%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL009-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:34:41 PM UTC 2026
% Result : Unsatisfiable 13.99s 12.19s
% Output : Proof 13.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 12
% Syntax : Number of formulae : 99 ( 95 unt; 0 def)
% Number of atoms : 103 ( 102 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 11 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 12 con; 0-4 aty)
% Number of variables : 41 ( 2 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f14,negated_conjecture,
( join(composition(sk3,sk1),composition(sk3,sk2)) != composition(sk3,sk2)
| join(composition(sk1,sk3),composition(sk2,sk3)) != composition(sk2,sk3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_15) ).
fof(f14_nnf,plain,
( join(composition(sk3,sk1),composition(sk3,sk2)) != composition(sk3,sk2)
| join(composition(sk1,sk3),composition(sk2,sk3)) != composition(sk2,sk3) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
( join(composition(sk3,sk1),composition(sk3,sk2)) != composition(sk3,sk2)
| join(composition(sk1,sk3),composition(sk2,sk3)) != composition(sk2,sk3) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( join(composition(sk3,sk1),composition(sk3,sk2)) != composition(sk3,sk2)
| join(composition(sk1,sk3),composition(sk2,sk3)) != composition(sk2,sk3) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t14,plain,
ifeq(join(composition(sk1,sk3),composition(sk2,sk3)),composition(sk2,sk3),ifeq(join(composition(sk3,sk1),composition(sk3,sk2)),composition(sk3,sk2),false,true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
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(t11,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t141,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(orient,[status(thm)],[t11]) ).
cnf(t8721,plain,
ifeq(composition(join(sk1,sk2),sk3),composition(sk2,sk3),ifeq(join(composition(sk3,sk1),composition(sk3,sk2)),composition(sk3,sk2),false,true),true) = true,
inference(step,[status(thm)],[t14,t141]) ).
cnf(t16,axiom,
sF1 = composition(sk1,sk3),
introduced(definition) ).
cnf(t29,plain,
composition(sk1,sk3) = sF1,
inference(orient,[status(thm)],[t16]) ).
cnf(t142,plain,
composition(join(sk1,X1),sk3) = join(sF1,composition(X1,sk3)),
inference(cp,[status(thm)],[t141,t29]) ).
cnf(t263,plain,
composition(join(sk1,X1),sk3) = join(sF1,composition(X1,sk3)),
inference(orient,[status(thm)],[t142]) ).
cnf(t8722,plain,
ifeq(join(sF1,composition(sk2,sk3)),composition(sk2,sk3),ifeq(join(composition(sk3,sk1),composition(sk3,sk2)),composition(sk3,sk2),false,true),true) = true,
inference(step,[status(thm)],[t8721,t263]) ).
cnf(t15,axiom,
sF0 = join(sk1,sk2),
introduced(definition) ).
cnf(f13,negated_conjecture,
join(sk1,sk2) = sk2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
fof(f13_nnf,plain,
join(sk1,sk2) = sk2,
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
join(sk1,sk2) = sk2,
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(t2,plain,
join(sk1,sk2) = sk2,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t26,plain,
join(sk1,sk2) = sk2,
inference(orient,[status(thm)],[t2]) ).
cnf(t8698,plain,
sF0 = sk2,
inference(step,[status(thm)],[t15,t26]) ).
cnf(t27,plain,
sk2 = sF0,
inference(orient,[status(thm)],[t8698]) ).
cnf(t8723,plain,
ifeq(join(sF1,composition(sF0,sk3)),composition(sk2,sk3),ifeq(join(composition(sk3,sk1),composition(sk3,sk2)),composition(sk3,sk2),false,true),true) = true,
inference(step,[status(thm)],[t8722,t27]) ).
cnf(t17,axiom,
sF2 = composition(sk2,sk3),
introduced(definition) ).
cnf(t8699,plain,
sF2 = composition(sF0,sk3),
inference(step,[status(thm)],[t17,t27]) ).
cnf(t30,plain,
composition(sF0,sk3) = sF2,
inference(orient,[status(thm)],[t8699]) ).
cnf(t8724,plain,
ifeq(join(sF1,sF2),composition(sk2,sk3),ifeq(join(composition(sk3,sk1),composition(sk3,sk2)),composition(sk3,sk2),false,true),true) = true,
inference(step,[status(thm)],[t8723,t30]) ).
cnf(t143,plain,
composition(join(X1,sk1),sk3) = join(composition(X1,sk3),sF1),
inference(cp,[status(thm)],[t141,t29]) ).
