%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET912+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 08:37:16 AM UTC 2026
% Result : Theorem 0.19s 5.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 10 unt; 0 def)
% Number of atoms : 34 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 9 ~; 4 |; 7 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 13 !; 3 ?)
% 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(t28_xboole_1,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('theBenchmark.p',t28_xboole_1) ).
fof(t38_zfmisc_1,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('theBenchmark.p',t38_zfmisc_1) ).
fof(t53_zfmisc_1,conjecture,
! [A,B,C] :
( ( in(C,B)
& in(A,B) )
=> set_intersection2(unordered_pair(A,C),B) = unordered_pair(A,C) ),
file('theBenchmark.p',t53_zfmisc_1) ).
fof(t53_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( in(C,B)
& in(A,B) )
=> set_intersection2(unordered_pair(A,C),B) = unordered_pair(A,C) ),
inference(assume_negation,[status(cth)],[t53_zfmisc_1]) ).
cnf(c_13,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_18,plain,
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t28_xboole_1]) ).
cnf(c_21,plain,
( ~ in(B,C)
| ~ in(A,C)
| subset(unordered_pair(A,B),C) ),
inference(clausify,[status(thm)],[t38_zfmisc_1]) ).
fof(nnf_10,plain,
? [A,B,C] :
( set_intersection2(unordered_pair(A,C),B) != unordered_pair(A,C)
& in(C,B)
& in(A,B) ),
inference(fof_nnf,[status(thm)],[t53_zfmisc_1_neg]) ).
fof(sk_t53_zfmisc_1_neg,plain,
( set_intersection2(unordered_pair(sK0,sK2),sK1) != unordered_pair(sK0,sK2)
& in(sK2,sK1)
& in(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_10]) ).
cnf(c_22,negated_conjecture,
in(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t53_zfmisc_1_neg]) ).
cnf(c_23,negated_conjecture,
in(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_t53_zfmisc_1_neg]) ).
cnf(c_24,negated_conjecture,
set_intersection2(unordered_pair(sK0,sK2),sK1) != unordered_pair(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_t53_zfmisc_1_neg]) ).
cnf(c_25,negated_conjecture,
set_intersection2(sK1,unordered_pair(sK0,sK2)) != unordered_pair(sK0,sK2),
inference(paramod,[status(thm)],[c_13,c_24]) ).
cnf(c_47,negated_conjecture,
( ~ in(A,sK1)
| subset(unordered_pair(sK0,A),sK1) ),
inference(resolve,[status(thm)],[c_21,c_22]) ).
cnf(c_31,negated_conjecture,
subset(unordered_pair(sK0,sK2),sK1),
inference(resolve,[status(thm)],[c_47,c_23]) ).
cnf(c_48,plain,
set_intersection2(unordered_pair(sK0,sK2),sK1) = unordered_pair(sK0,sK2),
inference(resolve,[status(thm)],[c_18,c_31]) ).
cnf(c_49,plain,
set_intersection2(sK1,unordered_pair(sK0,sK2)) = unordered_pair(sK0,sK2),
inference(paramod,[status(thm)],[c_13,c_48]) ).
cnf(c_46,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_25,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET912+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/5.46 % Computer : n008.cluster.edu
% 0.19/5.46 % Model : x86_64 x86_64
% 0.19/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.46 % Memory : 8046.5625MB
% 0.19/5.46 % OS : Linux 6.8.0-71-generic
% 0.19/5.46 % CPULimit : 300
% 0.19/5.46 % WCLimit : 300
% 0.19/5.46 % DateTime : Sat Sep 26 08:26:01 UTC 2026
% 0.19/5.46 % CPUTime :
% 0.19/5.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/5.46 % Process 3201044 was started by sandbox2 on n008,
% 0.19/5.46 % Sat Sep 26 08:26:01 2026
% 0.19/5.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/5.47
% 0.19/5.47 % From the command line: assign(max_seconds, 300).
% 0.19/5.48
% 0.19/5.48 % SZS status Theorem for theBenchmark
% 0.19/5.48
% 0.19/5.48 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.19/5.48 % Length of proof is 13.
% 0.19/5.48 % Level of proof is 3.
% 0.19/5.48 % Maximum clause weight is 11.000.
% 0.19/5.48 % Given clauses 23.
% 0.19/5.48
% 0.19/5.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------