%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET945+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 : Sun Sep 27 08:37:20 AM UTC 2026
% Result : Theorem 183.91s 24.81s
% Output : CNFRefutation 183.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 61 ( 23 unt; 0 def)
% Number of atoms : 207 ( 40 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 247 ( 101 ~; 96 |; 40 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 184 ( 26 sgn 93 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('theBenchmark.p',d4_tarski) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t4_xboole_0,axiom,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t4_xboole_0) ).
fof(t98_zfmisc_1,conjecture,
! [A,B] :
( ! [C] :
( in(C,A)
=> disjoint(C,B) )
=> disjoint(union(A),B) ),
file('theBenchmark.p',t98_zfmisc_1) ).
fof(t98_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( ! [C] :
( in(C,A)
=> disjoint(C,B) )
=> disjoint(union(A),B) ),
inference(assume_negation,[status(cth)],[t98_zfmisc_1]) ).
cnf(c_11,plain,
( ~ in(B,A)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[antisymmetry_r2_hidden]) ).
cnf(c_12,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(nnf_3,plain,
! [A,B,C] :
( ( ? [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| in(D,C) ) )
| set_intersection2(A,B) = C )
& ( ! [X0] :
( ( ~ in(X0,B)
| ~ in(X0,A)
| in(X0,C) )
& ( ( in(X0,B)
& in(X0,A) )
| ~ in(X0,C) ) )
| set_intersection2(A,B) != C ) ),
inference(fof_nnf,[status(thm)],[d3_xboole_0]) ).
fof(sk_d3_xboole_0_sk,plain,
! [A,B,C] :
( ( ( ( ~ in(sK0(A,B,C),B)
| ~ in(sK0(A,B,C),A)
| ~ in(sK0(A,B,C),C) )
& ( ( in(sK0(A,B,C),B)
& in(sK0(A,B,C),A) )
| in(sK0(A,B,C),C) ) )
| set_intersection2(A,B) = C )
& ( ! [X0] :
( ( ~ in(X0,B)
| ~ in(X0,A)
| in(X0,C) )
& ( ( in(X0,B)
& in(X0,A) )
| ~ in(X0,C) ) )
| set_intersection2(A,B) != C ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(D,sK0(A,B,C))],[nnf_3]) ).
fof(sk_d3_xboole_0,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ in(sK0(VAR_0,VAR_1,VAR_2),VAR_1)
| ~ in(sK0(VAR_0,VAR_1,VAR_2),VAR_0)
| ~ in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| set_intersection2(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK0(VAR_0,VAR_1,VAR_2),VAR_1)
| in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| set_intersection2(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK0(VAR_0,VAR_1,VAR_2),VAR_0)
| in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| set_intersection2(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ in(VAR_3,VAR_1)
| ~ in(VAR_3,VAR_0)
| in(VAR_3,VAR_2)
| set_intersection2(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(VAR_3,VAR_1)
| ~ in(VAR_3,VAR_2)
| set_intersection2(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(VAR_3,VAR_0)
| ~ in(VAR_3,VAR_2)
| set_intersection2(VAR_0,VAR_1) != VAR_2 ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_xboole_0_sk]) ).
cnf(c_13,plain,
( in(D,A)
| ~ in(D,C)
| set_intersection2(A,B) != C ),
inference(split_conjunct,[status(thm)],[sk_d3_xboole_0]) ).
cnf(c_14,plain,
( in(D,B)
| ~ in(D,C)
| set_intersection2(A,B) != C ),
inference(split_conjunct,[status(thm)],[sk_d3_xboole_0]) ).
cnf(c_15,plain,
( ~ in(D,B)
| ~ in(D,A)
| in(D,C)
| set_intersection2(A,B) != C ),
inference(split_conjunct,[status(thm)],[sk_d3_xboole_0]) ).
cnf(c_16,plain,
( in(sK0(A,B,C),A)
| in(sK0(A,B,C),C)
| set_intersection2(A,B) = C ),
inference(split_conjunct,[status(thm)],[sk_d3_xboole_0]) ).
fof(nnf_4,plain,
! [A,B] :
( ( ? [C] :
( ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| ~ in(C,B) )
& ( ? [X0] :
( in(X0,A)
& in(C,X0) )
| in(C,B) ) )
| union(A) = B )
& ( ! [X1] :
( ( ! [X3] :
( ~ in(X3,A)
| ~ in(X1,X3) )
| in(X1,B) )
& ( ? [X2] :
( in(X2,A)
& in(X1,X2) )
| ~ in(X1,B) ) )
| union(A) != B ) ),
inference(fof_nnf,[status(thm)],[d4_tarski]) ).
