%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET601+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 : n016.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 08:36:34 AM UTC 2026
% Result : Theorem 0.18s 0.66s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 73
% Number of leaves : 8
% Syntax : Number of formulae : 102 ( 102 unt; 0 def)
% Number of atoms : 102 ( 101 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 72 ( 72 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 4 sgn 22 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_of_union,axiom,
! [B,C,D] : union(union(B,C),D) = union(B,union(C,D)),
file('theBenchmark.p',associativity_of_union) ).
fof(idempotency_of_intersection,axiom,
! [B] : intersection(B,B) = B,
file('theBenchmark.p',idempotency_of_intersection) ).
fof(associativity_of_intersection,axiom,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
file('theBenchmark.p',associativity_of_intersection) ).
fof(union_intersection,axiom,
! [B,C] : union(B,intersection(B,C)) = B,
file('theBenchmark.p',union_intersection) ).
fof(union_distributes_over_intersection,axiom,
! [B,C,D] : union(B,intersection(C,D)) = intersection(union(B,C),union(B,D)),
file('theBenchmark.p',union_distributes_over_intersection) ).
fof(commutativity_of_union,axiom,
! [B,C] : union(B,C) = union(C,B),
file('theBenchmark.p',commutativity_of_union) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('theBenchmark.p',commutativity_of_intersection) ).
fof(prove_th72,conjecture,
! [B,C,D] : union(union(intersection(B,C),intersection(C,D)),intersection(D,B)) = intersection(intersection(union(B,C),union(C,D)),union(D,B)),
file('theBenchmark.p',prove_th72) ).
fof(prove_th72_neg,negated_conjecture,
~ ! [B,C,D] : union(union(intersection(B,C),intersection(C,D)),intersection(D,B)) = intersection(intersection(union(B,C),union(C,D)),union(D,B)),
inference(assume_negation,[status(cth)],[prove_th72]) ).
cnf(c_15,plain,
union(union(A,B),C) = union(A,union(B,C)),
inference(clausify,[status(thm)],[associativity_of_union]) ).
cnf(c_16,plain,
intersection(A,A) = A,
inference(clausify,[status(thm)],[idempotency_of_intersection]) ).
cnf(c_17,plain,
intersection(intersection(A,B),C) = intersection(A,intersection(B,C)),
inference(clausify,[status(thm)],[associativity_of_intersection]) ).
cnf(c_18,plain,
union(A,intersection(A,B)) = A,
inference(clausify,[status(thm)],[union_intersection]) ).
cnf(c_19,plain,
intersection(union(A,B),union(A,C)) = union(A,intersection(B,C)),
inference(clausify,[status(thm)],[union_distributes_over_intersection]) ).
cnf(c_20,plain,
union(A,intersection(B,C)) = intersection(union(A,B),union(A,C)),
inference(copy,[status(thm)],[c_19]) ).
cnf(c_30,plain,
union(A,B) = union(B,A),
inference(clausify,[status(thm)],[commutativity_of_union]) ).
cnf(c_31,plain,
intersection(A,B) = intersection(B,A),
inference(clausify,[status(thm)],[commutativity_of_intersection]) ).
fof(nnf_14,plain,
? [B,C,D] : intersection(intersection(union(B,C),union(C,D)),union(D,B)) != union(union(intersection(B,C),intersection(C,D)),intersection(D,B)),
inference(fof_nnf,[status(thm)],[prove_th72_neg]) ).
fof(sk_prove_th72_neg,plain,
intersection(intersection(union(sK0,sK1),union(sK1,sK2)),union(sK2,sK0)) != union(union(intersection(sK0,sK1),intersection(sK1,sK2)),intersection(sK2,sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(B,sK0),skolemize(C,sK1),skolemize(D,sK2)],[nnf_14]) ).
cnf(c_40,negated_conjecture,
intersection(intersection(union(sK0,sK1),union(sK1,sK2)),union(sK2,sK0)) != union(union(intersection(sK0,sK1),intersection(sK1,sK2)),intersection(sK2,sK0)),
inference(split_conjunct,[status(thm)],[sk_prove_th72_neg]) ).
