%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU140+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 : 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 08:45:08 AM UTC 2026
% Result : Theorem 1.02s 0.60s
% Output : CNFRefutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 62 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 65 ( 26 ~; 18 |; 17 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 25 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(t3_xboole_0,axiom,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t3_xboole_0) ).
fof(t63_xboole_1,conjecture,
! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
file('theBenchmark.p',t63_xboole_1) ).
fof(t63_xboole_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
inference(assume_negation,[status(cth)],[t63_xboole_1]) ).
cnf(c_71,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[d3_tarski]) ).
fof(nnf_42,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ( ? [X0] :
( in(X0,B)
& in(X0,A) )
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t3_xboole_0]) ).
fof(sk_t3_xboole_0_sk,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ( ( in(sK0(A,B),B)
& in(sK0(A,B),A) )
| disjoint(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(A,B))],[nnf_42]) ).
fof(sk_t3_xboole_0,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ disjoint(VAR_1,VAR_2)
| ~ in(VAR_0,VAR_2)
| ~ in(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK0(VAR_0,VAR_1),VAR_1)
| disjoint(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK0(VAR_0,VAR_1),VAR_0)
| disjoint(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_t3_xboole_0_sk]) ).
cnf(c_118,plain,
( in(sK0(A,B),A)
| disjoint(A,B) ),
inference(split_conjunct,[status(thm)],[sk_t3_xboole_0]) ).
cnf(c_119,plain,
( in(sK0(A,B),B)
| disjoint(A,B) ),
inference(split_conjunct,[status(thm)],[sk_t3_xboole_0]) ).
cnf(c_120,plain,
( ~ disjoint(B,C)
| ~ in(A,C)
| ~ in(A,B) ),
inference(split_conjunct,[status(thm)],[sk_t3_xboole_0]) ).
fof(nnf_55,plain,
? [A,B,C] :
( ~ disjoint(A,C)
& disjoint(B,C)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1_neg]) ).
fof(sk_t63_xboole_1_neg,plain,
( ~ disjoint(sK1,sK3)
& disjoint(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_55]) ).
cnf(c_137,negated_conjecture,
subset(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t63_xboole_1_neg]) ).
cnf(c_138,negated_conjecture,
disjoint(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_t63_xboole_1_neg]) ).
cnf(c_139,negated_conjecture,
~ disjoint(sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_t63_xboole_1_neg]) ).
cnf(c_568,plain,
( in(A,sK2)
| ~ in(A,sK1) ),
inference(resolve,[status(thm)],[c_137,c_71]) ).
cnf(c_571,plain,
( ~ in(A,sK3)
| ~ in(A,sK2) ),
inference(resolve,[status(thm)],[c_138,c_120]) ).
cnf(c_574,plain,
in(sK0(sK1,sK3),sK3),
inference(resolve,[status(thm)],[c_139,c_119]) ).
cnf(c_575,plain,
in(sK0(sK1,sK3),sK1),
inference(resolve,[status(thm)],[c_139,c_118]) ).
cnf(c_1262,plain,
~ in(sK0(sK1,sK3),sK2),
inference(resolve,[status(thm)],[c_574,c_571]) ).
cnf(c_1321,plain,
in(sK0(sK1,sK3),sK2),
inference(resolve,[status(thm)],[c_575,c_568]) ).
cnf(c_1320,plain,
$false,
inference(resolve,[status(thm)],[c_1262,c_1321]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU140+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n001.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 08:45:57 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.36 % Process 1400179 was started by sandbox on n001,
% 0.07/0.36 % Sat Sep 26 08:45:57 2026
% 0.07/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 1.02/0.60
% 1.02/0.60 % Assigning unary symbol f1 kb_weight 0 and highest precedence (23).
% 1.02/0.60
% 1.02/0.60 % SZS status Theorem for theBenchmark
% 1.02/0.60
% 1.02/0.60 % Proof 1 at 0.16 (+ 0.05) seconds.
% 1.02/0.60 % Length of proof is 16.
% 1.02/0.60 % Level of proof is 4.
% 1.02/0.60 % Maximum clause weight is 18.000.
% 1.02/0.60 % Given clauses 134.
% 1.02/0.60
% 1.02/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------