%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL005-4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:34:39 PM UTC 2026
% Result : Unsatisfiable 81.81s 11.08s
% Output : Proof 81.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 104
% Number of leaves : 10
% Syntax : Number of formulae : 190 ( 186 unt; 0 def)
% Number of atoms : 194 ( 193 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 46 ( 42 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 212 ( 19 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
join(A,B) = join(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
fof(f0_nnf,plain,
! [A,B] : join(A,B) = join(B,A),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] : join(A,B) = join(B,A),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t4,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t55,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(f8,axiom,
converse(join(A,B)) = join(converse(A),converse(B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f8_nnf,plain,
! [A,B] : converse(join(A,B)) = join(converse(A),converse(B)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B] : converse(join(A,B)) = join(converse(A),converse(B)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t7,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t80,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(orient,[status(thm)],[t7]) ).
cnf(f7,axiom,
converse(converse(A)) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f7_nnf,plain,
! [A] : converse(converse(A)) = A,
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A] : converse(converse(A)) = A,
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
converse(converse(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t1,plain,
converse(converse(X1)) = X1,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t21,plain,
converse(converse(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t82,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(cp,[status(thm)],[t80,t21]) ).
cnf(t117,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(orient,[status(thm)],[t82]) ).
cnf(f1,axiom,
join(A,join(B,C)) = join(join(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
fof(f1_nnf,plain,
! [A,B,C] : join(A,join(B,C)) = join(join(A,B),C),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] : join(A,join(B,C)) = join(join(A,B),C),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t9,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t62,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(f2,axiom,
A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
fof(f2_nnf,plain,
! [A,B] : A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] : A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t12,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t17,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t12]) ).
cnf(t56,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[t17]) ).
cnf(t23762,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t56,t55]) ).
cnf(t327,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(orient,[status(thm)],[t23762]) ).
cnf(f11,axiom,
top = join(A,complement(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top_12) ).
fof(f11_nnf,plain,
! [A] : top = join(A,complement(A)),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A] : top = join(A,complement(A)),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
top = join(X0,complement(X0)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t2,plain,
join(X1,complement(X1)) = top,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t60,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t2]) ).
cnf(t63,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(cp,[status(thm)],[t62,t60]) ).
cnf(t423,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(orient,[status(thm)],[t63]) ).
cnf(t65,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(cp,[status(thm)],[t62,t60]) ).
cnf(t235,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(orient,[status(thm)],[t65]) ).
cnf(t241,plain,
join(top,X1) = join(X2,join(X1,complement(X2))),
inference(cp,[status(thm)],[t235,t55]) ).
cnf(t275,plain,
join(X1,join(X2,complement(X1))) = join(top,X2),
inference(orient,[status(thm)],[t241]) ).
cnf(t337,plain,
X1 = join(complement(join(complement(X1),complement(X1))),complement(top)),
inference(cp,[status(thm)],[t327,t60]) ).
cnf(t23772,plain,
X1 = join(complement(top),complement(join(complement(X1),complement(X1)))),
inference(step,[status(thm)],[t337,t55]) ).
cnf(f12,axiom,
zero = meet(A,complement(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero_13) ).
fof(f12_nnf,plain,
! [A] : zero = meet(A,complement(A)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A] : zero = meet(A,complement(A)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(u0,axiom,
zero = meet(X0,complement(X0)),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(f3,axiom,
meet(A,B) = complement(join(complement(A),complement(B))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
fof(f3_nnf,plain,
! [A,B] : meet(A,B) = complement(join(complement(A),complement(B))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] : meet(A,B) = complement(join(complement(A),complement(B))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(d0,axiom,
meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t5,plain,
complement(join(complement(X1),complement(complement(X1)))) = zero,
inference(definition_unfolding,[status(thm)],[u0,d0]) ).
cnf(t26,plain,
complement(join(complement(X1),complement(complement(X1)))) = zero,
inference(orient,[status(thm)],[t5]) ).
cnf(t23744,plain,
complement(top) = zero,
inference(step,[status(thm)],[t26,t60]) ).
cnf(t61,plain,
complement(top) = zero,
inference(rw,[status(thm)],[t23744]) ).
cnf(t101,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t61]) ).
cnf(t23773,plain,
X1 = join(zero,complement(join(complement(X1),complement(X1)))),
inference(step,[status(thm)],[t23772,t101]) ).