cnf(c_119,negated_conjecture,
intersection(intersection(union(sK0,sK1),union(sK1,sK2)),union(sK0,sK2)) != union(union(intersection(sK0,sK1),intersection(sK1,sK2)),intersection(sK2,sK0)),
inference(paramod,[status(thm)],[c_30,c_40]) ).
cnf(c_120,negated_conjecture,
intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))) != union(union(intersection(sK0,sK1),intersection(sK1,sK2)),intersection(sK2,sK0)),
inference(paramod,[status(thm)],[c_31,c_119]) ).
cnf(c_121,negated_conjecture,
intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))) != union(intersection(union(intersection(sK0,sK1),sK1),union(intersection(sK0,sK1),sK2)),intersection(sK2,sK0)),
inference(paramod,[status(thm)],[c_20,c_120]) ).
cnf(c_122,negated_conjecture,
intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))) != union(intersection(union(sK1,intersection(sK0,sK1)),union(intersection(sK0,sK1),sK2)),intersection(sK2,sK0)),
inference(paramod,[status(thm)],[c_30,c_121]) ).
cnf(c_123,negated_conjecture,
intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))) != union(intersection(intersection(union(sK1,sK0),union(sK1,sK1)),union(intersection(sK0,sK1),sK2)),intersection(sK2,sK0)),
inference(paramod,[status(thm)],[c_20,c_122]) ).
cnf(c_124,negated_conjecture,
intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))) != union(intersection(intersection(union(sK0,sK1),union(sK1,sK1)),union(intersection(sK0,sK1),sK2)),intersection(sK2,sK0)),
inference(paramod,[status(thm)],[c_30,c_123]) ).
cnf(c_125,negated_conjecture,
intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))) != union(intersection(intersection(union(sK0,sK1),union(sK1,sK1)),union(sK2,intersection(sK0,sK1))),intersection(sK2,sK0)),
inference(paramod,[status(thm)],[c_30,c_124]) ).
cnf(c_126,negated_conjecture,
intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))) != union(intersection(intersection(union(sK0,sK1),union(sK1,sK1)),intersection(union(sK2,sK0),union(sK2,sK1))),intersection(sK2,sK0)),
inference(paramod,[status(thm)],[c_20,c_125]) ).
cnf(c_127,negated_conjecture,
intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))) != union(intersection(intersection(union(sK0,sK1),union(sK1,sK1)),intersection(union(sK0,sK2),union(sK2,sK1))),intersection(sK2,sK0)),
inference(paramod,[status(thm)],[c_30,c_126]) ).
cnf(c_128,negated_conjecture,
intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))) != union(intersection(intersection(union(sK0,sK1),union(sK1,sK1)),intersection(union(sK0,sK2),union(sK1,sK2))),intersection(sK2,sK0)),
inference(paramod,[status(thm)],[c_30,c_127]) ).
cnf(c_129,negated_conjecture,
intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))) != union(intersection(union(sK0,sK1),intersection(union(sK1,sK1),intersection(union(sK0,sK2),union(sK1,sK2)))),intersection(sK2,sK0)),
inference(paramod,[status(thm)],[c_17,c_128]) ).
cnf(c_130,negated_conjecture,
intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))) != union(intersection(union(sK0,sK1),intersection(union(sK1,sK1),intersection(union(sK0,sK2),union(sK1,sK2)))),intersection(sK0,sK2)),
inference(paramod,[status(thm)],[c_31,c_129]) ).
cnf(c_131,negated_conjecture,
intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))) != union(intersection(sK0,sK2),intersection(union(sK0,sK1),intersection(union(sK1,sK1),intersection(union(sK0,sK2),union(sK1,sK2))))),
inference(paramod,[status(thm)],[c_30,c_130]) ).
cnf(c_132,negated_conjecture,
intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))) != intersection(union(intersection(sK0,sK2),union(sK0,sK1)),union(intersection(sK0,sK2),intersection(union(sK1,sK1),intersection(union(sK0,sK2),union(sK1,sK2))))),
inference(paramod,[status(thm)],[c_20,c_131]) ).
