%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL008-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 02:34:40 PM UTC 2026
% Result : Unsatisfiable 38.68s 5.34s
% Output : Proof 38.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 14
% Syntax : Number of formulae : 173 ( 169 unt; 0 def)
% Number of atoms : 177 ( 176 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 37 ( 33 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 248 ( 2 sgn 44 !; 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(t20,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t4]) ).
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(t22,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t23,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(cp,[status(thm)],[t22,t20]) ).
cnf(t302,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(orient,[status(thm)],[t23]) ).
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(t35,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(orient,[status(thm)],[t7]) ).
cnf(f9,axiom,
converse(composition(A,B)) = composition(converse(B),converse(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
fof(f9_nnf,plain,
! [A,B] : converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B] : converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t6,plain,
composition(converse(X1),converse(X2)) = converse(composition(X2,X1)),
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t45,plain,
composition(converse(X1),converse(X2)) = converse(composition(X2,X1)),
inference(orient,[status(thm)],[t6]) ).
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(t18,plain,
converse(converse(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t47,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(cp,[status(thm)],[t45,t18]) ).
cnf(t97,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(orient,[status(thm)],[t47]) ).
cnf(t106,plain,
converse(join(X1,composition(converse(X2),X3))) = join(converse(X1),composition(converse(X3),X2)),
inference(cp,[status(thm)],[t35,t97]) ).
cnf(t6592,plain,
converse(join(X1,composition(converse(X2),X3))) = join(converse(X1),composition(converse(X3),X2)),
inference(orient,[status(thm)],[t106]) ).
cnf(f6,axiom,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f6_nnf,plain,
! [A,B,C] : composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] : composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t10,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t28,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(orient,[status(thm)],[t10]) ).
cnf(t49,plain,
composition(join(converse(X1),X2),converse(X3)) = join(converse(composition(X3,X1)),composition(X2,converse(X3))),
inference(cp,[status(thm)],[t28,t45]) ).
cnf(t20778,plain,
join(converse(composition(X1,X2)),composition(X3,converse(X1))) = composition(join(converse(X2),X3),converse(X1)),
inference(orient,[status(thm)],[t49]) ).
cnf(t20938,plain,
join(converse(converse(composition(X1,X2))),composition(converse(converse(X1)),X3)) = converse(composition(join(converse(X2),converse(X3)),converse(X1))),
inference(cp,[status(thm)],[t6592,t20778]) ).
cnf(t21641,plain,
join(composition(X1,X2),composition(converse(converse(X1)),X3)) = converse(composition(join(converse(X2),converse(X3)),converse(X1))),
inference(step,[status(thm)],[t20938,t18]) ).
cnf(t21642,plain,
join(composition(X1,X2),composition(X1,X3)) = converse(composition(join(converse(X2),converse(X3)),converse(X1))),
inference(step,[status(thm)],[t21641,t18]) ).
cnf(t37,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(cp,[status(thm)],[t35,t18]) ).
cnf(t66,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(orient,[status(thm)],[t37]) ).
cnf(t71,plain,
converse(composition(join(converse(X1),X2),X3)) = composition(converse(X3),join(X1,converse(X2))),
inference(cp,[status(thm)],[t45,t66]) ).
cnf(t5825,plain,
converse(composition(join(converse(X1),X2),X3)) = composition(converse(X3),join(X1,converse(X2))),
inference(orient,[status(thm)],[t71]) ).
cnf(t21643,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(converse(converse(X1)),join(X2,converse(converse(X3)))),
inference(step,[status(thm)],[t21642,t5825]) ).
cnf(t21644,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,converse(converse(X3)))),
inference(step,[status(thm)],[t21643,t18]) ).
cnf(t21645,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(step,[status(thm)],[t21644,t18]) ).
cnf(t20946,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(orient,[status(thm)],[t21645]) ).
cnf(f10,axiom,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity_11) ).
fof(f10_nnf,plain,
! [A,B] : join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A,B] : join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t11,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t21148,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(step,[status(thm)],[t11,t20]) ).
cnf(t31,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t21148]) ).