cnf(t473,plain,
join(zero,complement(join(complement(X1),complement(X1)))) = X1,
inference(orient,[status(thm)],[t23773]) ).
cnf(t480,plain,
join(top,zero) = join(join(complement(X1),complement(X1)),X1),
inference(cp,[status(thm)],[t275,t473]) ).
cnf(t23775,plain,
join(zero,top) = join(join(complement(X1),complement(X1)),X1),
inference(step,[status(thm)],[t480,t55]) ).
cnf(t102,plain,
top = join(top,zero),
inference(cp,[status(thm)],[t60,t101]) ).
cnf(t23752,plain,
top = join(zero,top),
inference(step,[status(thm)],[t102,t55]) ).
cnf(t106,plain,
join(zero,top) = top,
inference(orient,[status(thm)],[t23752]) ).
cnf(t23776,plain,
top = join(join(complement(X1),complement(X1)),X1),
inference(step,[status(thm)],[t23775,t106]) ).
cnf(t23777,plain,
top = join(complement(X1),join(complement(X1),X1)),
inference(step,[status(thm)],[t23776,t62]) ).
cnf(t23778,plain,
top = join(complement(X1),join(X1,complement(X1))),
inference(step,[status(thm)],[t23777,t55]) ).
cnf(t23779,plain,
top = join(complement(X1),top),
inference(step,[status(thm)],[t23778,t60]) ).
cnf(t23780,plain,
top = join(top,complement(X1)),
inference(step,[status(thm)],[t23779,t55]) ).
cnf(t492,plain,
join(top,complement(X1)) = top,
inference(orient,[status(thm)],[t23780]) ).
cnf(t499,plain,
top = join(X1,top),
inference(cp,[status(thm)],[t423,t492]) ).
cnf(t504,plain,
join(X1,top) = top,
inference(orient,[status(thm)],[t499]) ).
cnf(t511,plain,
X1 = join(complement(top),complement(join(complement(X1),complement(top)))),
inference(cp,[status(thm)],[t327,t504]) ).
cnf(t23801,plain,
X1 = join(zero,complement(join(complement(X1),complement(top)))),
inference(step,[status(thm)],[t511,t101]) ).
cnf(t23802,plain,
X1 = join(zero,complement(join(complement(X1),zero))),
inference(step,[status(thm)],[t23801,t101]) ).
cnf(t23803,plain,
X1 = join(zero,complement(join(zero,complement(X1)))),
inference(step,[status(thm)],[t23802,t55]) ).
cnf(t560,plain,
join(zero,complement(join(zero,complement(X1)))) = X1,
inference(orient,[status(thm)],[t23803]) ).
cnf(t562,plain,
zero = join(zero,complement(top)),
inference(cp,[status(thm)],[t560,t60]) ).
cnf(t23804,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t562,t101]) ).
cnf(t566,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t23804]) ).
cnf(t567,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t62,t566]) ).
cnf(t568,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t567]) ).
cnf(t569,plain,
join(zero,complement(join(complement(X1),complement(X1)))) = join(zero,X1),
inference(cp,[status(thm)],[t568,t473]) ).
cnf(t23805,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t569,t473]) ).
cnf(t572,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t23805]) ).
cnf(t23806,plain,
complement(join(zero,complement(X1))) = X1,
inference(step,[status(thm)],[t560,t572]) ).
cnf(t23807,plain,
complement(complement(X1)) = X1,
inference(step,[status(thm)],[t23806,t572]) ).
cnf(t581,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[t23807]) ).
cnf(t591,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t581]) ).
cnf(t23808,plain,
complement(join(complement(X1),complement(X1))) = X1,
inference(step,[status(thm)],[t473,t572]) ).
cnf(t582,plain,
complement(join(complement(X1),complement(X1))) = X1,
inference(rw,[status(thm)],[t23808]) ).
cnf(t653,plain,
complement(join(complement(X1),complement(X1))) = X1,
inference(orient,[status(thm)],[t582]) ).
cnf(t654,plain,
complement(X1) = complement(join(X1,complement(complement(X1)))),
inference(cp,[status(thm)],[t653,t591]) ).
cnf(t23811,plain,
complement(X1) = complement(join(X1,X1)),
inference(step,[status(thm)],[t654,t591]) ).
cnf(t673,plain,
complement(join(X1,X1)) = complement(X1),
inference(orient,[status(thm)],[t23811]) ).