cnf(c_133,negated_conjecture,
intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))) != intersection(union(intersection(sK0,sK2),union(sK0,sK1)),intersection(union(intersection(sK0,sK2),union(sK1,sK1)),union(intersection(sK0,sK2),intersection(union(sK0,sK2),union(sK1,sK2))))),
inference(paramod,[status(thm)],[c_20,c_132]) ).
cnf(c_134,negated_conjecture,
intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))) != intersection(union(intersection(sK0,sK2),union(sK0,sK1)),intersection(union(intersection(sK0,sK2),union(sK1,sK1)),intersection(union(intersection(sK0,sK2),union(sK0,sK2)),union(intersection(sK0,sK2),union(sK1,sK2))))),
inference(paramod,[status(thm)],[c_20,c_133]) ).
cnf(c_41,negated_conjecture,
intersection(union(intersection(sK0,sK2),union(sK0,sK1)),intersection(union(intersection(sK0,sK2),union(sK1,sK1)),intersection(union(intersection(sK0,sK2),union(sK0,sK2)),union(intersection(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(copy,[status(thm)],[c_134]) ).
cnf(c_42,plain,
intersection(union(A,A),union(A,B)) = A,
inference(paramod,[status(thm)],[c_20,c_18]) ).
cnf(c_135,plain,
intersection(A,B) = intersection(A,intersection(A,B)),
inference(paramod,[status(thm)],[c_16,c_17]) ).
cnf(c_45,plain,
intersection(A,intersection(A,B)) = intersection(A,B),
inference(copy,[status(thm)],[c_135]) ).
cnf(c_136,plain,
union(union(A,B),C) = union(B,union(A,C)),
inference(paramod,[status(thm)],[c_30,c_15]) ).
cnf(c_55,plain,
union(A,union(B,C)) = union(B,union(A,C)),
inference(paramod,[status(thm)],[c_15,c_136]) ).
cnf(c_137,negated_conjecture,
intersection(union(sK0,union(intersection(sK0,sK2),sK1)),intersection(union(intersection(sK0,sK2),union(sK1,sK1)),intersection(union(intersection(sK0,sK2),union(sK0,sK2)),union(intersection(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_55,c_41]) ).
cnf(c_138,negated_conjecture,
intersection(union(sK0,union(sK1,intersection(sK0,sK2))),intersection(union(intersection(sK0,sK2),union(sK1,sK1)),intersection(union(intersection(sK0,sK2),union(sK0,sK2)),union(intersection(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_30,c_137]) ).
cnf(c_139,negated_conjecture,
intersection(union(sK0,intersection(union(sK1,sK0),union(sK1,sK2))),intersection(union(intersection(sK0,sK2),union(sK1,sK1)),intersection(union(intersection(sK0,sK2),union(sK0,sK2)),union(intersection(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_20,c_138]) ).
cnf(c_140,negated_conjecture,
intersection(union(sK0,intersection(union(sK0,sK1),union(sK1,sK2))),intersection(union(intersection(sK0,sK2),union(sK1,sK1)),intersection(union(intersection(sK0,sK2),union(sK0,sK2)),union(intersection(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_30,c_139]) ).
cnf(c_141,negated_conjecture,
intersection(intersection(union(sK0,union(sK0,sK1)),union(sK0,union(sK1,sK2))),intersection(union(intersection(sK0,sK2),union(sK1,sK1)),intersection(union(intersection(sK0,sK2),union(sK0,sK2)),union(intersection(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_20,c_140]) ).
cnf(c_142,negated_conjecture,
intersection(intersection(union(sK0,union(sK0,sK1)),union(sK0,union(sK1,sK2))),intersection(union(sK1,union(intersection(sK0,sK2),sK1)),intersection(union(intersection(sK0,sK2),union(sK0,sK2)),union(intersection(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_55,c_141]) ).
cnf(c_143,negated_conjecture,
intersection(intersection(union(sK0,union(sK0,sK1)),union(sK0,union(sK1,sK2))),intersection(union(sK1,union(sK1,intersection(sK0,sK2))),intersection(union(intersection(sK0,sK2),union(sK0,sK2)),union(intersection(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_30,c_142]) ).
