%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU129+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Sun Sep 27 08:45:06 AM UTC 2026
% Result : Theorem 0.13s 0.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 10 unt; 0 def)
% Number of atoms : 34 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 6 |; 4 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 3 sgn 16 !; 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(t17_xboole_1,axiom,
! [A,B] : subset(set_intersection2(A,B),A),
file('theBenchmark.p',t17_xboole_1) ).
fof(t19_xboole_1,axiom,
! [A,B,C] :
( ( subset(A,C)
& subset(A,B) )
=> subset(A,set_intersection2(B,C)) ),
file('theBenchmark.p',t19_xboole_1) ).
fof(t1_xboole_1,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t26_xboole_1,conjecture,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
file('theBenchmark.p',t26_xboole_1) ).
fof(t26_xboole_1_neg,negated_conjecture,
~ ! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
inference(assume_negation,[status(cth)],[t26_xboole_1]) ).
cnf(c_39,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_72,plain,
subset(set_intersection2(A,B),A),
inference(clausify,[status(thm)],[t17_xboole_1]) ).
cnf(c_73,plain,
( subset(A,set_intersection2(B,C))
| ~ subset(A,C)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t19_xboole_1]) ).
cnf(c_75,plain,
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t1_xboole_1]) ).
fof(nnf_36,plain,
? [A,B,C] :
( ~ subset(set_intersection2(A,C),set_intersection2(B,C))
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[t26_xboole_1_neg]) ).
fof(sk_t26_xboole_1_neg,plain,
( ~ subset(set_intersection2(sK0,sK2),set_intersection2(sK1,sK2))
& subset(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_36]) ).
cnf(c_89,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t26_xboole_1_neg]) ).
cnf(c_90,negated_conjecture,
~ subset(set_intersection2(sK0,sK2),set_intersection2(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_t26_xboole_1_neg]) ).
cnf(c_378,plain,
subset(set_intersection2(A,B),B),
inference(paramod,[status(thm)],[c_39,c_72]) ).
cnf(c_475,plain,
( subset(A,sK1)
| ~ subset(A,sK0) ),
inference(resolve,[status(thm)],[c_89,c_75]) ).
cnf(c_747,plain,
subset(set_intersection2(sK0,A),sK1),
inference(resolve,[status(thm)],[c_475,c_72]) ).
cnf(c_880,plain,
( subset(set_intersection2(A,B),set_intersection2(C,B))
| ~ subset(set_intersection2(A,B),C) ),
inference(resolve,[status(thm)],[c_73,c_378]) ).
cnf(c_881,negated_conjecture,
~ subset(set_intersection2(sK0,sK2),sK1),
inference(resolve,[status(thm)],[c_880,c_90]) ).
cnf(c_879,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_747,c_881]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU129+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:38:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2669198 was started by sandbox on n014,
% 0.09/0.36 % Sat Sep 26 08:38:17 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.45
% 0.13/0.45 % SZS status Theorem for theBenchmark
% 0.13/0.45
% 0.13/0.45 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.13/0.45 % Length of proof is 15.
% 0.13/0.45 % Level of proof is 4.
% 0.13/0.45 % Maximum clause weight is 21.000.
% 0.13/0.45 % Given clauses 103.
% 0.13/0.45
% 0.13/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------