%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU112+1 : TPTP v9.3.1. Released v3.2.0.
% 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 08:45:02 AM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 14 unt; 0 def)
% Number of atoms : 26 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 4 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 4 sgn 13 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t23_finsub_1,axiom,
! [A,B] :
( subset(A,B)
=> subset(finite_subsets(A),finite_subsets(B)) ),
file('theBenchmark.p',t23_finsub_1) ).
fof(t7_xboole_1,axiom,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
fof(t8_xboole_1,axiom,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('theBenchmark.p',t8_xboole_1) ).
fof(t25_finsub_1,conjecture,
! [A,B] : subset(set_union2(finite_subsets(A),finite_subsets(B)),finite_subsets(set_union2(A,B))),
file('theBenchmark.p',t25_finsub_1) ).
fof(t25_finsub_1_neg,negated_conjecture,
~ ! [A,B] : subset(set_union2(finite_subsets(A),finite_subsets(B)),finite_subsets(set_union2(A,B))),
inference(assume_negation,[status(cth)],[t25_finsub_1]) ).
fof(nnf_39,plain,
? [A,B] : ~ subset(set_union2(finite_subsets(A),finite_subsets(B)),finite_subsets(set_union2(A,B))),
inference(fof_nnf,[status(thm)],[t25_finsub_1_neg]) ).
fof(sk_t25_finsub_1_neg,plain,
~ subset(set_union2(finite_subsets(sK0),finite_subsets(sK1)),finite_subsets(set_union2(sK0,sK1))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_39]) ).
cnf(c_47,negated_conjecture,
~ subset(set_union2(finite_subsets(sK0),finite_subsets(sK1)),finite_subsets(set_union2(sK0,sK1))),
inference(split_conjunct,[status(thm)],[sk_t25_finsub_1_neg]) ).
cnf(c_48,plain,
( subset(set_union2(A,C),B)
| ~ subset(C,B)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t8_xboole_1]) ).
cnf(c_50,plain,
subset(A,set_union2(A,B)),
inference(clausify,[status(thm)],[t7_xboole_1]) ).
cnf(c_58,plain,
( subset(finite_subsets(A),finite_subsets(B))
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t23_finsub_1]) ).
cnf(c_88,plain,
set_union2(A,B) = set_union2(B,A),
inference(clausify,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_98,plain,
subset(finite_subsets(A),finite_subsets(set_union2(A,B))),
inference(resolve,[status(thm)],[c_58,c_50]) ).
cnf(c_148,plain,
subset(A,set_union2(B,A)),
inference(paramod,[status(thm)],[c_88,c_50]) ).
cnf(c_236,plain,
subset(finite_subsets(A),finite_subsets(set_union2(B,A))),
inference(resolve,[status(thm)],[c_148,c_58]) ).
cnf(c_278,plain,
( subset(set_union2(finite_subsets(B),A),finite_subsets(set_union2(B,C)))
| ~ subset(A,finite_subsets(set_union2(B,C))) ),
inference(resolve,[status(thm)],[c_48,c_98]) ).
cnf(c_279,negated_conjecture,
~ subset(finite_subsets(sK1),finite_subsets(set_union2(sK0,sK1))),
inference(resolve,[status(thm)],[c_278,c_47]) ).
cnf(c_277,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_236,c_279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU112+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n012.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 08:36:49 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 157289 was started by sandbox2 on n012,
% 0.10/0.36 % Sat Sep 26 08:36:49 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Theorem for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.10/0.39 % Length of proof is 14.
% 0.10/0.39 % Level of proof is 4.
% 0.10/0.39 % Maximum clause weight is 11.000.
% 0.10/0.39 % Given clauses 82.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------