.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 78 ( 30 unt; 0 def)
% Number of atoms : 189 ( 46 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 222 ( 111 ~; 61 |; 40 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-4 aty)
% Number of variables : 137 ( 7 sgn 93 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f31,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f31_nnf,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c83,plain,
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(hi54,axiom,
ifeq(in(X0,X1),true,subset(singleton(X0),X1),true) = true,
inference(equality_encoding,[status(esa)],[c83]) ).
fof(f30,conjecture,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(f30_neg,negated_conjecture,
~ ! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f30_nnf,plain,
? [A,B] :
( set_union2(singleton(A),B) != B
& in(A,B) ),
inference(nnf_transformation,[status(thm)],[f30_neg]) ).
fof(f30_sk,plain,
( set_union2(singleton(sk8),sk9) != sk9
& in(sk8,sk9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9])],[f30_nnf]) ).
cnf(c80,plain,
in(sk8,sk9),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(hi52,negated_conjecture,
in(sk8,sk9) = true,
inference(equality_encoding,[status(esa)],[c80]) ).
fof(f65,lemma,
! [A] : unordered_pair(A,A) = singleton(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f65_nnf,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(nnf_transformation,[status(thm)],[f65]) ).
fof(f65_sk,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(skolemisation,[status(esa)],[f65_nnf]) ).
cnf(c127,plain,
unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
cnf(hi8,axiom,
unordered_pair(X0,X0) = singleton(X0),
inference(equality_encoding,[status(esa)],[c127]) ).
cnf(h166,plain,
subset(unordered_pair(sk8,sk8),sk9) = true,
inference(hyper_resolution,[status(thm)],[hi54,hi52,hi8]) ).
fof(f40,lemma,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f40_nnf,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c95,plain,
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(hi65,axiom,
ifeq(subset(X0,X1),true,set_union2(X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c95]) ).
cnf(h4058,plain,
set_union2(unordered_pair(sk8,sk8),sk9) = sk9,
inference(hyper_resolution,[status(thm)],[hi65,h166]) ).
cnf(c81,plain,
set_union2(singleton(sk8),sk9) != sk9,
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(hi107,negated_conjecture,
ifeq(set_union2(singleton(sk8),sk9),sk9,false,true) = true,
inference(equality_encoding,[status(esa)],[c81]) ).
cnf(t1,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi107,h4058,hi8]) ).
cnf(t280,plain,
false = true,
inference(orient,[status(thm)],[t1]) ).
fof(f0,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/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/sandbox2/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(f7,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f7_nnf,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B] :
( ( in(sk1(A),A)
| A = empty_set )
& ( ~ in(B,A)
| A != empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f7_nnf]) ).
cnf(c14,plain,
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f13,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f13_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)],[f13]) ).
fof(f13_sk,plain,
! [C,A,B,D] :
( ( ( ~ in(sk7(A,B,C),B)
& in(sk7(A,B,C),A)
& ~ in(sk7(A,B,C),C) )
| ( ( in(sk7(A,B,C),B)
| ~ in(sk7(A,B,C),A) )
& in(sk7(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,[sk7])],[f13_nnf]) ).
cnf(c53,plain,
( ~ in(X3,X1)
| ~ in(X3,X2)
| X2 != set_difference(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
fof(f15,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f15_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)],[f15]) ).
fof(f15_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)],[f15_nnf]) ).
cnf(c64,plain,
( X0 != X1
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
fof(f28,axiom,
! [A,B] : ~ proper_subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(f28_nnf,plain,
! [A,B] : ~ proper_subset(A,A),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [A] : ~ proper_subset(A,A),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c78,plain,
~ proper_subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
fof(f29,lemma,
! [A] : singleton(A) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f29_nnf,plain,
! [A] : singleton(A) != empty_set,
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [A] : singleton(A) != empty_set,
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c79,plain,
singleton(X0) != empty_set,
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
fof(f36,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f36_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
~ empty(sk11),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f36_nnf]) ).
cnf(c91,plain,
~ empty(sk11),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
fof(f56,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/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f56_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)],[f56]) ).
fof(f56_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,B)
| ~ in(C,A) )
& ( ( in(sk13(A,B),B)
& in(sk13(A,B),A) )
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13])],[f56_nnf]) ).
cnf(c117,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
fof(f62,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/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f62_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)],[f62]) ).
fof(f62_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,set_intersection2(A,B)) )
& ( in(sk14(A,B),set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk14])],[f62_nnf]) ).
cnf(c124,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f62_sk]) ).
fof(f63,lemma,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(f63_nnf,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f63]) ).
fof(f63_sk,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f63_nnf]) ).
cnf(c125,plain,
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f63_sk]) ).
fof(f68,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f68_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f68]) ).
fof(f68_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f68_nnf]) ).
cnf(c130,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f68_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c14,c53,c64,c78,c79,c81,c91,c117,c124,c125,c130]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t280]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU152+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n018.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 13:00:18 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 17.32/2.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.32/2.67 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------