%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET971+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 : n001.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 08:37:23 AM UTC 2026
% Result : Theorem 0.07s 0.36s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 26 unt; 0 def)
% Number of atoms : 42 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 10 ~; 1 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 1 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t123_zfmisc_1,axiom,
! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
file('theBenchmark.p',t123_zfmisc_1) ).
fof(t28_xboole_1,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('theBenchmark.p',t28_xboole_1) ).
fof(t124_zfmisc_1,conjecture,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) = cartesian_product2(A,C) ),
file('theBenchmark.p',t124_zfmisc_1) ).
fof(t124_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) = cartesian_product2(A,C) ),
inference(assume_negation,[status(cth)],[t124_zfmisc_1]) ).
cnf(c_9,plain,
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t28_xboole_1]) ).
cnf(c_10,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
fof(nnf_8,plain,
? [A,B,C,D] :
( cartesian_product2(A,C) != set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C))
& subset(C,D)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[t124_zfmisc_1_neg]) ).
fof(sk_t124_zfmisc_1_neg,plain,
( cartesian_product2(sK0,sK2) != set_intersection2(cartesian_product2(sK0,sK3),cartesian_product2(sK1,sK2))
& subset(sK2,sK3)
& subset(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3)],[nnf_8]) ).
cnf(c_11,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t124_zfmisc_1_neg]) ).
cnf(c_12,negated_conjecture,
subset(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_t124_zfmisc_1_neg]) ).
cnf(c_13,negated_conjecture,
set_intersection2(sK2,sK3) = sK2,
inference(resolve,[status(thm)],[c_12,c_9]) ).
cnf(c_14,negated_conjecture,
set_intersection2(sK0,sK1) = sK0,
inference(resolve,[status(thm)],[c_11,c_9]) ).
cnf(c_15,plain,
set_intersection2(A,A) = A,
inference(resolve,[status(thm)],[c_9,c_10]) ).
cnf(c_16,negated_conjecture,
cartesian_product2(sK0,sK2) != set_intersection2(cartesian_product2(sK0,sK3),cartesian_product2(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_t124_zfmisc_1_neg]) ).
cnf(c_17,negated_conjecture,
set_intersection2(cartesian_product2(sK0,sK3),cartesian_product2(sK1,sK2)) != cartesian_product2(sK0,sK2),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_18,plain,
cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
inference(clausify,[status(thm)],[t123_zfmisc_1]) ).
cnf(c_22,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_24,plain,
cartesian_product2(set_intersection2(A,B),sK2) = set_intersection2(cartesian_product2(A,sK2),cartesian_product2(B,sK3)),
inference(paramod,[status(thm)],[c_13,c_18]) ).
cnf(c_25,plain,
cartesian_product2(sK0,set_intersection2(A,B)) = set_intersection2(cartesian_product2(sK0,A),cartesian_product2(sK1,B)),
inference(paramod,[status(thm)],[c_14,c_18]) ).
cnf(c_27,plain,
cartesian_product2(A,set_intersection2(B,C)) = set_intersection2(cartesian_product2(A,B),cartesian_product2(A,C)),
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_28,plain,
cartesian_product2(set_intersection2(A,B),C) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,C)),
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_37,plain,
set_intersection2(cartesian_product2(sK0,A),cartesian_product2(sK0,B)) = set_intersection2(cartesian_product2(sK0,A),cartesian_product2(sK1,B)),
inference(paramod,[status(thm)],[c_27,c_25]) ).
cnf(c_31,plain,
set_intersection2(cartesian_product2(sK0,A),cartesian_product2(sK1,B)) = set_intersection2(cartesian_product2(sK0,A),cartesian_product2(sK0,B)),
inference(copy,[status(thm)],[c_37]) ).
cnf(c_38,plain,
set_intersection2(cartesian_product2(A,sK2),cartesian_product2(B,sK2)) = set_intersection2(cartesian_product2(A,sK2),cartesian_product2(B,sK3)),
inference(paramod,[status(thm)],[c_28,c_24]) ).
cnf(c_35,plain,
set_intersection2(cartesian_product2(A,sK2),cartesian_product2(B,sK3)) = set_intersection2(cartesian_product2(A,sK2),cartesian_product2(B,sK2)),
inference(copy,[status(thm)],[c_38]) ).
cnf(c_39,negated_conjecture,
set_intersection2(cartesian_product2(sK0,sK3),cartesian_product2(sK0,sK2)) != cartesian_product2(sK0,sK2),
inference(paramod,[status(thm)],[c_31,c_17]) ).
cnf(c_40,negated_conjecture,
set_intersection2(cartesian_product2(sK0,sK2),cartesian_product2(sK0,sK3)) != cartesian_product2(sK0,sK2),
inference(paramod,[status(thm)],[c_22,c_39]) ).
cnf(c_41,negated_conjecture,
set_intersection2(cartesian_product2(sK0,sK2),cartesian_product2(sK0,sK2)) != cartesian_product2(sK0,sK2),
inference(paramod,[status(thm)],[c_35,c_40]) ).
cnf(c_42,negated_conjecture,
cartesian_product2(sK0,sK2) != cartesian_product2(sK0,sK2),
inference(paramod,[status(thm)],[c_15,c_41]) ).
cnf(c_36,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET971+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n001.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 : Sat Sep 26 08:33:42 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 1382283 was started by sandbox on n001,
% 0.07/0.35 % Sat Sep 26 08:33:42 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 0.07/0.36
% 0.07/0.36 % SZS status Theorem for theBenchmark
% 0.07/0.36
% 0.07/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.07/0.36 % Length of proof is 23.
% 0.07/0.36 % Level of proof is 5.
% 0.07/0.36 % Maximum clause weight is 15.000.
% 0.07/0.36 % Given clauses 5.
% 0.07/0.36
% 0.07/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------