cnf(f5,axiom,
composition(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f5_nnf,plain,
! [A] : composition(A,one) = A,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] : composition(A,one) = A,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
composition(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t0,plain,
composition(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t17,plain,
composition(X1,one) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t98,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t97,t17]) ).
cnf(t21158,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t98,t18]) ).
cnf(t112,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t21158]) ).
cnf(t113,plain,
one = converse(one),
inference(cp,[status(thm)],[t112,t17]) ).
cnf(t119,plain,
converse(one) = one,
inference(orient,[status(thm)],[t113]) ).
cnf(t21159,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t112,t119]) ).
cnf(t129,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t21159]) ).
cnf(t130,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t129]) ).
cnf(t133,plain,
complement(X1) = join(complement(X1),composition(converse(one),complement(X1))),
inference(cp,[status(thm)],[t31,t130]) ).
cnf(t21161,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t133,t119]) ).
cnf(t21162,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t21161,t130]) ).
cnf(t157,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t21162]) ).
cnf(t323,plain,
join(complement(X1),join(X2,complement(X1))) = join(X2,complement(X1)),
inference(cp,[status(thm)],[t302,t157]) ).
cnf(t673,plain,
join(complement(X1),join(X2,complement(X1))) = join(X2,complement(X1)),
inference(orient,[status(thm)],[t323]) ).
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(t14,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t12]) ).
cnf(t21,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[t14]) ).
cnf(t21273,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t21,t20]) ).
cnf(t2409,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(orient,[status(thm)],[t21273]) ).
cnf(t2415,plain,
X1 = join(complement(complement(X1)),complement(join(complement(X1),complement(complement(X1))))),
inference(cp,[status(thm)],[t2409,t157]) ).
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(t25,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t2]) ).
cnf(t21274,plain,
X1 = join(complement(complement(X1)),complement(top)),
inference(step,[status(thm)],[t2415,t25]) ).
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(t21149,plain,
complement(top) = zero,
inference(step,[status(thm)],[t5,t25]) ).
cnf(t52,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t21149]) ).
cnf(t21275,plain,
X1 = join(complement(complement(X1)),zero),
inference(step,[status(thm)],[t21274,t52]) ).
cnf(t21276,plain,
X1 = join(zero,complement(complement(X1))),
inference(step,[status(thm)],[t21275,t20]) ).
cnf(t2465,plain,
join(zero,complement(complement(X1))) = X1,
inference(orient,[status(thm)],[t21276]) ).
cnf(t158,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t157,t52]) ).
cnf(t21163,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t158,t52]) ).
cnf(t21164,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t21163,t52]) ).
cnf(t161,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t21164]) ).
cnf(t162,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t22,t161]) ).
cnf(t165,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t162]) ).
cnf(t2466,plain,
join(zero,complement(complement(X1))) = join(zero,X1),
inference(cp,[status(thm)],[t165,t2465]) ).
cnf(t21277,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t2466,t2465]) ).
cnf(t2481,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t21277]) ).
cnf(t21281,plain,
complement(complement(X1)) = X1,
inference(step,[status(thm)],[t2465,t2481]) ).
cnf(t2517,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[t21281]) ).
cnf(t2550,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t2517]) ).
cnf(t2557,plain,
join(X1,complement(complement(X2))) = join(X2,join(X1,complement(complement(X2)))),
inference(cp,[status(thm)],[t673,t2550]) ).
cnf(t21310,plain,
join(X1,X2) = join(X2,join(X1,complement(complement(X2)))),
inference(step,[status(thm)],[t2557,t2550]) ).
cnf(t21311,plain,
join(X1,X2) = join(X2,join(X1,X2)),
inference(step,[status(thm)],[t21310,t2550]) ).
cnf(t2681,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(orient,[status(thm)],[t21311]) ).
cnf(t160,plain,
join(complement(X1),join(complement(X1),X2)) = join(complement(X1),X2),
inference(cp,[status(thm)],[t22,t157]) ).
cnf(t660,plain,
join(complement(X1),join(complement(X1),X2)) = join(complement(X1),X2),
inference(orient,[status(thm)],[t160]) ).
cnf(t2559,plain,
join(complement(complement(X1)),X2) = join(X1,join(complement(complement(X1)),X2)),
inference(cp,[status(thm)],[t660,t2550]) ).