cnf(t677,plain,
join(X1,X1) = complement(complement(X1)),
inference(cp,[status(thm)],[t591,t673]) ).
cnf(t23812,plain,
join(X1,X1) = X1,
inference(step,[status(thm)],[t677,t591]) ).
cnf(t688,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t23812]) ).
cnf(t690,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t62,t688]) ).
cnf(t695,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t690]) ).
cnf(t698,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = join(complement(join(complement(X1),X2)),X1),
inference(cp,[status(thm)],[t695,t327]) ).
cnf(t23813,plain,
X1 = join(complement(join(complement(X1),X2)),X1),
inference(step,[status(thm)],[t698,t327]) ).
cnf(t23814,plain,
X1 = join(X1,complement(join(complement(X1),X2))),
inference(step,[status(thm)],[t23813,t55]) ).
cnf(t738,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t23814]) ).
cnf(t741,plain,
X1 = join(X1,complement(join(X2,complement(X1)))),
inference(cp,[status(thm)],[t738,t55]) ).
cnf(t749,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(orient,[status(thm)],[t741]) ).
cnf(t757,plain,
join(X1,converse(complement(join(X2,complement(converse(X1)))))) = converse(converse(X1)),
inference(cp,[status(thm)],[t117,t749]) ).
cnf(t23855,plain,
join(X1,converse(complement(join(X2,complement(converse(X1)))))) = X1,
inference(step,[status(thm)],[t757,t21]) ).
cnf(t1890,plain,
join(X1,converse(complement(join(X2,complement(converse(X1)))))) = X1,
inference(orient,[status(thm)],[t23855]) ).
cnf(t756,plain,
join(X1,join(complement(join(X2,complement(X1))),X3)) = join(X1,X3),
inference(cp,[status(thm)],[t62,t749]) ).
cnf(t22115,plain,
join(X1,join(complement(join(X2,complement(X1))),X3)) = join(X1,X3),
inference(orient,[status(thm)],[t756]) ).
cnf(t22126,plain,
join(X1,complement(join(complement(X2),complement(complement(X1))))) = join(X1,X2),
inference(cp,[status(thm)],[t22115,t327]) ).
cnf(t24300,plain,
join(X1,complement(join(complement(X2),X1))) = join(X1,X2),
inference(step,[status(thm)],[t22126,t591]) ).
cnf(t22330,plain,
join(X1,complement(join(complement(X2),X1))) = join(X1,X2),
inference(orient,[status(thm)],[t24300]) ).
cnf(t22421,plain,
join(X1,complement(X2)) = join(X1,complement(join(X2,X1))),
inference(cp,[status(thm)],[t22330,t591]) ).
cnf(t22490,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t22421]) ).
cnf(t22593,plain,
join(X1,complement(X2)) = join(X1,complement(join(X1,X2))),
inference(cp,[status(thm)],[t22490,t55]) ).
cnf(t22665,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t22593]) ).
cnf(t118,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(cp,[status(thm)],[t117,t60]) ).
cnf(t219,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(orient,[status(thm)],[t118]) ).
cnf(t507,plain,
top = join(top,X1),
inference(cp,[status(thm)],[t504,t55]) ).
cnf(t513,plain,
join(top,X1) = top,
inference(orient,[status(thm)],[t507]) ).
cnf(t522,plain,
top = converse(top),
inference(cp,[status(thm)],[t513,t219]) ).
cnf(t525,plain,
converse(top) = top,
inference(orient,[status(thm)],[t522]) ).
cnf(t23799,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(step,[status(thm)],[t219,t525]) ).
cnf(t528,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(orient,[status(thm)],[t23799]) ).
cnf(t22701,plain,
join(X1,complement(converse(complement(converse(X1))))) = join(X1,complement(top)),
inference(cp,[status(thm)],[t22665,t528]) ).
cnf(t24301,plain,
join(X1,complement(converse(complement(converse(X1))))) = join(X1,zero),
inference(step,[status(thm)],[t22701,t101]) ).
cnf(t577,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t572,t55]) ).
cnf(t587,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t577]) ).
cnf(t24302,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(step,[status(thm)],[t24301,t587]) ).
cnf(t22806,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(orient,[status(thm)],[t24302]) ).
