%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU128+2 : 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 : n012.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 205.21s 31.28s
% Output : CNFRefutation 205.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 67 ( 5 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 69 ( 28 ~; 22 |; 13 &)
% ( 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 : 46 ( 0 sgn 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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(t19_xboole_1,conjecture,
! [A,B,C] :
( ( subset(A,C)
& subset(A,B) )
=> subset(A,set_intersection2(B,C)) ),
file('theBenchmark.p',t19_xboole_1) ).
fof(t19_xboole_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( subset(A,C)
& subset(A,B) )
=> subset(A,set_intersection2(B,C)) ),
inference(assume_negation,[status(cth)],[t19_xboole_1]) ).
fof(nnf_7,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_7]) ).
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_50,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_51,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_52,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_55,plain,
( ~ in(D,B)
| ~ in(D,A)
| in(D,C)
| set_intersection2(A,B) != C ),
inference(clausify,[status(thm)],[d3_xboole_0]) ).
fof(nnf_35,plain,
? [A,B,C] :
( ~ subset(A,set_intersection2(B,C))
& subset(A,C)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[t19_xboole_1_neg]) ).
fof(sk_t19_xboole_1_neg,plain,
( ~ subset(sK1,set_intersection2(sK2,sK3))
& subset(sK1,sK3)
& subset(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK3)],[nnf_35]) ).
cnf(c_87,negated_conjecture,
subset(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t19_xboole_1_neg]) ).
cnf(c_88,negated_conjecture,
subset(sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_t19_xboole_1_neg]) ).
cnf(c_89,negated_conjecture,
~ subset(sK1,set_intersection2(sK2,sK3)),
inference(split_conjunct,[status(thm)],[sk_t19_xboole_1_neg]) ).
cnf(c_403,plain,
( in(A,sK2)
| ~ in(A,sK1) ),
inference(resolve,[status(thm)],[c_87,c_50]) ).
cnf(c_410,plain,
( in(A,sK3)
| ~ in(A,sK1) ),
inference(resolve,[status(thm)],[c_88,c_50]) ).
cnf(c_412,plain,
in(sK0(sK1,set_intersection2(sK2,sK3)),sK1),
inference(resolve,[status(thm)],[c_89,c_51]) ).
cnf(c_418,negated_conjecture,
~ in(sK0(sK1,set_intersection2(sK2,sK3)),set_intersection2(sK2,sK3)),
inference(resolve,[status(thm)],[c_52,c_89]) ).
cnf(c_2450,plain,
in(sK0(sK1,set_intersection2(sK2,sK3)),sK3),
inference(resolve,[status(thm)],[c_412,c_410]) ).
cnf(c_2451,plain,
in(sK0(sK1,set_intersection2(sK2,sK3)),sK2),
inference(resolve,[status(thm)],[c_412,c_403]) ).
cnf(c_22805,plain,
( ~ in(sK0(sK1,set_intersection2(sK2,sK3)),B)
| ~ in(sK0(sK1,set_intersection2(sK2,sK3)),A)
| set_intersection2(A,B) != set_intersection2(sK2,sK3) ),
inference(resolve,[status(thm)],[c_55,c_418]) ).
cnf(c_22806,plain,
( ~ in(sK0(sK1,set_intersection2(sK2,sK3)),A)
| set_intersection2(sK2,A) != set_intersection2(sK2,sK3) ),
inference(resolve,[status(thm)],[c_22805,c_2451]) ).
cnf(c_22807,plain,
set_intersection2(sK2,sK3) != set_intersection2(sK2,sK3),
inference(resolve,[status(thm)],[c_22806,c_2450]) ).
cnf(c_22804,plain,
$false,
inference(copy,[status(thm)],[c_22807]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU128+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n012.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Sat Sep 26 08:37:56 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.37 % Process 160267 was started by sandbox2 on n012,
% 0.08/5.37 % Sat Sep 26 08:37:56 2026
% 0.08/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/5.38
% 0.08/5.38 % From the command line: assign(max_seconds, 300).
% 205.21/31.28
% 205.21/31.28 % given #500 (T,wt=7): 6851 in(f3(c3,f6(c3,c5)),c4). [resolve(6576,a,403,a)].
% 205.21/31.28
% 205.21/31.28 % given #1000 (F,wt=7): 688 set_intersection2(f6(c3,c3),A) != c3. [ur(53,b,669,a,c,90,a)].
% 205.21/31.28
% 205.21/31.28 % given #1500 (A,wt=28): 264 set_intersection2(A,B) = C | in(f4(A,B,C),A) | set_intersection2(D,C) != E | in(f4(A,B,C),E) | -in(f4(A,B,C),D). [resolve(56,b,55,d)].
% 205.21/31.28
% 205.21/31.28 % given #2000 (T,wt=9): 8975 in(f3(c3,f5(c4,c3)),set_union2(c3,A)). [resolve(387,a,4722,a)].
% 205.21/31.28
% 205.21/31.28 % SZS status Theorem for theBenchmark
% 205.21/31.28
% 205.21/31.28 % Proof 1 at 18.82 (+ 6.97) seconds.
% 205.21/31.28 % Length of proof is 17.
% 205.21/31.28 % Level of proof is 4.
% 205.21/31.28 % Maximum clause weight is 14.000.
% 205.21/31.28 % Given clauses 2463.
% 205.21/31.28
% 205.21/31.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------