cnf(t21312,plain,
join(X1,X2) = join(X1,join(complement(complement(X1)),X2)),
inference(step,[status(thm)],[t2559,t2550]) ).
cnf(t21313,plain,
join(X1,X2) = join(X1,join(X1,X2)),
inference(step,[status(thm)],[t21312,t2550]) ).
cnf(t2717,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t21313]) ).
cnf(t3,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t19,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t3]) ).
cnf(t2551,plain,
complement(complement(X1)) = join(X1,complement(complement(X1))),
inference(cp,[status(thm)],[t157,t2550]) ).
cnf(t21299,plain,
X1 = join(X1,complement(complement(X1))),
inference(step,[status(thm)],[t2551,t2550]) ).
cnf(t21300,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t21299,t2550]) ).
cnf(t2568,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t21300]) ).
cnf(f13,negated_conjecture,
( join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))) != composition(sk1,join(sk2,sk3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
fof(f13_nnf,plain,
( join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))) != composition(sk1,join(sk2,sk3)) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
( join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))) != composition(sk1,join(sk2,sk3)) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))) != composition(sk1,join(sk2,sk3)) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(g0_0,plain,
true != ifeq(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk3,sk2)))),composition(sk1,join(sk3,sk2)),ifeq(join(composition(sk1,join(sk3,sk2)),join(composition(sk1,sk3),composition(sk1,sk2))),join(composition(sk1,sk3),composition(sk1,sk2)),false,true),true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(join(composition(sk1,sk2),join(composition(sk1,join(sk3,sk2)),composition(sk1,sk3))),composition(sk1,join(sk3,sk2)),ifeq(join(composition(sk1,join(sk3,sk2)),join(composition(sk1,sk3),composition(sk1,sk2))),join(composition(sk1,sk3),composition(sk1,sk2)),false,true),true),
inference(rw,[status(thm)],[g0_0,t20]) ).
cnf(g0_2,plain,
true != ifeq(join(composition(sk1,sk2),join(composition(sk1,join(sk3,sk2)),composition(sk1,sk3))),composition(sk1,join(sk3,sk2)),ifeq(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk3,sk2)))),join(composition(sk1,sk3),composition(sk1,sk2)),false,true),true),
inference(rw,[status(thm)],[g0_1,t302]) ).
cnf(g0_3,plain,
true != ifeq(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk3,sk2)))),composition(sk1,join(sk3,sk2)),ifeq(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk3,sk2)))),join(composition(sk1,sk3),composition(sk1,sk2)),false,true),true),
inference(rw,[status(thm)],[g0_2,t302]) ).
cnf(g0_4,plain,
true != ifeq(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk3,sk2)))),composition(sk1,join(sk3,sk2)),ifeq(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk3,sk2)))),composition(sk1,join(sk3,sk2)),false,true),true),
inference(rw,[status(thm)],[g0_3,t20946]) ).
cnf(g0_5,plain,
true != ifeq(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk3,sk2)))),composition(sk1,join(sk3,sk2)),ifeq(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk3,sk2)))),composition(sk1,join(sk2,sk3)),false,true),true),
inference(rw,[status(thm)],[g0_4,t20]) ).
cnf(g0_6,plain,
true != ifeq(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk3,sk2)))),composition(sk1,join(sk3,sk2)),ifeq(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk2,sk3)))),composition(sk1,join(sk2,sk3)),false,true),true),
inference(rw,[status(thm)],[g0_5,t20]) ).
cnf(g0_7,plain,
true != ifeq(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk3,sk2)))),composition(sk1,join(sk3,sk2)),ifeq(join(composition(sk1,sk3),join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2))),composition(sk1,join(sk2,sk3)),false,true),true),
inference(rw,[status(thm)],[g0_6,t20]) ).
cnf(g0_8,plain,
true != ifeq(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk3,sk2)))),composition(sk1,join(sk3,sk2)),ifeq(join(composition(sk1,sk3),join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2))),composition(sk1,join(sk3,sk2)),false,true),true),
inference(rw,[status(thm)],[g0_7,t20]) ).
cnf(g0_9,plain,
true != ifeq(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk3,sk2)))),composition(sk1,join(sk3,sk2)),ifeq(join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)),composition(sk1,join(sk3,sk2)),false,true),true),
inference(rw,[status(thm)],[g0_8,t20]) ).