cnf(t22891,plain,
complement(converse(X1)) = join(complement(converse(X1)),converse(complement(X1))),
inference(cp,[status(thm)],[t1890,t22806]) ).
cnf(t24305,plain,
complement(converse(X1)) = join(converse(complement(X1)),complement(converse(X1))),
inference(step,[status(thm)],[t22891,t55]) ).
cnf(t23081,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(orient,[status(thm)],[t24305]) ).
cnf(t23082,plain,
complement(converse(complement(X1))) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t23081,t591]) ).
cnf(t22837,plain,
converse(X1) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t22806,t21]) ).
cnf(t22955,plain,
join(converse(X1),complement(converse(complement(X1)))) = converse(X1),
inference(orient,[status(thm)],[t22837]) ).
cnf(t24306,plain,
complement(converse(complement(X1))) = converse(X1),
inference(step,[status(thm)],[t23082,t22955]) ).
cnf(t23491,plain,
complement(converse(complement(X1))) = converse(X1),
inference(orient,[status(thm)],[t24306]) ).
cnf(t23492,plain,
converse(complement(X1)) = complement(converse(X1)),
inference(cp,[status(thm)],[t23491,t591]) ).
cnf(t23606,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(orient,[status(thm)],[t23492]) ).
cnf(t3,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t22,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t3]) ).
cnf(f16,negated_conjecture,
( join(meet(converse(sk1),converse(sk2)),converse(meet(sk1,sk2))) != converse(meet(sk1,sk2))
| join(converse(meet(sk1,sk2)),meet(converse(sk1),converse(sk2))) != meet(converse(sk1),converse(sk2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_17) ).
fof(f16_nnf,plain,
( join(meet(converse(sk1),converse(sk2)),converse(meet(sk1,sk2))) != converse(meet(sk1,sk2))
| join(converse(meet(sk1,sk2)),meet(converse(sk1),converse(sk2))) != meet(converse(sk1),converse(sk2)) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
( join(meet(converse(sk1),converse(sk2)),converse(meet(sk1,sk2))) != converse(meet(sk1,sk2))
| join(converse(meet(sk1,sk2)),meet(converse(sk1),converse(sk2))) != meet(converse(sk1),converse(sk2)) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( join(meet(converse(sk1),converse(sk2)),converse(meet(sk1,sk2))) != converse(meet(sk1,sk2))
| join(converse(meet(sk1,sk2)),meet(converse(sk1),converse(sk2))) != meet(converse(sk1),converse(sk2)) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(g0_0,plain,
true != ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(complement(converse(sk2)),complement(converse(sk1))))),complement(join(complement(converse(sk2)),complement(converse(sk1)))),ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(complement(converse(sk2)),complement(converse(sk1))))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(complement(converse(sk2)),complement(converse(sk1))))),complement(join(complement(converse(sk2)),complement(converse(sk1)))),ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(complement(converse(sk2)),complement(converse(sk1))))),converse(complement(join(complement(sk1),complement(sk2)))),false,true),true),
inference(rw,[status(thm)],[g0_0,t55]) ).
cnf(g0_2,plain,
true != ifeq(join(converse(complement(join(complement(sk1),complement(sk2)))),complement(join(complement(converse(sk2)),complement(converse(sk1))))),complement(join(complement(converse(sk2)),complement(converse(sk1)))),ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(complement(converse(sk2)),complement(converse(sk1))))),converse(complement(join(complement(sk1),complement(sk2)))),false,true),true),
inference(rw,[status(thm)],[g0_1,t55]) ).
cnf(g0_3,plain,
true != ifeq(join(complement(join(complement(converse(sk2)),complement(converse(sk1)))),converse(complement(join(complement(sk1),complement(sk2))))),complement(join(complement(converse(sk2)),complement(converse(sk1)))),ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(complement(converse(sk2)),complement(converse(sk1))))),converse(complement(join(complement(sk1),complement(sk2)))),false,true),true),
inference(rw,[status(thm)],[g0_2,t55]) ).
cnf(g0_4,plain,
true != ifeq(join(complement(join(complement(converse(sk2)),complement(converse(sk1)))),converse(complement(join(complement(sk1),complement(sk2))))),complement(join(complement(converse(sk2)),complement(converse(sk1)))),ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(complement(converse(sk2)),converse(complement(sk1))))),converse(complement(join(complement(sk1),complement(sk2)))),false,true),true),
inference(rw,[status(thm)],[g0_3,t23606]) ).
