%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET621+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 08:36:38 AM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 17 unt; 0 def)
% Number of atoms : 17 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 14 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(symmetric_difference_defn,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('theBenchmark.p',symmetric_difference_defn) ).
fof(difference_difference_union,axiom,
! [B,C,D] : difference(difference(B,C),D) = difference(B,union(C,D)),
file('theBenchmark.p',difference_difference_union) ).
fof(difference_distributes_over_union,axiom,
! [B,C,D] : difference(union(B,C),D) = union(difference(B,D),difference(C,D)),
file('theBenchmark.p',difference_distributes_over_union) ).
fof(prove_th97,conjecture,
! [B,C,D] : difference(symmetric_difference(B,C),D) = union(difference(B,union(C,D)),difference(C,union(B,D))),
file('theBenchmark.p',prove_th97) ).
fof(prove_th97_neg,negated_conjecture,
~ ! [B,C,D] : difference(symmetric_difference(B,C),D) = union(difference(B,union(C,D)),difference(C,union(B,D))),
inference(assume_negation,[status(cth)],[prove_th97]) ).
cnf(c_13,plain,
union(difference(A,B),difference(B,A)) = symmetric_difference(A,B),
inference(clausify,[status(thm)],[symmetric_difference_defn]) ).
cnf(c_14,plain,
symmetric_difference(A,B) = union(difference(A,B),difference(B,A)),
inference(copy,[status(thm)],[c_13]) ).
cnf(c_15,plain,
difference(difference(A,B),C) = difference(A,union(B,C)),
inference(clausify,[status(thm)],[difference_difference_union]) ).
cnf(c_16,plain,
union(difference(A,B),difference(C,B)) = difference(union(A,C),B),
inference(clausify,[status(thm)],[difference_distributes_over_union]) ).
fof(nnf_12,plain,
? [B,C,D] : union(difference(B,union(C,D)),difference(C,union(B,D))) != difference(symmetric_difference(B,C),D),
inference(fof_nnf,[status(thm)],[prove_th97_neg]) ).
fof(sk_prove_th97_neg,plain,
union(difference(sK0,union(sK1,sK2)),difference(sK1,union(sK0,sK2))) != difference(symmetric_difference(sK0,sK1),sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(B,sK0),skolemize(C,sK1),skolemize(D,sK2)],[nnf_12]) ).
cnf(c_36,negated_conjecture,
union(difference(sK0,union(sK1,sK2)),difference(sK1,union(sK0,sK2))) != difference(symmetric_difference(sK0,sK1),sK2),
inference(split_conjunct,[status(thm)],[sk_prove_th97_neg]) ).
cnf(c_38,negated_conjecture,
union(difference(difference(sK0,sK1),sK2),difference(sK1,union(sK0,sK2))) != difference(symmetric_difference(sK0,sK1),sK2),
inference(paramod,[status(thm)],[c_15,c_36]) ).
cnf(c_39,negated_conjecture,
union(difference(difference(sK0,sK1),sK2),difference(difference(sK1,sK0),sK2)) != difference(symmetric_difference(sK0,sK1),sK2),
inference(paramod,[status(thm)],[c_15,c_38]) ).
cnf(c_40,negated_conjecture,
difference(union(difference(sK0,sK1),difference(sK1,sK0)),sK2) != difference(symmetric_difference(sK0,sK1),sK2),
inference(paramod,[status(thm)],[c_16,c_39]) ).
cnf(c_41,negated_conjecture,
difference(union(difference(sK0,sK1),difference(sK1,sK0)),sK2) != difference(union(difference(sK0,sK1),difference(sK1,sK0)),sK2),
inference(paramod,[status(thm)],[c_14,c_40]) ).
cnf(c_37,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET621+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n010.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 08:01:29 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 2859447 was started by sandbox2 on n010,
% 0.12/0.38 % Sat Sep 26 08:01:29 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 0.12/0.39
% 0.12/0.39 % SZS status Theorem for theBenchmark
% 0.12/0.39
% 0.12/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.39 % Length of proof is 10.
% 0.12/0.39 % Level of proof is 3.
% 0.12/0.39 % Maximum clause weight is 13.000.
% 0.12/0.39 % Given clauses 0.
% 0.12/0.39
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------