%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU151+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 : n014.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 108.00s 15.17s
% Output : Proof 108.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 99 ( 54 unt; 0 def)
% Number of atoms : 236 ( 103 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 267 ( 130 ~; 73 |; 56 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-4 aty)
% Number of variables : 191 ( 16 sgn 100 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f9_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)],[f9]) ).
fof(f9_sk,plain,
! [C,A,B,D] :
( ( ( ( sk3(A,B,C) = B
| sk3(A,B,C) = A )
& ~ in(sk3(A,B,C),C) )
| ( sk3(A,B,C) != B
& sk3(A,B,C) != A
& in(sk3(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,[sk3])],[f9_nnf]) ).
cnf(c22,plain,
( X3 = X1
| X3 = X0
| ~ in(X3,X2)
| X2 != unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t225,plain,
ifeq(X1,unordered_pair(X2,X3),ifeq(in(X4,X1),true,or(eq(X4,X2),eq(X4,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t427,plain,
ifeq(X1,unordered_pair(X2,X3),ifeq(in(X4,X1),true,or(eq(X4,X2),eq(X4,X3)),true),true) = true,
inference(orient,[status(thm)],[t225]) ).
cnf(t66,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t66]) ).
cnf(t428,plain,
true = ifeq(in(X1,unordered_pair(X2,X3)),true,or(eq(X1,X2),eq(X1,X3)),true),
inference(cp,[status(thm)],[t427,t256]) ).
cnf(t29022,plain,
ifeq(in(X1,unordered_pair(X2,X3)),true,or(eq(X1,X2),eq(X1,X3)),true) = true,
inference(orient,[status(thm)],[t428]) ).
cnf(c24,plain,
( X3 != X1
| in(X3,X2)
| X2 != unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t186,plain,
ifeq(X1,unordered_pair(X2,X3),ifeq(X4,X3,in(X4,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t409,plain,
ifeq(X1,unordered_pair(X2,X3),ifeq(X4,X3,in(X4,X1),true),true) = true,
inference(orient,[status(thm)],[t186]) ).
cnf(t410,plain,
true = ifeq(X1,X2,in(X1,unordered_pair(X3,X2)),true),
inference(cp,[status(thm)],[t409,t256]) ).
cnf(t4242,plain,
ifeq(X1,X2,in(X1,unordered_pair(X3,X2)),true) = true,
inference(orient,[status(thm)],[t410]) ).
cnf(t4243,plain,
true = in(X1,unordered_pair(X2,X1)),
inference(cp,[status(thm)],[t4242,t256]) ).
cnf(t4250,plain,
in(X1,unordered_pair(X2,X1)) = true,
inference(orient,[status(thm)],[t4243]) ).
fof(f38,conjecture,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(f38_neg,negated_conjecture,
~ ! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f38_nnf,plain,
? [A,B,C,D] :
( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
inference(nnf_transformation,[status(thm)],[f38_neg]) ).
fof(f38_sk,plain,
( sk10 != sk13
& sk10 != sk12
& unordered_pair(sk10,sk11) = unordered_pair(sk12,sk13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10,sk11,sk12,sk13])],[f38_nnf]) ).
cnf(c92,plain,
unordered_pair(sk10,sk11) = unordered_pair(sk12,sk13),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(t96,plain,
unordered_pair(sk12,sk13) = unordered_pair(sk10,sk11),
inference(equality_encoding,[status(esa)],[c92]) ).
fof(f2,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f2_nnf,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t95,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t1816,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(orient,[status(thm)],[t95]) ).
cnf(t29508,plain,
unordered_pair(sk13,sk12) = unordered_pair(sk10,sk11),
inference(step,[status(thm)],[t96,t1816]) ).
cnf(t29509,plain,
unordered_pair(sk13,sk12) = unordered_pair(sk11,sk10),
inference(step,[status(thm)],[t29508,t1816]) ).
cnf(t1836,plain,
unordered_pair(sk11,sk10) = unordered_pair(sk13,sk12),
inference(orient,[status(thm)],[t29509]) ).
cnf(t4251,plain,
true = in(sk10,unordered_pair(sk13,sk12)),
inference(cp,[status(thm)],[t4250,t1836]) ).
cnf(t4282,plain,
in(sk10,unordered_pair(sk13,sk12)) = true,
inference(orient,[status(thm)],[t4251]) ).
cnf(t29039,plain,
true = ifeq(true,true,or(eq(sk10,sk13),eq(sk10,sk12)),true),
inference(cp,[status(thm)],[t29022,t4282]) ).
cnf(t29996,plain,
true = or(eq(sk10,sk13),eq(sk10,sk12)),
inference(step,[status(thm)],[t29039,t256]) ).
cnf(c94,plain,
sk10 != sk13,
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(t16,plain,
eq(sk10,sk13) = false,
inference(equality_encoding,[status(esa)],[c94]) ).
cnf(t1350,plain,
eq(sk10,sk13) = false,
inference(orient,[status(thm)],[t16]) ).
cnf(t29997,plain,
true = or(false,eq(sk10,sk12)),
inference(step,[status(thm)],[t29996,t1350]) ).
cnf(t19,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t271,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t19]) ).
cnf(t29998,plain,
true = eq(sk10,sk12),
inference(step,[status(thm)],[t29997,t271]) ).
cnf(c93,plain,
sk10 != sk12,
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(t15,plain,
eq(sk10,sk12) = false,
inference(equality_encoding,[status(esa)],[c93]) ).
cnf(t1344,plain,
eq(sk10,sk12) = false,
inference(orient,[status(thm)],[t15]) ).
cnf(t29999,plain,
true = false,
inference(step,[status(thm)],[t29998,t1344]) ).
cnf(t29088,plain,
false = true,
inference(orient,[status(thm)],[t29999]) ).
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(f35,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f35_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
~ empty(sk9),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9])],[f35_nnf]) ).
cnf(c89,plain,
~ empty(sk9),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
fof(f55,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(f55_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)],[f55]) ).
fof(f55_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,B)
| ~ in(C,A) )
& ( ( in(sk15(A,B),B)
& in(sk15(A,B),A) )
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk15])],[f55_nnf]) ).
cnf(c117,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
fof(f61,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(f61_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)],[f61]) ).
fof(f61_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,set_intersection2(A,B)) )
& ( in(sk16(A,B),set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16])],[f61_nnf]) ).
cnf(c124,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f61_sk]) ).
fof(f62,lemma,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(f62_nnf,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f62]) ).
fof(f62_sk,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f62_nnf]) ).
cnf(c125,plain,
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f62_sk]) ).
fof(f67,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f67_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f67]) ).
fof(f67_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f67_nnf]) ).
cnf(c130,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c14,c53,c64,c78,c79,c89,c93,c94,c117,c124,c125,c130]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t29088]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU151+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.06/0.32 % Computer : n014.cluster.edu
% 0.06/0.32 % Model : x86_64 x86_64
% 0.06/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.32 % Memory : 8046.5625MB
% 0.06/0.32 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Thu Sep 24 12:57:48 UTC 2026
% 0.06/0.33 % CPUTime :
% 0.06/0.33 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 108.00/15.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 108.00/15.17 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------