%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM383+1 : TPTP v9.3.1. Released v3.2.0.
% 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 08:16:53 AM UTC 2026
% Result : Theorem 0.14s 5.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 8 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 45 ( 22 ~; 12 |; 7 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 34 ( 1 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t7_ordinal1,conjecture,
! [A,B] :
~ ( subset(B,A)
& in(A,B) ),
file('theBenchmark.p',t7_ordinal1) ).
fof(t7_ordinal1_neg,negated_conjecture,
~ ! [A,B] :
~ ( subset(B,A)
& in(A,B) ),
inference(assume_negation,[status(cth)],[t7_ordinal1]) ).
cnf(c_47,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
fof(nnf_27,plain,
? [A,B] :
( subset(B,A)
& in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_ordinal1_neg]) ).
fof(sk_t7_ordinal1_neg,plain,
( subset(sK0,sK1)
& in(sK1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_27]) ).
cnf(c_48,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t7_ordinal1_neg]) ).
cnf(c_52,negated_conjecture,
element(sK0,powerset(sK1)),
inference(resolve,[status(thm)],[c_47,c_48]) ).
cnf(c_53,plain,
( ~ in(B,A)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[antisymmetry_r2_hidden]) ).
cnf(c_62,plain,
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
cnf(c_63,plain,
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t4_subset]) ).
cnf(c_64,plain,
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t5_subset]) ).
cnf(c_68,negated_conjecture,
in(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t7_ordinal1_neg]) ).
cnf(c_69,plain,
~ in(A,A),
inference(factor,[status(thm)],[c_53]) ).
cnf(c_134,negated_conjecture,
( ~ empty(A)
| ~ element(sK0,powerset(A)) ),
inference(resolve,[status(thm)],[c_64,c_68]) ).
cnf(c_96,negated_conjecture,
~ empty(sK1),
inference(resolve,[status(thm)],[c_134,c_52]) ).
cnf(c_135,plain,
( in(A,sK1)
| ~ element(A,sK1) ),
inference(resolve,[status(thm)],[c_62,c_96]) ).
cnf(c_118,plain,
~ element(sK1,sK1),
inference(resolve,[status(thm)],[c_135,c_69]) ).
cnf(c_136,negated_conjecture,
( element(A,sK1)
| ~ in(A,sK0) ),
inference(resolve,[status(thm)],[c_63,c_52]) ).
cnf(c_137,negated_conjecture,
~ in(sK1,sK0),
inference(resolve,[status(thm)],[c_136,c_118]) ).
cnf(c_133,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_68,c_137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM383+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n003.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 26 02:39:13 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 1843317 was started by sandbox on n003,
% 0.10/5.38 % Sat Sep 26 02:39:13 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.39
% 0.10/5.39 % From the command line: assign(max_seconds, 300).
% 0.14/5.40
% 0.14/5.40 % SZS status Theorem for theBenchmark
% 0.14/5.40
% 0.14/5.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/5.40 % Length of proof is 18.
% 0.14/5.40 % Level of proof is 5.
% 0.14/5.40 % Maximum clause weight is 20.000.
% 0.14/5.40 % Given clauses 44.
% 0.14/5.40
% 0.14/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------