cnf(c_144,negated_conjecture,
intersection(intersection(union(sK0,union(sK0,sK1)),union(sK0,union(sK1,sK2))),intersection(union(sK1,intersection(union(sK1,sK0),union(sK1,sK2))),intersection(union(intersection(sK0,sK2),union(sK0,sK2)),union(intersection(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_20,c_143]) ).
cnf(c_145,negated_conjecture,
intersection(intersection(union(sK0,union(sK0,sK1)),union(sK0,union(sK1,sK2))),intersection(union(sK1,intersection(union(sK0,sK1),union(sK1,sK2))),intersection(union(intersection(sK0,sK2),union(sK0,sK2)),union(intersection(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_30,c_144]) ).
cnf(c_146,negated_conjecture,
intersection(intersection(union(sK0,union(sK0,sK1)),union(sK0,union(sK1,sK2))),intersection(intersection(union(sK1,union(sK0,sK1)),union(sK1,union(sK1,sK2))),intersection(union(intersection(sK0,sK2),union(sK0,sK2)),union(intersection(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_20,c_145]) ).
cnf(c_147,negated_conjecture,
intersection(intersection(union(sK0,union(sK0,sK1)),union(sK0,union(sK1,sK2))),intersection(intersection(union(sK0,union(sK1,sK1)),union(sK1,union(sK1,sK2))),intersection(union(intersection(sK0,sK2),union(sK0,sK2)),union(intersection(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_55,c_146]) ).
cnf(c_148,negated_conjecture,
intersection(intersection(union(sK0,union(sK0,sK1)),union(sK0,union(sK1,sK2))),intersection(intersection(union(sK0,union(sK1,sK1)),union(sK1,union(sK1,sK2))),intersection(union(sK0,union(intersection(sK0,sK2),sK2)),union(intersection(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_55,c_147]) ).
cnf(c_149,negated_conjecture,
intersection(intersection(union(sK0,union(sK0,sK1)),union(sK0,union(sK1,sK2))),intersection(intersection(union(sK0,union(sK1,sK1)),union(sK1,union(sK1,sK2))),intersection(union(sK0,union(sK2,intersection(sK0,sK2))),union(intersection(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_30,c_148]) ).
cnf(c_150,negated_conjecture,
intersection(intersection(union(sK0,union(sK0,sK1)),union(sK0,union(sK1,sK2))),intersection(intersection(union(sK0,union(sK1,sK1)),union(sK1,union(sK1,sK2))),intersection(union(sK0,intersection(union(sK2,sK0),union(sK2,sK2))),union(intersection(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_20,c_149]) ).
cnf(c_151,negated_conjecture,
intersection(intersection(union(sK0,union(sK0,sK1)),union(sK0,union(sK1,sK2))),intersection(intersection(union(sK0,union(sK1,sK1)),union(sK1,union(sK1,sK2))),intersection(union(sK0,intersection(union(sK0,sK2),union(sK2,sK2))),union(intersection(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_30,c_150]) ).
cnf(c_152,negated_conjecture,
intersection(intersection(union(sK0,union(sK0,sK1)),union(sK0,union(sK1,sK2))),intersection(intersection(union(sK0,union(sK1,sK1)),union(sK1,union(sK1,sK2))),intersection(intersection(union(sK0,union(sK0,sK2)),union(sK0,union(sK2,sK2))),union(intersection(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_20,c_151]) ).
cnf(c_153,negated_conjecture,
intersection(intersection(union(sK0,union(sK0,sK1)),union(sK0,union(sK1,sK2))),intersection(intersection(union(sK0,union(sK1,sK1)),union(sK1,union(sK1,sK2))),intersection(intersection(union(sK0,union(sK0,sK2)),union(sK0,union(sK2,sK2))),union(sK1,union(intersection(sK0,sK2),sK2))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_55,c_152]) ).
