%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET912+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 02:44:16 PM UTC 2026
% Result : Theorem 4.94s 1.07s
% Output : Proof 4.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 33 unt; 0 def)
% Number of atoms : 79 ( 34 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 58 ( 28 ~; 14 |; 11 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 62 ( 2 sgn 33 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,conjecture,
! [A,B,C] :
( ( in(C,B)
& in(A,B) )
=> set_intersection2(unordered_pair(A,C),B) = unordered_pair(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_zfmisc_1) ).
fof(f9_neg,negated_conjecture,
~ ! [A,B,C] :
( ( in(C,B)
& in(A,B) )
=> set_intersection2(unordered_pair(A,C),B) = unordered_pair(A,C) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f9_nnf,plain,
? [A,B,C] :
( set_intersection2(unordered_pair(A,C),B) != unordered_pair(A,C)
& in(C,B)
& in(A,B) ),
inference(nnf_transformation,[status(thm)],[f9_neg]) ).
fof(f9_sk,plain,
( set_intersection2(unordered_pair(sk2,sk4),sk3) != unordered_pair(sk2,sk4)
& in(sk4,sk3)
& in(sk2,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f9_nnf]) ).
cnf(c13,plain,
set_intersection2(unordered_pair(sk2,sk4),sk3) != unordered_pair(sk2,sk4),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t29,plain,
ifeq(set_intersection2(unordered_pair(sk2,sk4),sk3),unordered_pair(sk2,sk4),false,true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
fof(f1,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f1_nnf,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t14,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t38,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(orient,[status(thm)],[t14]) ).
cnf(t70,plain,
ifeq(set_intersection2(unordered_pair(sk4,sk2),sk3),unordered_pair(sk2,sk4),false,true) = true,
inference(step,[status(thm)],[t29,t38]) ).
fof(f8,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f8_nnf,plain,
! [A,B,C] :
( ( ~ in(B,C)
| ~ in(A,C)
| subset(unordered_pair(A,B),C) )
& ( ( in(B,C)
& in(A,C) )
| ~ subset(unordered_pair(A,B),C) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C] :
( ( ~ in(B,C)
| ~ in(A,C)
| subset(unordered_pair(A,B),C) )
& ( ( in(B,C)
& in(A,C) )
| ~ subset(unordered_pair(A,B),C) ) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c10,plain,
( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,axiom,
ifeq(in(X0,X1),true,ifeq(in(X2,X1),true,subset(unordered_pair(X0,X2),X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(c11,plain,
in(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,negated_conjecture,
in(sk2,sk3) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(c12,plain,
in(sk4,sk3),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi10,negated_conjecture,
in(sk4,sk3) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h4,plain,
subset(unordered_pair(sk2,sk4),sk3) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi9,hi10]) ).
fof(f7,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f7_nnf,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi5,axiom,
ifeq(subset(X0,X1),true,set_intersection2(X0,X1),X0) = X0,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t17,plain,
set_intersection2(unordered_pair(sk2,sk4),sk3) = unordered_pair(sk2,sk4),
inference(hyper_resolution,[status(thm)],[hi5,h4]) ).
cnf(t67,plain,
set_intersection2(unordered_pair(sk4,sk2),sk3) = unordered_pair(sk2,sk4),
inference(step,[status(thm)],[t17,t38]) ).
cnf(t68,plain,
set_intersection2(unordered_pair(sk4,sk2),sk3) = unordered_pair(sk4,sk2),
inference(step,[status(thm)],[t67,t38]) ).
cnf(t49,plain,
set_intersection2(unordered_pair(sk4,sk2),sk3) = unordered_pair(sk4,sk2),
inference(orient,[status(thm)],[t68]) ).
cnf(t71,plain,
ifeq(unordered_pair(sk4,sk2),unordered_pair(sk2,sk4),false,true) = true,
inference(step,[status(thm)],[t70,t49]) ).
cnf(t72,plain,
ifeq(unordered_pair(sk4,sk2),unordered_pair(sk4,sk2),false,true) = true,
inference(step,[status(thm)],[t71,t38]) ).
cnf(t6,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t35,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(t73,plain,
false = true,
inference(step,[status(thm)],[t72,t35]) ).
cnf(t66,plain,
false = true,
inference(orient,[status(thm)],[t73]) ).
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(f5,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f5_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
~ empty(sk1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f5_nnf]) ).
cnf(c5,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c5,c13]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t66]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET912+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.34 % Computer : n014.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Thu Sep 24 12:22:05 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.94/1.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.94/1.07 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------