cnf(g0_5,plain,
true != ifeq(join(complement(join(complement(converse(sk2)),complement(converse(sk1)))),converse(complement(join(complement(sk1),complement(sk2))))),complement(join(complement(converse(sk2)),complement(converse(sk1)))),ifeq(join(complement(join(complement(converse(sk2)),converse(complement(sk1)))),converse(complement(join(complement(sk2),complement(sk1))))),converse(complement(join(complement(sk1),complement(sk2)))),false,true),true),
inference(rw,[status(thm)],[g0_4,t55]) ).
cnf(g0_6,plain,
true != ifeq(join(complement(join(complement(converse(sk2)),complement(converse(sk1)))),converse(complement(join(complement(sk1),complement(sk2))))),complement(join(complement(converse(sk2)),complement(converse(sk1)))),ifeq(join(complement(join(complement(converse(sk2)),converse(complement(sk1)))),converse(complement(join(complement(sk2),complement(sk1))))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),true),
inference(rw,[status(thm)],[g0_5,t55]) ).
cnf(g0_7,plain,
true != ifeq(join(complement(join(complement(converse(sk2)),complement(converse(sk1)))),converse(complement(join(complement(sk1),complement(sk2))))),complement(join(complement(converse(sk2)),complement(converse(sk1)))),ifeq(join(complement(join(complement(converse(sk2)),converse(complement(sk1)))),converse(complement(join(complement(sk1),complement(sk2))))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),true),
inference(rw,[status(thm)],[g0_6,t55]) ).
cnf(g0_8,plain,
true != ifeq(join(complement(join(complement(converse(sk2)),complement(converse(sk1)))),converse(complement(join(complement(sk1),complement(sk2))))),complement(join(complement(converse(sk2)),complement(converse(sk1)))),ifeq(join(complement(join(converse(complement(sk1)),complement(converse(sk2)))),converse(complement(join(complement(sk1),complement(sk2))))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),true),
inference(rw,[status(thm)],[g0_7,t55]) ).
cnf(g0_9,plain,
true != ifeq(join(complement(join(complement(converse(sk2)),complement(converse(sk1)))),converse(complement(join(complement(sk1),complement(sk2))))),complement(join(complement(converse(sk2)),complement(converse(sk1)))),ifeq(join(complement(join(converse(complement(sk1)),converse(complement(sk2)))),converse(complement(join(complement(sk1),complement(sk2))))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),true),
inference(rw,[status(thm)],[g0_8,t23606]) ).
cnf(g0_10,plain,
true != ifeq(join(complement(join(complement(converse(sk2)),complement(converse(sk1)))),converse(complement(join(complement(sk1),complement(sk2))))),complement(join(complement(converse(sk2)),complement(converse(sk1)))),ifeq(join(complement(join(converse(complement(sk1)),converse(complement(sk2)))),converse(complement(join(complement(sk2),complement(sk1))))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),true),
inference(rw,[status(thm)],[g0_9,t55]) ).
cnf(g0_11,plain,
true != ifeq(join(complement(join(complement(converse(sk2)),complement(converse(sk1)))),converse(complement(join(complement(sk1),complement(sk2))))),complement(join(complement(converse(sk2)),complement(converse(sk1)))),ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(converse(complement(sk1)),converse(complement(sk2))))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),true),
inference(rw,[status(thm)],[g0_10,t55]) ).
cnf(g0_12,plain,
true != ifeq(join(complement(join(complement(converse(sk2)),complement(converse(sk1)))),converse(complement(join(complement(sk1),complement(sk2))))),complement(join(complement(converse(sk2)),complement(converse(sk1)))),ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(converse(complement(sk2)),converse(complement(sk1))))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),true),
inference(rw,[status(thm)],[g0_11,t55]) ).
cnf(g0_13,plain,
true != ifeq(join(complement(join(complement(converse(sk2)),complement(converse(sk1)))),converse(complement(join(complement(sk2),complement(sk1))))),complement(join(complement(converse(sk2)),complement(converse(sk1)))),ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(converse(complement(sk2)),converse(complement(sk1))))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),true),
inference(rw,[status(thm)],[g0_12,t55]) ).
cnf(g0_14,plain,
true != ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(complement(converse(sk2)),complement(converse(sk1))))),complement(join(complement(converse(sk2)),complement(converse(sk1)))),ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(converse(complement(sk2)),converse(complement(sk1))))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),true),
inference(rw,[status(thm)],[g0_13,t55]) ).
