%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU121+1 : 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 : n003.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 08:45:04 AM UTC 2026
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 7 unt; 0 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 54 ( 20 ~; 18 |; 12 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 22 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(t1_xboole_1,conjecture,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t1_xboole_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
inference(assume_negation,[status(cth)],[t1_xboole_1]) ).
fof(nnf_2,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_2]) ).
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_12,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_13,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_14,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
fof(nnf_10,plain,
? [A,B,C] :
( ~ subset(A,C)
& subset(B,C)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1_neg]) ).
fof(sk_t1_xboole_1_neg,plain,
( ~ subset(sK1,sK3)
& subset(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_10]) ).
cnf(c_22,negated_conjecture,
subset(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t1_xboole_1_neg]) ).
cnf(c_23,negated_conjecture,
subset(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_t1_xboole_1_neg]) ).
cnf(c_24,negated_conjecture,
~ subset(sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_t1_xboole_1_neg]) ).
cnf(c_26,plain,
( in(sK0(A,B),C)
| ~ subset(A,C)
| subset(A,B) ),
inference(resolve,[status(thm)],[c_13,c_12]) ).
cnf(c_31,negated_conjecture,
~ in(sK0(sK1,sK3),sK3),
inference(resolve,[status(thm)],[c_14,c_24]) ).
cnf(c_35,plain,
( in(sK0(sK1,A),sK2)
| subset(sK1,A) ),
inference(resolve,[status(thm)],[c_26,c_22]) ).
cnf(c_59,negated_conjecture,
( in(A,sK3)
| ~ in(A,sK2) ),
inference(resolve,[status(thm)],[c_12,c_23]) ).
cnf(c_44,negated_conjecture,
~ in(sK0(sK1,sK3),sK2),
inference(resolve,[status(thm)],[c_59,c_31]) ).
cnf(c_60,plain,
subset(sK1,sK3),
inference(resolve,[status(thm)],[c_44,c_35]) ).
cnf(c_58,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_24,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU121+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:39:08 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2464645 was started by sandbox on n003,
% 0.08/0.36 % Sat Sep 26 08:39:08 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.37
% 0.12/0.37 % SZS status Theorem for theBenchmark
% 0.12/0.37
% 0.12/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.37 % Length of proof is 13.
% 0.12/0.37 % Level of proof is 4.
% 0.12/0.37 % Maximum clause weight is 11.000.
% 0.12/0.37 % Given clauses 37.
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------