%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU129+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 17.45s 2.66s
% Output : Proof 17.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 9
% Syntax : Number of formulae : 92 ( 68 unt; 0 def)
% Number of atoms : 156 ( 69 equ)
% Maximal formula atoms : 14 ( 1 avg)
% Number of connectives : 118 ( 54 ~; 37 |; 20 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 151 ( 13 sgn 45 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f2_nnf,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk0(A,B),B)
& in(sk0(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c4,plain,
( ~ in(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t26,plain,
ifeq(in(sk0(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t55,plain,
ifeq(in(sk0(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(orient,[status(thm)],[t26]) ).
fof(f3,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f3_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_intersection2(A,B) )
& ( ! [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [C,A,B,D] :
( ( ( in(sk1(A,B,C),B)
& in(sk1(A,B,C),A)
& ~ in(sk1(A,B,C),C) )
| ( ( ~ in(sk1(A,B,C),B)
| ~ in(sk1(A,B,C),A) )
& in(sk1(A,B,C),C) )
| C = set_intersection2(A,B) )
& ( ( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f3_nnf]) ).
cnf(c7,plain,
( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2)
| X2 != set_intersection2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t35,plain,
ifeq(X1,set_intersection2(X2,X3),ifeq(in(X4,X2),true,ifeq(in(X4,X3),true,in(X4,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t44,plain,
ifeq(X1,set_intersection2(X2,X3),ifeq(in(X4,X2),true,ifeq(in(X4,X3),true,in(X4,X1),true),true),true) = true,
inference(orient,[status(thm)],[t35]) ).
cnf(c5,plain,
( in(X3,X0)
| ~ in(X3,X2)
| X2 != set_intersection2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t30,plain,
ifeq(X1,set_intersection2(X2,X3),ifeq(in(X4,X1),true,in(X4,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t50,plain,
ifeq(X1,set_intersection2(X2,X3),ifeq(in(X4,X1),true,in(X4,X2),true),true) = true,
inference(orient,[status(thm)],[t30]) ).
cnf(t15,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t37,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t15]) ).
cnf(t51,plain,
true = ifeq(in(X1,set_intersection2(X2,X3)),true,in(X1,X2),true),
inference(cp,[status(thm)],[t50,t37]) ).
cnf(t243,plain,
ifeq(in(X1,set_intersection2(X2,X3)),true,in(X1,X2),true) = true,
inference(orient,[status(thm)],[t51]) ).
cnf(c3,plain,
( in(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t24,plain,
or(subset(X1,X2),in(sk0(X1,X2),X1)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t64,plain,
or(subset(X1,X2),in(sk0(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t24]) ).
fof(f11,conjecture,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(f11_neg,negated_conjecture,
~ ! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
? [A,B,C] :
( ~ subset(set_intersection2(A,C),set_intersection2(B,C))
& subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
( ~ subset(set_intersection2(sk4,sk6),set_intersection2(sk5,sk6))
& subset(sk4,sk5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6])],[f11_nnf]) ).
cnf(c22,plain,
~ subset(set_intersection2(sk4,sk6),set_intersection2(sk5,sk6)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t21,plain,
subset(set_intersection2(sk4,sk6),set_intersection2(sk5,sk6)) = false,
inference(equality_encoding,[status(esa)],[c22]) ).
fof(f1,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f1_nnf,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t16,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t94,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(orient,[status(thm)],[t16]) ).
cnf(t2730,plain,
subset(set_intersection2(sk6,sk4),set_intersection2(sk5,sk6)) = false,
inference(step,[status(thm)],[t21,t94]) ).
cnf(t2731,plain,
subset(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)) = false,
inference(step,[status(thm)],[t2730,t94]) ).
cnf(t120,plain,
subset(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)) = false,
inference(orient,[status(thm)],[t2731]) ).
cnf(t121,plain,
true = or(false,in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),set_intersection2(sk6,sk4))),
inference(cp,[status(thm)],[t64,t120]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t43,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t2752,plain,
true = in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),set_intersection2(sk6,sk4)),
inference(step,[status(thm)],[t121,t43]) ).
cnf(t246,plain,
in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),set_intersection2(sk6,sk4)) = true,
inference(orient,[status(thm)],[t2752]) ).
cnf(t247,plain,
true = ifeq(true,true,in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),sk6),true),
inference(cp,[status(thm)],[t243,t246]) ).
cnf(t2756,plain,
true = in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),sk6),
inference(step,[status(thm)],[t247,t37]) ).
cnf(t279,plain,
in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),sk6) = true,
inference(orient,[status(thm)],[t2756]) ).