cnf(g0_15,plain,
true != ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(complement(converse(sk2)),complement(converse(sk1))))),complement(join(complement(converse(sk2)),complement(converse(sk1)))),ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(converse(join(complement(sk2),complement(sk1))))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),true),
inference(rw,[status(thm)],[g0_14,t80]) ).
cnf(g0_16,plain,
true != ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(complement(converse(sk2)),complement(converse(sk1))))),complement(join(complement(converse(sk2)),complement(converse(sk1)))),ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),converse(complement(join(complement(sk2),complement(sk1))))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),true),
inference(rw,[status(thm)],[g0_15,t23606]) ).
cnf(g0_17,plain,
true != ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(complement(converse(sk2)),complement(converse(sk1))))),complement(join(complement(converse(sk2)),complement(converse(sk1)))),ifeq(converse(complement(join(complement(sk2),complement(sk1)))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),true),
inference(rw,[status(thm)],[g0_16,t688]) ).
cnf(g0_18,plain,
true != ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(complement(converse(sk2)),complement(converse(sk1))))),complement(join(complement(converse(sk2)),complement(converse(sk1)))),false,true),
inference(rw,[status(thm)],[g0_17,t22]) ).
cnf(g0_19,plain,
true != ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(complement(converse(sk2)),complement(converse(sk1))))),complement(join(complement(converse(sk2)),converse(complement(sk1)))),false,true),
inference(rw,[status(thm)],[g0_18,t23606]) ).
cnf(g0_20,plain,
true != ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(complement(converse(sk2)),complement(converse(sk1))))),complement(join(converse(complement(sk1)),complement(converse(sk2)))),false,true),
inference(rw,[status(thm)],[g0_19,t55]) ).
cnf(g0_21,plain,
true != ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(complement(converse(sk2)),complement(converse(sk1))))),complement(join(converse(complement(sk1)),converse(complement(sk2)))),false,true),
inference(rw,[status(thm)],[g0_20,t23606]) ).
cnf(g0_22,plain,
true != ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(complement(converse(sk2)),complement(converse(sk1))))),complement(converse(join(complement(sk1),complement(sk2)))),false,true),
inference(rw,[status(thm)],[g0_21,t80]) ).
cnf(g0_23,plain,
true != ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(complement(converse(sk2)),complement(converse(sk1))))),complement(converse(join(complement(sk2),complement(sk1)))),false,true),
inference(rw,[status(thm)],[g0_22,t55]) ).
cnf(g0_24,plain,
true != ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(complement(converse(sk2)),complement(converse(sk1))))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),
inference(rw,[status(thm)],[g0_23,t23606]) ).
cnf(g0_25,plain,
true != ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(complement(converse(sk2)),converse(complement(sk1))))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),
inference(rw,[status(thm)],[g0_24,t23606]) ).
cnf(g0_26,plain,
true != ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(converse(complement(sk1)),complement(converse(sk2))))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),
inference(rw,[status(thm)],[g0_25,t55]) ).
cnf(g0_27,plain,
true != ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(join(converse(complement(sk1)),converse(complement(sk2))))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),
inference(rw,[status(thm)],[g0_26,t23606]) ).
cnf(g0_28,plain,
true != ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(converse(join(complement(sk1),complement(sk2))))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),
inference(rw,[status(thm)],[g0_27,t80]) ).
cnf(g0_29,plain,
true != ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),complement(converse(join(complement(sk2),complement(sk1))))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),
inference(rw,[status(thm)],[g0_28,t55]) ).
cnf(g0_30,plain,
true != ifeq(join(converse(complement(join(complement(sk2),complement(sk1)))),converse(complement(join(complement(sk2),complement(sk1))))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),
inference(rw,[status(thm)],[g0_29,t23606]) ).
cnf(g0_31,plain,
true != ifeq(converse(complement(join(complement(sk2),complement(sk1)))),converse(complement(join(complement(sk2),complement(sk1)))),false,true),
inference(rw,[status(thm)],[g0_30,t688]) ).
cnf(g0_32,plain,
true != false,
inference(rw,[status(thm)],[g0_31,t22]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL005-4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Thu Sep 24 07:08:22 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 81.81/11.08 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 81.81/11.08 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------