fof(sk_d4_tarski_sk,plain,
! [A,B] :
( ( ( ( ! [D] :
( ~ in(D,A)
| ~ in(sK5(A,B),D) )
| ~ in(sK5(A,B),B) )
& ( ( in(sK6(A,B),A)
& in(sK5(A,B),sK6(A,B)) )
| in(sK5(A,B),B) ) )
| union(A) = B )
& ( ! [X1] :
( ( ! [X3] :
( ~ in(X3,A)
| ~ in(X1,X3) )
| in(X1,B) )
& ( ( in(sK1(A,B,X1),A)
& in(X1,sK1(A,B,X1)) )
| ~ in(X1,B) ) )
| union(A) != B ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK5,sK6]),skolemize(X2,sK1(A,B,X1)),skolemize(C,sK5(A,B)),skolemize(X0,sK6(A,B))],[nnf_4]) ).
fof(sk_d4_tarski,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ in(VAR_2,VAR_0)
| ~ in(sK5(VAR_0,VAR_1),VAR_2)
| ~ in(sK5(VAR_0,VAR_1),VAR_1)
| union(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1] :
( in(sK6(VAR_0,VAR_1),VAR_0)
| in(sK5(VAR_0,VAR_1),VAR_1)
| union(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1] :
( in(sK5(VAR_0,VAR_1),sK6(VAR_0,VAR_1))
| in(sK5(VAR_0,VAR_1),VAR_1)
| union(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ in(VAR_3,VAR_0)
| ~ in(VAR_2,VAR_3)
| in(VAR_2,VAR_1)
| union(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK1(VAR_0,VAR_1,VAR_2),VAR_0)
| ~ in(VAR_2,VAR_1)
| union(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,sK1(VAR_0,VAR_1,VAR_2))
| ~ in(VAR_2,VAR_1)
| union(VAR_0) != VAR_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_d4_tarski_sk]) ).
cnf(c_19,plain,
( in(C,sK1(A,B,C))
| ~ in(C,B)
| union(A) != B ),
inference(split_conjunct,[status(thm)],[sk_d4_tarski]) ).
cnf(c_20,plain,
( in(sK1(A,B,C),A)
| ~ in(C,B)
| union(A) != B ),
inference(split_conjunct,[status(thm)],[sk_d4_tarski]) ).
cnf(c_25,plain,
set_intersection2(A,A) = A,
inference(clausify,[status(thm)],[idempotence_k3_xboole_0]) ).
cnf(c_28,plain,
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(nnf_9,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( ? [X0] : in(X0,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t4_xboole_0]) ).
fof(sk_t4_xboole_0_sk,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( in(sK2(A,B),set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2(A,B))],[nnf_9]) ).
fof(sk_t4_xboole_0,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ disjoint(VAR_1,VAR_2)
| ~ in(VAR_0,set_intersection2(VAR_1,VAR_2)) )
& ! [VAR_0,VAR_1] :
( in(sK2(VAR_0,VAR_1),set_intersection2(VAR_0,VAR_1))
| disjoint(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_t4_xboole_0_sk]) ).
cnf(c_29,plain,
( in(sK2(A,B),set_intersection2(A,B))
| disjoint(A,B) ),
inference(split_conjunct,[status(thm)],[sk_t4_xboole_0]) ).
cnf(c_30,plain,
( ~ disjoint(B,C)
| ~ in(A,set_intersection2(B,C)) ),
inference(split_conjunct,[status(thm)],[sk_t4_xboole_0]) ).
fof(nnf_10,plain,
? [A,B] :
( ~ disjoint(union(A),B)
& ! [C] :
( disjoint(C,B)
| ~ in(C,A) ) ),
inference(fof_nnf,[status(thm)],[t98_zfmisc_1_neg]) ).
fof(sk_t98_zfmisc_1_neg,plain,
( ~ disjoint(union(sK3),sK4)
& ! [C] :
( disjoint(C,sK4)
| ~ in(C,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(A,sK3),skolemize(B,sK4)],[nnf_10]) ).
cnf(c_31,negated_conjecture,
( disjoint(A,sK4)
| ~ in(A,sK3) ),
inference(split_conjunct,[status(thm)],[sk_t98_zfmisc_1_neg]) ).
cnf(c_32,negated_conjecture,
~ disjoint(union(sK3),sK4),
inference(split_conjunct,[status(thm)],[sk_t98_zfmisc_1_neg]) ).
cnf(c_33,plain,
~ in(A,A),
inference(factor,[status(thm)],[c_11]) ).
cnf(c_35,plain,
( in(sK0(A,B,A),A)
| set_intersection2(A,B) = A ),
inference(factor,[status(thm)],[c_16]) ).
cnf(c_41,plain,
( in(A,C)
| ~ in(A,set_intersection2(B,C)) ),
inference(resolve,[status(thm)],[c_13,c_12]) ).
cnf(c_42,plain,
( in(A,B)
| ~ in(A,set_intersection2(B,C)) ),
inference(xxres,[status(thm)],[c_13]) ).
cnf(c_80,plain,
( in(A,sK1(B,union(B),A))
| ~ in(A,union(B)) ),
inference(xxres,[status(thm)],[c_19]) ).
cnf(c_85,plain,
( in(sK1(B,union(B),A),B)
| ~ in(A,union(B)) ),
inference(xxres,[status(thm)],[c_20]) ).