cnf(c_154,negated_conjecture,
intersection(intersection(union(sK0,union(sK0,sK1)),union(sK0,union(sK1,sK2))),intersection(intersection(union(sK0,union(sK1,sK1)),union(sK1,union(sK1,sK2))),intersection(intersection(union(sK0,union(sK0,sK2)),union(sK0,union(sK2,sK2))),union(sK1,union(sK2,intersection(sK0,sK2)))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_30,c_153]) ).
cnf(c_155,negated_conjecture,
intersection(intersection(union(sK0,union(sK0,sK1)),union(sK0,union(sK1,sK2))),intersection(intersection(union(sK0,union(sK1,sK1)),union(sK1,union(sK1,sK2))),intersection(intersection(union(sK0,union(sK0,sK2)),union(sK0,union(sK2,sK2))),union(sK1,intersection(union(sK2,sK0),union(sK2,sK2)))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_20,c_154]) ).
cnf(c_156,negated_conjecture,
intersection(intersection(union(sK0,union(sK0,sK1)),union(sK0,union(sK1,sK2))),intersection(intersection(union(sK0,union(sK1,sK1)),union(sK1,union(sK1,sK2))),intersection(intersection(union(sK0,union(sK0,sK2)),union(sK0,union(sK2,sK2))),union(sK1,intersection(union(sK0,sK2),union(sK2,sK2)))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_30,c_155]) ).
cnf(c_157,negated_conjecture,
intersection(intersection(union(sK0,union(sK0,sK1)),union(sK0,union(sK1,sK2))),intersection(intersection(union(sK0,union(sK1,sK1)),union(sK1,union(sK1,sK2))),intersection(intersection(union(sK0,union(sK0,sK2)),union(sK0,union(sK2,sK2))),intersection(union(sK1,union(sK0,sK2)),union(sK1,union(sK2,sK2)))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_20,c_156]) ).
cnf(c_158,negated_conjecture,
intersection(intersection(union(sK0,union(sK0,sK1)),union(sK0,union(sK1,sK2))),intersection(intersection(union(sK0,union(sK1,sK1)),union(sK1,union(sK1,sK2))),intersection(intersection(union(sK0,union(sK0,sK2)),union(sK0,union(sK2,sK2))),intersection(union(sK0,union(sK1,sK2)),union(sK1,union(sK2,sK2)))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_55,c_157]) ).
cnf(c_159,negated_conjecture,
intersection(intersection(union(sK0,union(sK0,sK1)),union(sK0,union(sK1,sK2))),intersection(intersection(union(sK0,union(sK1,sK1)),union(sK1,union(sK1,sK2))),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK0,union(sK2,sK2)),intersection(union(sK0,union(sK1,sK2)),union(sK1,union(sK2,sK2))))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_17,c_158]) ).
cnf(c_160,negated_conjecture,
intersection(intersection(union(sK0,union(sK0,sK1)),union(sK0,union(sK1,sK2))),intersection(union(sK0,union(sK1,sK1)),intersection(union(sK1,union(sK1,sK2)),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK0,union(sK2,sK2)),intersection(union(sK0,union(sK1,sK2)),union(sK1,union(sK2,sK2)))))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_17,c_159]) ).
cnf(c_57,negated_conjecture,
intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,union(sK1,sK2)),intersection(union(sK0,union(sK1,sK1)),intersection(union(sK1,union(sK1,sK2)),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK0,union(sK2,sK2)),intersection(union(sK0,union(sK1,sK2)),union(sK1,union(sK2,sK2))))))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_17,c_160]) ).
cnf(c_161,plain,
intersection(intersection(A,B),C) = intersection(B,intersection(A,C)),
inference(paramod,[status(thm)],[c_31,c_17]) ).
cnf(c_59,plain,
intersection(A,intersection(B,C)) = intersection(B,intersection(A,C)),
inference(paramod,[status(thm)],[c_17,c_161]) ).
cnf(c_162,negated_conjecture,
intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,union(sK1,sK2)),intersection(union(sK0,union(sK1,sK1)),intersection(union(sK1,union(sK1,sK2)),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK0,union(sK1,sK2)),intersection(union(sK0,union(sK2,sK2)),union(sK1,union(sK2,sK2))))))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_59,c_57]) ).
