%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU129+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 : n002.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 02:51:01 PM UTC 2026
% Result : Theorem 75.08s 15.03s
% Output : Proof 75.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of formulae : 91 ( 55 unt; 0 def)
% Number of atoms : 167 ( 56 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 149 ( 73 ~; 43 |; 26 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 157 ( 13 sgn 78 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f23,lemma,
! [A,B,C] :
( ( subset(A,C)
& subset(A,B) )
=> subset(A,set_intersection2(B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(f23_nnf,plain,
! [A,B,C] :
( subset(A,set_intersection2(B,C))
| ~ subset(A,C)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A,B,C] :
( subset(A,set_intersection2(B,C))
| ~ subset(A,C)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c45,plain,
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(t233,plain,
ifeq(subset(X1,X2),true,ifeq(subset(X1,X3),true,subset(X1,set_intersection2(X2,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
cnf(t564,plain,
ifeq(subset(X1,X2),true,ifeq(subset(X1,X3),true,subset(X1,set_intersection2(X2,X3)),true),true) = true,
inference(orient,[status(thm)],[t233]) ).
fof(f26,conjecture,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(f26_neg,negated_conjecture,
~ ! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f26_nnf,plain,
? [A,B,C] :
( ~ subset(set_intersection2(A,C),set_intersection2(B,C))
& subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f26_neg]) ).
fof(f26_sk,plain,
( ~ subset(set_intersection2(sk6,sk8),set_intersection2(sk7,sk8))
& subset(sk6,sk7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk6,sk7,sk8])],[f26_nnf]) ).
cnf(c49,plain,
~ subset(set_intersection2(sk6,sk8),set_intersection2(sk7,sk8)),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(t179,plain,
subset(set_intersection2(sk6,sk8),set_intersection2(sk7,sk8)) = false,
inference(equality_encoding,[status(esa)],[c49]) ).
fof(f2,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f2_nnf,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t100,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t778,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(orient,[status(thm)],[t100]) ).
cnf(t1253,plain,
subset(set_intersection2(sk8,sk6),set_intersection2(sk7,sk8)) = false,
inference(step,[status(thm)],[t179,t778]) ).
cnf(t1254,plain,
subset(set_intersection2(sk8,sk6),set_intersection2(sk8,sk7)) = false,
inference(step,[status(thm)],[t1253,t778]) ).
cnf(t816,plain,
subset(set_intersection2(sk8,sk6),set_intersection2(sk8,sk7)) = false,
inference(orient,[status(thm)],[t1254]) ).
cnf(t830,plain,
true = ifeq(subset(set_intersection2(sk8,sk6),sk8),true,ifeq(subset(set_intersection2(sk8,sk6),sk7),true,false,true),true),
inference(cp,[status(thm)],[t564,t816]) ).
fof(f22,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f22_nnf,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c44,plain,
subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t142,plain,
subset(set_intersection2(X1,X2),X1) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
cnf(t342,plain,
subset(set_intersection2(X1,X2),X1) = true,
inference(orient,[status(thm)],[t142]) ).
cnf(t1291,plain,
true = ifeq(true,true,ifeq(subset(set_intersection2(sk8,sk6),sk7),true,false,true),true),
inference(step,[status(thm)],[t830,t342]) ).
cnf(t99,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t264,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t99]) ).
cnf(t1292,plain,
true = ifeq(subset(set_intersection2(sk8,sk6),sk7),true,false,true),
inference(step,[status(thm)],[t1291,t264]) ).
fof(f25,lemma,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f25_nnf,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c47,plain,
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(t229,plain,
ifeq(subset(X1,X2),true,ifeq(subset(X2,X3),true,subset(X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c47]) ).
cnf(t520,plain,
ifeq(subset(X1,X2),true,ifeq(subset(X2,X3),true,subset(X1,X3),true),true) = true,
inference(orient,[status(thm)],[t229]) ).
fof(f3,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f3_nnf,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi2,axiom,
ifeq(X0,X1,subset(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(hi63,axiom,
or(false,X0) = X0,
introduced(definition) ).
cnf(h117,plain,
subset(or(false,V0),V0) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi63]) ).
cnf(hi35,axiom,
ifeq(subset(X0,X1),true,ifeq(subset(X1,X2),true,subset(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c47]) ).
cnf(c48,plain,
subset(sk6,sk7),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(hi36,negated_conjecture,
subset(sk6,sk7) = true,
inference(equality_encoding,[status(esa)],[c48]) ).
cnf(t140,plain,
subset(or(false,sk6),sk7) = true,
inference(hyper_resolution,[status(thm)],[hi35,h117,hi36]) ).
cnf(t23,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t257,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t23]) ).
cnf(t1221,plain,
subset(sk6,sk7) = true,
inference(step,[status(thm)],[t140,t257]) ).
cnf(t338,plain,
subset(sk6,sk7) = true,
inference(orient,[status(thm)],[t1221]) ).
cnf(t544,plain,
true = ifeq(subset(X1,sk6),true,ifeq(true,true,subset(X1,sk7),true),true),
inference(cp,[status(thm)],[t520,t338]) ).
cnf(t1284,plain,
true = ifeq(subset(X1,sk6),true,subset(X1,sk7),true),
inference(step,[status(thm)],[t544,t264]) ).
cnf(t1112,plain,
ifeq(subset(X1,sk6),true,subset(X1,sk7),true) = true,
inference(orient,[status(thm)],[t1284]) ).
cnf(t780,plain,
true = subset(set_intersection2(X1,X2),X2),
inference(cp,[status(thm)],[t342,t778]) ).
cnf(t882,plain,
subset(set_intersection2(X1,X2),X2) = true,
inference(orient,[status(thm)],[t780]) ).
cnf(t1113,plain,
true = ifeq(true,true,subset(set_intersection2(X1,sk6),sk7),true),
inference(cp,[status(thm)],[t1112,t882]) ).
cnf(t1285,plain,
true = subset(set_intersection2(X1,sk6),sk7),
inference(step,[status(thm)],[t1113,t264]) ).
cnf(t1115,plain,
subset(set_intersection2(X1,sk6),sk7) = true,
inference(orient,[status(thm)],[t1285]) ).
cnf(t1293,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t1292,t1115]) ).
cnf(t1294,plain,
true = false,
inference(step,[status(thm)],[t1293,t264]) ).
cnf(t1198,plain,
false = true,
inference(orient,[status(thm)],[t1294]) ).
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(f4,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f4_nnf,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( ( in(sk0(A),A)
| A = empty_set )
& ( ~ in(B,A)
| A != empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f4_nnf]) ).
cnf(c6,plain,
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f18,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f18_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
~ empty(sk5),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f18_nnf]) ).
cnf(c40,plain,
~ empty(sk5),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f29,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(f29_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)],[f29]) ).
fof(f29_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,B)
| ~ in(C,A) )
& ( ( in(sk9(A,B),B)
& in(sk9(A,B),A) )
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9])],[f29_nnf]) ).
cnf(c54,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
fof(f31,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(f31_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)],[f31]) ).
fof(f31_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,set_intersection2(A,B)) )
& ( in(sk10(A,B),set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f31_nnf]) ).
cnf(c57,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
fof(f33,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f33_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c59,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c6,c40,c49,c54,c57,c59]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1198]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU129+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.36 % Computer : n002.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Thu Sep 24 12:54:40 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 75.08/15.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 75.08/15.03 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------