cnf(t294,plain,
true = ifeq(X1,set_intersection2(sk6,X2),ifeq(true,true,ifeq(in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),X2),true,in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),X1),true),true),true),
inference(cp,[status(thm)],[t44,t279]) ).
cnf(t3156,plain,
true = ifeq(X1,set_intersection2(sk6,X2),ifeq(in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),X2),true,in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),X1),true),true),
inference(step,[status(thm)],[t294,t37]) ).
cnf(t2402,plain,
ifeq(X1,set_intersection2(sk6,X2),ifeq(in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),X2),true,in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),X1),true),true) = true,
inference(orient,[status(thm)],[t3156]) ).
cnf(c2,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t32,plain,
ifeq(subset(X1,X2),true,ifeq(in(X3,X1),true,in(X3,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t58,plain,
ifeq(subset(X1,X2),true,ifeq(in(X3,X1),true,in(X3,X2),true),true) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(c21,plain,
subset(sk4,sk5),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t14,plain,
subset(sk4,sk5) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t83,plain,
subset(sk4,sk5) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t84,plain,
true = ifeq(true,true,ifeq(in(X1,sk4),true,in(X1,sk5),true),true),
inference(cp,[status(thm)],[t58,t83]) ).
cnf(t2746,plain,
true = ifeq(in(X1,sk4),true,in(X1,sk5),true),
inference(step,[status(thm)],[t84,t37]) ).
cnf(t198,plain,
ifeq(in(X1,sk4),true,in(X1,sk5),true) = true,
inference(orient,[status(thm)],[t2746]) ).
cnf(c6,plain,
( in(X3,X1)
| ~ in(X3,X2)
| X2 != set_intersection2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t31,plain,
ifeq(X1,set_intersection2(X2,X3),ifeq(in(X4,X1),true,in(X4,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t47,plain,
ifeq(X1,set_intersection2(X2,X3),ifeq(in(X4,X1),true,in(X4,X3),true),true) = true,
inference(orient,[status(thm)],[t31]) ).
cnf(t48,plain,
true = ifeq(in(X1,set_intersection2(X2,X3)),true,in(X1,X3),true),
inference(cp,[status(thm)],[t47,t37]) ).
cnf(t218,plain,
ifeq(in(X1,set_intersection2(X2,X3)),true,in(X1,X3),true) = true,
inference(orient,[status(thm)],[t48]) ).
cnf(t249,plain,
true = ifeq(true,true,in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),sk4),true),
inference(cp,[status(thm)],[t218,t246]) ).
cnf(t2761,plain,
true = in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),sk4),
inference(step,[status(thm)],[t249,t37]) ).
cnf(t311,plain,
in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),sk4) = true,
inference(orient,[status(thm)],[t2761]) ).
cnf(t312,plain,
true = ifeq(true,true,in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),sk5),true),
inference(cp,[status(thm)],[t198,t311]) ).
cnf(t2768,plain,
true = in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),sk5),
inference(step,[status(thm)],[t312,t37]) ).
cnf(t362,plain,
in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),sk5) = true,
inference(orient,[status(thm)],[t2768]) ).
cnf(t2413,plain,
true = ifeq(X1,set_intersection2(sk6,sk5),ifeq(true,true,in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),X1),true),true),
inference(cp,[status(thm)],[t2402,t362]) ).
cnf(t3158,plain,
true = ifeq(X1,set_intersection2(sk6,sk5),in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),X1),true),
inference(step,[status(thm)],[t2413,t37]) ).
cnf(t2431,plain,
ifeq(X1,set_intersection2(sk6,sk5),in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),X1),true) = true,
inference(orient,[status(thm)],[t3158]) ).
cnf(t2432,plain,
true = in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),set_intersection2(sk6,sk5)),
inference(cp,[status(thm)],[t2431,t37]) ).
cnf(t2433,plain,
in(sk0(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),set_intersection2(sk6,sk5)) = true,
inference(orient,[status(thm)],[t2432]) ).
cnf(t2443,plain,
true = ifeq(true,true,subset(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),true),
inference(cp,[status(thm)],[t55,t2433]) ).
cnf(t3161,plain,
true = subset(set_intersection2(sk6,sk4),set_intersection2(sk6,sk5)),
inference(step,[status(thm)],[t2443,t37]) ).
cnf(t3162,plain,
true = false,
inference(step,[status(thm)],[t3161,t120]) ).
cnf(t2484,plain,
false = true,
inference(orient,[status(thm)],[t3162]) ).
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(f9,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f9_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
~ empty(sk3),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f9_nnf]) ).
cnf(c19,plain,
~ empty(sk3),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
fof(f14,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f14_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c25,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c19,c22,c25]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2484]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU129+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n007.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 12:49:07 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 17.45/2.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.45/2.66 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------