%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU129+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 42.06s 6.42s
% Output : CNFRefutation 42.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 11 unt; 0 def)
% Number of atoms : 70 ( 7 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 70 ( 30 ~; 25 |; 9 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 57 ( 3 sgn 28 !; 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(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
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(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_17,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(nnf_3,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(sk_d3_tarski_sk,plain,
! [A,B] :
( ( ( ~ in(sK0(A,B),B)
& in(sK0(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_3]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK0(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,VAR_1)
| ~ in(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_tarski_sk]) ).
cnf(c_18,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_19,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_20,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_22,plain,
( in(D,B)
| ~ in(D,C)
| set_intersection2(A,B) != C ),
inference(clausify,[status(thm)],[d3_xboole_0]) ).
cnf(c_23,plain,
( ~ in(D,B)
| ~ in(D,A)
| in(D,C)
| set_intersection2(A,B) != C ),
inference(clausify,[status(thm)],[d3_xboole_0]) ).
fof(nnf_15,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(sK1,sK3),set_intersection2(sK2,sK3))
& subset(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK3)],[nnf_15]) ).
cnf(c_36,negated_conjecture,
subset(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t26_xboole_1_neg]) ).
cnf(c_37,negated_conjecture,
~ subset(set_intersection2(sK1,sK3),set_intersection2(sK2,sK3)),
inference(split_conjunct,[status(thm)],[sk_t26_xboole_1_neg]) ).
cnf(c_89,plain,
( in(A,sK2)
| ~ in(A,sK1) ),
inference(resolve,[status(thm)],[c_36,c_18]) ).
cnf(c_90,plain,
in(sK0(set_intersection2(sK1,sK3),set_intersection2(sK2,sK3)),set_intersection2(sK1,sK3)),
inference(resolve,[status(thm)],[c_37,c_19]) ).
cnf(c_91,negated_conjecture,
~ in(sK0(set_intersection2(sK1,sK3),set_intersection2(sK2,sK3)),set_intersection2(sK2,sK3)),
inference(resolve,[status(thm)],[c_20,c_37]) ).
cnf(c_12906,plain,
( in(sK0(set_intersection2(sK1,sK3),set_intersection2(sK2,sK3)),B)
| set_intersection2(A,B) != set_intersection2(sK1,sK3) ),
inference(resolve,[status(thm)],[c_90,c_22]) ).
cnf(c_221,plain,
( in(sK0(set_intersection2(sK1,sK3),set_intersection2(sK2,sK3)),B)
| set_intersection2(sK1,sK3) != set_intersection2(A,B) ),
inference(copy,[status(thm)],[c_12906]) ).
cnf(c_12832,plain,
in(sK0(set_intersection2(sK1,sK3),set_intersection2(sK2,sK3)),sK1),
inference(resolve,[status(thm)],[c_221,c_17]) ).
cnf(c_12833,plain,
in(sK0(set_intersection2(sK1,sK3),set_intersection2(sK2,sK3)),sK3),
inference(xxres,[status(thm)],[c_221]) ).
cnf(c_12840,plain,
in(sK0(set_intersection2(sK1,sK3),set_intersection2(sK2,sK3)),sK2),
inference(resolve,[status(thm)],[c_12832,c_89]) ).
cnf(c_12907,plain,
( ~ in(A,C)
| ~ in(A,B)
| in(A,set_intersection2(B,C)) ),
inference(xxres,[status(thm)],[c_23]) ).
cnf(c_12908,plain,
( ~ in(sK0(set_intersection2(sK1,sK3),set_intersection2(sK2,sK3)),sK3)
| ~ in(sK0(set_intersection2(sK1,sK3),set_intersection2(sK2,sK3)),sK2) ),
inference(resolve,[status(thm)],[c_12907,c_91]) ).
cnf(c_12909,plain,
~ in(sK0(set_intersection2(sK1,sK3),set_intersection2(sK2,sK3)),sK2),
inference(resolve,[status(thm)],[c_12908,c_12833]) ).
cnf(c_12905,plain,
$false,
inference(resolve,[status(thm)],[c_12840,c_12909]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU129+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n009.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 08:37:59 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3871246 was started by sandbox2 on n009,
% 0.08/0.35 % Sat Sep 26 08:37:59 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 42.06/6.42
% 42.06/6.42 % given #500 (F,wt=8): 5669 f2(c3,f1(c3,empty_set),c3) != c3. [ur(104,a,743,a,c,38,a),flip(a)].
% 42.06/6.42
% 42.06/6.42 % SZS status Theorem for theBenchmark
% 42.06/6.42
% 42.06/6.42 % Proof 1 at 4.43 (+ 1.61) seconds.
% 42.06/6.42 % Length of proof is 20.
% 42.06/6.42 % Level of proof is 6.
% 42.06/6.42 % Maximum clause weight is 16.000.
% 42.06/6.42 % Given clauses 909.
% 42.06/6.42
% 42.06/6.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------