%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU143+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 : n026.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 02:51:04 PM UTC 2026
% Result : Theorem 10.75s 1.97s
% Output : Proof 10.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 76 ( 36 unt; 0 def)
% Number of atoms : 202 ( 67 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 240 ( 114 ~; 70 |; 48 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-4 aty)
% Number of variables : 140 ( 11 sgn 93 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f8_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( D = B
| D = A )
& ~ in(D,C) )
| ( D != B
& D != A
& in(D,C) ) )
| C = unordered_pair(A,B) )
& ( ! [D] :
( ( ( D != B
& D != A )
| in(D,C) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [C,A,B,D] :
( ( ( ( sk2(A,B,C) = B
| sk2(A,B,C) = A )
& ~ in(sk2(A,B,C),C) )
| ( sk2(A,B,C) != B
& sk2(A,B,C) != A
& in(sk2(A,B,C),C) )
| C = unordered_pair(A,B) )
& ( ( ( ( D != B
& D != A )
| in(D,C) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f8_nnf]) ).
cnf(c18,plain,
( X3 != X1
| in(X3,X2)
| X2 != unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi15,axiom,
ifeq(X0,unordered_pair(X1,X2),ifeq(X3,X2,in(X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
fof(f27,conjecture,
! [A] : singleton(A) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f27_neg,negated_conjecture,
~ ! [A] : singleton(A) != empty_set,
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f27_nnf,plain,
? [A] : singleton(A) = empty_set,
inference(nnf_transformation,[status(thm)],[f27_neg]) ).
fof(f27_sk,plain,
singleton(sk7) = empty_set,
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7])],[f27_nnf]) ).
cnf(c72,plain,
singleton(sk7) = empty_set,
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(hi48,negated_conjecture,
singleton(sk7) = empty_set,
inference(equality_encoding,[status(esa)],[c72]) ).
fof(f24,axiom,
! [A,B] : set_union2(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f24_nnf,plain,
! [A,B] : set_union2(A,A) = A,
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A] : set_union2(A,A) = A,
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c69,plain,
set_union2(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi46,axiom,
set_union2(X0,X0) = X0,
inference(equality_encoding,[status(esa)],[c69]) ).
fof(f57,lemma,
! [A] : unordered_pair(A,A) = singleton(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f57_nnf,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(nnf_transformation,[status(thm)],[f57]) ).
fof(f57_sk,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(skolemisation,[status(esa)],[f57_nnf]) ).
cnf(c110,plain,
unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f57_sk]) ).
cnf(hi8,axiom,
unordered_pair(X0,X0) = singleton(X0),
inference(equality_encoding,[status(esa)],[c110]) ).
cnf(h45,plain,
in(set_union2(sk7,sk7),empty_set) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi48,hi46,hi8]) ).
fof(f59,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f59_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f59]) ).
fof(f59_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f59_nnf]) ).
cnf(c112,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f59_sk]) ).
cnf(hi95,axiom,
ifeq(in(X0,X1),true,ifeq(empty(X1),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c112]) ).
fof(f21,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f21_nnf,plain,
empty(empty_set),
inference(nnf_transformation,[status(thm)],[f21]) ).
cnf(c66,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f21_nnf]) ).
cnf(hi43,axiom,
empty(empty_set) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t1,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi95,h45,hi43]) ).
cnf(t293,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(f12,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(f12_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)],[f12]) ).
fof(f12_sk,plain,
! [C,A,B,D] :
( ( ( ~ in(sk6(A,B,C),B)
& in(sk6(A,B,C),A)
& ~ in(sk6(A,B,C),C) )
| ( ( in(sk6(A,B,C),B)
| ~ in(sk6(A,B,C),A) )
& in(sk6(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,[sk6])],[f12_nnf]) ).
cnf(c47,plain,
( ~ in(X3,X1)
| ~ in(X3,X2)
| X2 != set_difference(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
fof(f14,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f14_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)],[f14]) ).
fof(f14_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)],[f14_nnf]) ).
cnf(c58,plain,
( X0 != X1
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f26,axiom,
! [A,B] : ~ proper_subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(f26_nnf,plain,
! [A,B] : ~ proper_subset(A,A),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [A] : ~ proper_subset(A,A),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c71,plain,
~ proper_subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
fof(f30,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f30_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
~ empty(sk9),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9])],[f30_nnf]) ).
cnf(c76,plain,
~ empty(sk9),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f48,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(f48_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)],[f48]) ).
fof(f48_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,B)
| ~ in(C,A) )
& ( ( in(sk11(A,B),B)
& in(sk11(A,B),A) )
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f48_nnf]) ).
cnf(c100,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
fof(f54,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(f54_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)],[f54]) ).
fof(f54_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,set_intersection2(A,B)) )
& ( in(sk12(A,B),set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12])],[f54_nnf]) ).
cnf(c107,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f54_sk]) ).
fof(f55,lemma,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(f55_nnf,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f55]) ).
fof(f55_sk,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f55_nnf]) ).
cnf(c108,plain,
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c14,c47,c58,c71,c76,c100,c107,c108,c112]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t293]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU143+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:58:54 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.75/1.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.75/1.97 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------