cnf(c_167,negated_conjecture,
~ disjoint(sK4,union(sK3)),
inference(resolve,[status(thm)],[c_28,c_32]) ).
cnf(c_1129,plain,
A = set_intersection2(A,A),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_1130,plain,
( in(A,C)
| ~ in(A,set_intersection2(set_intersection2(B,C),set_intersection2(B,C))) ),
inference(resolve,[status(thm)],[c_14,c_1129]) ).
cnf(c_1131,plain,
~ in(A,set_intersection2(set_intersection2(B,A),set_intersection2(B,A))),
inference(resolve,[status(thm)],[c_1130,c_33]) ).
cnf(c_169,plain,
~ in(A,set_intersection2(B,A)),
inference(paramod,[status(thm)],[c_25,c_1131]) ).
cnf(c_186,plain,
( ~ disjoint(A,B)
| set_intersection2(set_intersection2(A,B),C) = set_intersection2(A,B) ),
inference(resolve,[status(thm)],[c_35,c_30]) ).
cnf(c_241,plain,
in(sK2(sK4,union(sK3)),set_intersection2(sK4,union(sK3))),
inference(resolve,[status(thm)],[c_167,c_29]) ).
cnf(c_245,plain,
~ in(A,set_intersection2(B,set_intersection2(C,A))),
inference(resolve,[status(thm)],[c_41,c_169]) ).
cnf(c_314,plain,
in(sK2(sK4,union(sK3)),sK4),
inference(resolve,[status(thm)],[c_241,c_42]) ).
cnf(c_315,plain,
in(sK2(sK4,union(sK3)),union(sK3)),
inference(resolve,[status(thm)],[c_241,c_41]) ).
cnf(c_485,plain,
~ in(A,set_intersection2(B,set_intersection2(C,set_intersection2(D,A)))),
inference(resolve,[status(thm)],[c_41,c_245]) ).
cnf(c_596,plain,
in(sK2(sK4,union(sK3)),sK1(sK3,union(sK3),sK2(sK4,union(sK3)))),
inference(resolve,[status(thm)],[c_80,c_315]) ).
cnf(c_606,plain,
in(sK1(sK3,union(sK3),sK2(sK4,union(sK3))),sK3),
inference(resolve,[status(thm)],[c_85,c_315]) ).
cnf(c_622,plain,
disjoint(sK1(sK3,union(sK3),sK2(sK4,union(sK3))),sK4),
inference(resolve,[status(thm)],[c_606,c_31]) ).
cnf(c_691,plain,
disjoint(sK4,sK1(sK3,union(sK3),sK2(sK4,union(sK3)))),
inference(resolve,[status(thm)],[c_622,c_28]) ).
cnf(c_957,plain,
set_intersection2(set_intersection2(sK4,sK1(sK3,union(sK3),sK2(sK4,union(sK3)))),A) = set_intersection2(sK4,sK1(sK3,union(sK3),sK2(sK4,union(sK3)))),
inference(resolve,[status(thm)],[c_186,c_691]) ).
cnf(c_1132,plain,
( ~ in(F,B)
| ~ in(F,A)
| set_intersection2(A,B) != set_intersection2(C,set_intersection2(D,set_intersection2(E,F))) ),
inference(resolve,[status(thm)],[c_15,c_485]) ).
cnf(c_1133,plain,
( ~ in(sK2(sK4,union(sK3)),A)
| set_intersection2(sK4,A) != set_intersection2(B,set_intersection2(C,set_intersection2(D,sK2(sK4,union(sK3))))) ),
inference(resolve,[status(thm)],[c_1132,c_314]) ).
cnf(c_1134,plain,
set_intersection2(sK4,sK1(sK3,union(sK3),sK2(sK4,union(sK3)))) != set_intersection2(A,set_intersection2(B,set_intersection2(C,sK2(sK4,union(sK3))))),
inference(resolve,[status(thm)],[c_1133,c_596]) ).
cnf(c_1127,plain,
set_intersection2(A,set_intersection2(B,set_intersection2(C,sK2(sK4,union(sK3))))) != set_intersection2(sK4,sK1(sK3,union(sK3),sK2(sK4,union(sK3)))),
inference(copy,[status(thm)],[c_1134]) ).
cnf(c_1128,plain,
$false,
inference(resolve,[status(thm)],[c_1127,c_957]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET945+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:30:28 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3577313 was started by sandbox on n015,
% 0.08/0.35 % Sat Sep 26 08:30:28 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 183.91/24.81
% 183.91/24.81 % Assigning unary symbol union kb_weight 0 and highest precedence (15).
% 183.91/24.81
% 183.91/24.81 % SZS status Theorem for theBenchmark
% 183.91/24.81
% 183.91/24.81 % Proof 1 at 0.23 (+ 0.07) seconds.
% 183.91/24.81 % Length of proof is 43.
% 183.91/24.81 % Level of proof is 9.
% 183.91/24.81 % Maximum clause weight is 23.000.
% 183.91/24.81 % Given clauses 219.
% 183.91/24.81
% 183.91/24.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------