%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET002+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 08:35:14 AM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 9 unt; 0 def)
% Number of atoms : 13 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 1 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 5 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_union,axiom,
! [B,C] :
( subset(B,C)
=> union(B,C) = C ),
file('theBenchmark.p',subset_union) ).
fof(reflexivity_of_subset,axiom,
! [B] : subset(B,B),
file('theBenchmark.p',reflexivity_of_subset) ).
fof(prove_idempotency_of_union,conjecture,
! [B] : union(B,B) = B,
file('theBenchmark.p',prove_idempotency_of_union) ).
fof(prove_idempotency_of_union_neg,negated_conjecture,
~ ! [B] : union(B,B) = B,
inference(assume_negation,[status(cth)],[prove_idempotency_of_union]) ).
cnf(c_9,plain,
( union(A,B) = B
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[subset_union]) ).
cnf(c_20,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_of_subset]) ).
fof(nnf_8,plain,
? [B] : union(B,B) != B,
inference(fof_nnf,[status(thm)],[prove_idempotency_of_union_neg]) ).
fof(sk_prove_idempotency_of_union_neg,plain,
union(sK0,sK0) != sK0,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0)],[nnf_8]) ).
cnf(c_25,negated_conjecture,
union(sK0,sK0) != sK0,
inference(split_conjunct,[status(thm)],[sk_prove_idempotency_of_union_neg]) ).
cnf(c_32,plain,
union(A,A) = A,
inference(resolve,[status(thm)],[c_20,c_9]) ).
cnf(c_33,plain,
$false,
inference(resolve,[status(thm)],[c_32,c_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET002+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 06:47:14 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 4007035 was started by sandbox on n011,
% 0.10/0.37 % Sat Sep 26 06:47:14 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.39 % Length of proof is 8.
% 0.14/0.39 % Level of proof is 3.
% 0.14/0.39 % Maximum clause weight is 8.000.
% 0.14/0.39 % Given clauses 12.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------