cnf(g0_10,plain,
true != ifeq(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk3,sk2)))),composition(sk1,join(sk3,sk2)),ifeq(join(join(composition(sk1,join(sk3,sk2)),composition(sk1,sk2)),composition(sk1,sk3)),composition(sk1,join(sk3,sk2)),false,true),true),
inference(rw,[status(thm)],[g0_9,t20]) ).
cnf(g0_11,plain,
true != ifeq(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk3,sk2)))),composition(sk1,join(sk3,sk2)),ifeq(join(composition(sk1,join(join(sk3,sk2),sk2)),composition(sk1,sk3)),composition(sk1,join(sk3,sk2)),false,true),true),
inference(rw,[status(thm)],[g0_10,t20946]) ).
cnf(g0_12,plain,
true != ifeq(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk3,sk2)))),composition(sk1,join(sk3,sk2)),ifeq(join(composition(sk1,join(sk2,join(sk3,sk2))),composition(sk1,sk3)),composition(sk1,join(sk3,sk2)),false,true),true),
inference(rw,[status(thm)],[g0_11,t20]) ).
cnf(g0_13,plain,
true != ifeq(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk3,sk2)))),composition(sk1,join(sk3,sk2)),ifeq(join(composition(sk1,join(sk3,sk2)),composition(sk1,sk3)),composition(sk1,join(sk3,sk2)),false,true),true),
inference(rw,[status(thm)],[g0_12,t2681]) ).
cnf(g0_14,plain,
true != ifeq(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk3,sk2)))),composition(sk1,join(sk3,sk2)),ifeq(join(composition(sk1,sk3),composition(sk1,join(sk3,sk2))),composition(sk1,join(sk3,sk2)),false,true),true),
inference(rw,[status(thm)],[g0_13,t20]) ).
cnf(g0_15,plain,
true != ifeq(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk3,sk2)))),composition(sk1,join(sk3,sk2)),ifeq(composition(sk1,join(sk3,join(sk3,sk2))),composition(sk1,join(sk3,sk2)),false,true),true),
inference(rw,[status(thm)],[g0_14,t20946]) ).
cnf(g0_16,plain,
true != ifeq(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk3,sk2)))),composition(sk1,join(sk3,sk2)),ifeq(composition(sk1,join(sk3,sk2)),composition(sk1,join(sk3,sk2)),false,true),true),
inference(rw,[status(thm)],[g0_15,t2717]) ).
cnf(g0_17,plain,
true != ifeq(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk3,sk2)))),composition(sk1,join(sk3,sk2)),false,true),
inference(rw,[status(thm)],[g0_16,t19]) ).
cnf(g0_18,plain,
true != ifeq(join(composition(sk1,sk3),composition(sk1,join(sk2,join(sk3,sk2)))),composition(sk1,join(sk3,sk2)),false,true),
inference(rw,[status(thm)],[g0_17,t20946]) ).
cnf(g0_19,plain,
true != ifeq(join(composition(sk1,sk3),composition(sk1,join(sk3,join(sk2,sk2)))),composition(sk1,join(sk3,sk2)),false,true),
inference(rw,[status(thm)],[g0_18,t302]) ).
cnf(g0_20,plain,
true != ifeq(composition(sk1,join(sk3,join(sk3,join(sk2,sk2)))),composition(sk1,join(sk3,sk2)),false,true),
inference(rw,[status(thm)],[g0_19,t20946]) ).
cnf(g0_21,plain,
true != ifeq(composition(sk1,join(sk3,join(sk3,sk2))),composition(sk1,join(sk3,sk2)),false,true),
inference(rw,[status(thm)],[g0_20,t2568]) ).
cnf(g0_22,plain,
true != ifeq(composition(sk1,join(sk3,sk2)),composition(sk1,join(sk3,sk2)),false,true),
inference(rw,[status(thm)],[g0_21,t2717]) ).
cnf(g0_23,plain,
true != false,
inference(rw,[status(thm)],[g0_22,t19]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL008-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n019.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 : Thu Sep 24 07:09:49 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 38.68/5.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 38.68/5.34 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------