%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU154+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 : n001.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 02:51:08 PM UTC 2026
% Result : Theorem 81.38s 10.73s
% Output : Proof 81.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 94 ( 44 unt; 0 def)
% Number of atoms : 221 ( 67 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 254 ( 127 ~; 70 |; 47 &)
% ( 6 <=>; 4 =>; 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 : 163 ( 9 sgn 93 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f58,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(f58_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)],[f58]) ).
fof(f58_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])],[f58_nnf]) ).
cnf(c118,plain,
( in(sk13(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
cnf(t171,plain,
or(disjoint(X1,X2),in(sk13(X1,X2),X2)) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(t904,plain,
or(disjoint(X1,X2),in(sk13(X1,X2),X2)) = true,
inference(orient,[status(thm)],[t171]) ).
fof(f6,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f6_nnf,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
& ~ in(C,B) )
| ( C != A
& in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [B,A,C] :
( ( ( sk0(A,B) = A
& ~ in(sk0(A,B),B) )
| ( sk0(A,B) != A
& in(sk0(A,B),B) )
| B = singleton(A) )
& ( ( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f6_nnf]) ).
cnf(c8,plain,
( X2 = X0
| ~ in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t197,plain,
ifeq(X1,singleton(X2),ifeq(in(X3,X1),true,X3,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t257,plain,
ifeq(X1,singleton(X2),ifeq(in(X3,X1),true,X3,X2),X2) = X2,
inference(orient,[status(thm)],[t197]) ).
cnf(t73,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t73]) ).
cnf(t258,plain,
X1 = ifeq(in(X2,singleton(X1)),true,X2,X1),
inference(cp,[status(thm)],[t257,t256]) ).
cnf(t2119,plain,
ifeq(in(X1,singleton(X2)),true,X1,X2) = X2,
inference(orient,[status(thm)],[t258]) ).
cnf(c117,plain,
( in(sk13(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
cnf(t170,plain,
or(disjoint(X1,X2),in(sk13(X1,X2),X1)) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(t905,plain,
or(disjoint(X1,X2),in(sk13(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t170]) ).
fof(f32,conjecture,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f32_neg,negated_conjecture,
~ ! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f32_nnf,plain,
? [A,B] :
( ~ disjoint(singleton(A),B)
& ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f32_neg]) ).
fof(f32_sk,plain,
( ~ disjoint(singleton(sk8),sk9)
& ~ in(sk8,sk9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9])],[f32_nnf]) ).
cnf(c83,plain,
~ disjoint(singleton(sk8),sk9),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(t56,plain,
disjoint(singleton(sk8),sk9) = false,
inference(equality_encoding,[status(esa)],[c83]) ).
cnf(t1771,plain,
disjoint(singleton(sk8),sk9) = false,
inference(orient,[status(thm)],[t56]) ).
cnf(t1777,plain,
true = or(false,in(sk13(singleton(sk8),sk9),singleton(sk8))),
inference(cp,[status(thm)],[t905,t1771]) ).
cnf(t18,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t272,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t18]) ).
cnf(t3307,plain,
true = in(sk13(singleton(sk8),sk9),singleton(sk8)),
inference(step,[status(thm)],[t1777,t272]) ).
cnf(t3070,plain,
in(sk13(singleton(sk8),sk9),singleton(sk8)) = true,
inference(orient,[status(thm)],[t3307]) ).
cnf(t3072,plain,
sk8 = ifeq(true,true,sk13(singleton(sk8),sk9),sk8),
inference(cp,[status(thm)],[t2119,t3070]) ).
cnf(t3308,plain,
sk8 = sk13(singleton(sk8),sk9),
inference(step,[status(thm)],[t3072,t256]) ).
cnf(t3116,plain,
sk13(singleton(sk8),sk9) = sk8,
inference(orient,[status(thm)],[t3308]) ).
cnf(t3117,plain,
true = or(disjoint(singleton(sk8),sk9),in(sk8,sk9)),
inference(cp,[status(thm)],[t904,t3116]) ).
cnf(t3311,plain,
true = or(false,in(sk8,sk9)),
inference(step,[status(thm)],[t3117,t1771]) ).
cnf(t3312,plain,
true = in(sk8,sk9),
inference(step,[status(thm)],[t3311,t272]) ).
cnf(c82,plain,
~ in(sk8,sk9),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(t15,plain,
in(sk8,sk9) = false,
inference(equality_encoding,[status(esa)],[c82]) ).
cnf(t1646,plain,
in(sk8,sk9) = false,
inference(orient,[status(thm)],[t15]) ).
cnf(t3313,plain,
true = false,
inference(step,[status(thm)],[t3312,t1646]) ).
cnf(t3119,plain,
false = true,
inference(orient,[status(thm)],[t3313]) ).
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(f7,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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(f31,lemma,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f31_nnf,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c81,plain,
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
fof(f38,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f38_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
~ empty(sk11),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f38_nnf]) ).
cnf(c93,plain,
~ empty(sk11),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(c119,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
fof(f64,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(f64_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)],[f64]) ).
fof(f64_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])],[f64_nnf]) ).
cnf(c126,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
fof(f65,lemma,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(f65_nnf,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f65]) ).
fof(f65_sk,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f65_nnf]) ).
cnf(c127,plain,
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
fof(f70,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f70_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f70]) ).
fof(f70_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f70_nnf]) ).
cnf(c132,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f70_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c14,c53,c64,c78,c79,c81,c82,c83,c93,c119,c126,c127,c132]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t3119]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU154+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 13:04:23 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 81.38/10.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 81.38/10.73 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------