cnf(c_163,negated_conjecture,
intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,union(sK1,sK2)),intersection(union(sK0,union(sK1,sK1)),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK1,union(sK1,sK2)),intersection(union(sK0,union(sK1,sK2)),intersection(union(sK0,union(sK2,sK2)),union(sK1,union(sK2,sK2))))))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_59,c_162]) ).
cnf(c_164,negated_conjecture,
intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,union(sK1,sK2)),intersection(union(sK0,union(sK1,sK1)),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK0,union(sK1,sK2)),intersection(union(sK1,union(sK1,sK2)),intersection(union(sK0,union(sK2,sK2)),union(sK1,union(sK2,sK2))))))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_59,c_163]) ).
cnf(c_165,negated_conjecture,
intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,union(sK1,sK2)),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK0,union(sK1,sK1)),intersection(union(sK0,union(sK1,sK2)),intersection(union(sK1,union(sK1,sK2)),intersection(union(sK0,union(sK2,sK2)),union(sK1,union(sK2,sK2))))))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_59,c_164]) ).
cnf(c_166,negated_conjecture,
intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK0,union(sK1,sK2)),intersection(union(sK0,union(sK1,sK1)),intersection(union(sK0,union(sK1,sK2)),intersection(union(sK1,union(sK1,sK2)),intersection(union(sK0,union(sK2,sK2)),union(sK1,union(sK2,sK2))))))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_59,c_165]) ).
cnf(c_167,negated_conjecture,
intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK0,union(sK1,sK1)),intersection(union(sK0,union(sK1,sK2)),intersection(union(sK0,union(sK1,sK2)),intersection(union(sK1,union(sK1,sK2)),intersection(union(sK0,union(sK2,sK2)),union(sK1,union(sK2,sK2))))))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_59,c_166]) ).
cnf(c_168,negated_conjecture,
intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK0,union(sK1,sK1)),intersection(union(sK0,union(sK1,sK2)),intersection(union(sK1,union(sK1,sK2)),intersection(union(sK0,union(sK2,sK2)),union(sK1,union(sK2,sK2)))))))) != intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_45,c_167]) ).
cnf(c_60,negated_conjecture,
intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK0,union(sK1,sK1)),intersection(union(sK0,union(sK1,sK2)),intersection(union(sK1,union(sK1,sK2)),intersection(union(sK0,union(sK2,sK2)),union(sK1,union(sK2,sK2)))))))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_59,c_168]) ).
cnf(c_169,plain,
A = union(A,A),
inference(paramod,[status(thm)],[c_42,c_16]) ).
cnf(c_105,plain,
union(A,A) = A,
inference(copy,[status(thm)],[c_169]) ).
cnf(c_170,plain,
intersection(union(A,A),union(B,A)) = A,
inference(paramod,[status(thm)],[c_30,c_42]) ).
cnf(c_110,plain,
intersection(A,union(B,A)) = A,
inference(paramod,[status(thm)],[c_105,c_170]) ).
cnf(c_171,negated_conjecture,
intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK0,sK1),intersection(union(sK0,union(sK1,sK2)),intersection(union(sK1,union(sK1,sK2)),intersection(union(sK0,union(sK2,sK2)),union(sK1,union(sK2,sK2)))))))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_105,c_60]) ).
cnf(c_172,negated_conjecture,
intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK0,sK1),intersection(union(sK0,union(sK1,sK2)),intersection(union(sK1,union(sK1,sK2)),intersection(union(sK0,sK2),union(sK1,union(sK2,sK2)))))))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_105,c_171]) ).
cnf(c_173,negated_conjecture,
intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK0,sK1),intersection(union(sK0,union(sK1,sK2)),intersection(union(sK1,union(sK1,sK2)),intersection(union(sK0,sK2),union(sK1,sK2))))))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_105,c_172]) ).
cnf(c_174,negated_conjecture,
intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK0,sK1),intersection(union(sK0,union(sK1,sK2)),intersection(intersection(union(sK0,sK2),union(sK1,sK2)),union(sK1,union(sK1,sK2))))))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_31,c_173]) ).
cnf(c_175,negated_conjecture,
intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK0,sK1),intersection(union(sK0,union(sK1,sK2)),intersection(union(sK0,sK2),intersection(union(sK1,sK2),union(sK1,union(sK1,sK2)))))))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_17,c_174]) ).
cnf(c_176,negated_conjecture,
intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK0,sK1),intersection(union(sK0,union(sK1,sK2)),intersection(union(sK0,sK2),union(sK1,sK2)))))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_110,c_175]) ).
cnf(c_177,negated_conjecture,
intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK0,sK1),intersection(intersection(union(sK0,sK2),union(sK1,sK2)),union(sK0,union(sK1,sK2)))))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_31,c_176]) ).
cnf(c_178,negated_conjecture,
intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK0,sK1),intersection(union(sK0,sK2),intersection(union(sK1,sK2),union(sK0,union(sK1,sK2))))))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_17,c_177]) ).
cnf(c_179,negated_conjecture,
intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_110,c_178]) ).
cnf(c_180,negated_conjecture,
intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,sK1),intersection(union(sK0,union(sK0,sK2)),intersection(union(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_59,c_179]) ).
cnf(c_181,negated_conjecture,
intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,sK1),intersection(union(sK0,sK2),intersection(union(sK0,union(sK0,sK2)),union(sK1,sK2))))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_59,c_180]) ).
cnf(c_182,negated_conjecture,
intersection(union(sK0,sK1),intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,sK2),intersection(union(sK0,union(sK0,sK2)),union(sK1,sK2))))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_59,c_181]) ).
cnf(c_112,negated_conjecture,
intersection(union(sK0,sK1),intersection(union(sK0,sK2),intersection(union(sK0,union(sK0,sK1)),intersection(union(sK0,union(sK0,sK2)),union(sK1,sK2))))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_59,c_182]) ).
cnf(c_183,plain,
union(A,B) = union(A,union(A,B)),
inference(paramod,[status(thm)],[c_105,c_15]) ).
cnf(c_115,plain,
union(A,union(A,B)) = union(A,B),
inference(copy,[status(thm)],[c_183]) ).
cnf(c_184,negated_conjecture,
intersection(union(sK0,sK1),intersection(union(sK0,sK2),intersection(union(sK0,sK1),intersection(union(sK0,union(sK0,sK2)),union(sK1,sK2))))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_115,c_112]) ).
cnf(c_185,negated_conjecture,
intersection(union(sK0,sK1),intersection(union(sK0,sK2),intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_115,c_184]) ).
cnf(c_186,negated_conjecture,
intersection(union(sK0,sK1),intersection(union(sK0,sK1),intersection(union(sK0,sK2),intersection(union(sK0,sK2),union(sK1,sK2))))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_59,c_185]) ).
cnf(c_187,negated_conjecture,
intersection(union(sK0,sK1),intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2)))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_45,c_186]) ).
cnf(c_188,negated_conjecture,
intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))),
inference(paramod,[status(thm)],[c_45,c_187]) ).
cnf(c_118,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET601+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.61 % Computer : n016.cluster.edu
% 0.14/0.61 % Model : x86_64 x86_64
% 0.14/0.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.61 % Memory : 8046.5625MB
% 0.14/0.61 % OS : Linux 6.8.0-71-generic
% 0.14/0.61 % CPULimit : 300
% 0.14/0.61 % WCLimit : 300
% 0.14/0.61 % DateTime : Sat Sep 26 08:03:15 UTC 2026
% 0.14/0.61 % CPUTime :
% 0.14/0.62 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.62 % Process 366236 was started by sandbox on n016,
% 0.14/0.62 % Sat Sep 26 08:03:15 2026
% 0.14/0.62 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.63
% 0.14/0.63 % From the command line: assign(max_seconds, 300).
% 0.18/0.66
% 0.18/0.66 % SZS status Theorem for theBenchmark
% 0.18/0.66
% 0.18/0.66 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.18/0.66 % Length of proof is 29.
% 0.18/0.66 % Level of proof is 7.
% 0.18/0.66 % Maximum clause weight is 59.000.
% 0.18/0.66 % Given clauses 27.
% 0.18/0.66
% 0.18/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------