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(t5,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t71,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t8714,plain,
composition(join(X1,sk1),sk3) = join(sF1,composition(X1,sk3)),
inference(step,[status(thm)],[t143,t71]) ).
cnf(t269,plain,
composition(join(X1,sk1),sk3) = join(sF1,composition(X1,sk3)),
inference(orient,[status(thm)],[t8714]) ).
cnf(t28,plain,
join(sk1,sF0) = sk2,
inference(rw,[status(thm)],[t26]) ).
cnf(t8701,plain,
join(sk1,sF0) = sF0,
inference(step,[status(thm)],[t28,t27]) ).
cnf(t33,plain,
join(sk1,sF0) = sF0,
inference(orient,[status(thm)],[t8701]) ).
cnf(t8704,plain,
join(sF0,sk1) = sF0,
inference(step,[status(thm)],[t33,t71]) ).
cnf(t72,plain,
join(sF0,sk1) = sF0,
inference(rw,[status(thm)],[t8704]) ).
cnf(t77,plain,
join(sF0,sk1) = sF0,
inference(orient,[status(thm)],[t72]) ).
cnf(t271,plain,
join(sF1,composition(sF0,sk3)) = composition(sF0,sk3),
inference(cp,[status(thm)],[t269,t77]) ).
cnf(t8715,plain,
join(sF1,sF2) = composition(sF0,sk3),
inference(step,[status(thm)],[t271,t30]) ).
cnf(t8716,plain,
join(sF1,sF2) = sF2,
inference(step,[status(thm)],[t8715,t30]) ).
cnf(t276,plain,
join(sF1,sF2) = sF2,
inference(orient,[status(thm)],[t8716]) ).
cnf(t8725,plain,
ifeq(sF2,composition(sk2,sk3),ifeq(join(composition(sk3,sk1),composition(sk3,sk2)),composition(sk3,sk2),false,true),true) = true,
inference(step,[status(thm)],[t8724,t276]) ).
cnf(t8726,plain,
ifeq(sF2,composition(sF0,sk3),ifeq(join(composition(sk3,sk1),composition(sk3,sk2)),composition(sk3,sk2),false,true),true) = true,
inference(step,[status(thm)],[t8725,t27]) ).
cnf(t8727,plain,
ifeq(sF2,sF2,ifeq(join(composition(sk3,sk1),composition(sk3,sk2)),composition(sk3,sk2),false,true),true) = true,
inference(step,[status(thm)],[t8726,t30]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t35,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t8728,plain,
ifeq(join(composition(sk3,sk1),composition(sk3,sk2)),composition(sk3,sk2),false,true) = true,
inference(step,[status(thm)],[t8727,t35]) ).
cnf(t8729,plain,
ifeq(join(composition(sk3,sk2),composition(sk3,sk1)),composition(sk3,sk2),false,true) = true,
inference(step,[status(thm)],[t8728,t71]) ).
cnf(t8730,plain,
ifeq(join(composition(sk3,sF0),composition(sk3,sk1)),composition(sk3,sk2),false,true) = true,
inference(step,[status(thm)],[t8729,t27]) ).
cnf(t20,axiom,
sF5 = composition(sk3,sk2),
introduced(definition) ).
cnf(t8700,plain,
sF5 = composition(sk3,sF0),
inference(step,[status(thm)],[t20,t27]) ).
cnf(t32,plain,
composition(sk3,sF0) = sF5,
inference(orient,[status(thm)],[t8700]) ).
cnf(t8731,plain,
ifeq(join(sF5,composition(sk3,sk1)),composition(sk3,sk2),false,true) = true,
inference(step,[status(thm)],[t8730,t32]) ).
cnf(t19,axiom,
sF4 = composition(sk3,sk1),
introduced(definition) ).
cnf(t31,plain,
composition(sk3,sk1) = sF4,
inference(orient,[status(thm)],[t19]) ).
cnf(t8732,plain,
ifeq(join(sF5,sF4),composition(sk3,sk2),false,true) = true,
inference(step,[status(thm)],[t8731,t31]) ).
cnf(t8733,plain,
ifeq(join(sF4,sF5),composition(sk3,sk2),false,true) = true,
inference(step,[status(thm)],[t8732,t71]) ).
cnf(t8734,plain,
ifeq(join(sF4,sF5),composition(sk3,sF0),false,true) = true,
inference(step,[status(thm)],[t8733,t27]) ).
cnf(t8735,plain,
ifeq(join(sF4,sF5),sF5,false,true) = true,
inference(step,[status(thm)],[t8734,t32]) ).
cnf(t331,plain,
ifeq(join(sF4,sF5),sF5,false,true) = true,
inference(orient,[status(thm)],[t8735]) ).
cnf(t21,axiom,
sF6 = join(composition(sk3,sk1),composition(sk3,sk2)),
introduced(definition) ).
cnf(t8748,plain,
sF6 = join(composition(sk3,sk2),composition(sk3,sk1)),
inference(step,[status(thm)],[t21,t71]) ).
cnf(t8749,plain,
sF6 = join(composition(sk3,sF0),composition(sk3,sk1)),
inference(step,[status(thm)],[t8748,t27]) ).
cnf(t8750,plain,
sF6 = join(sF5,composition(sk3,sk1)),
inference(step,[status(thm)],[t8749,t32]) ).
cnf(t8751,plain,
sF6 = join(sF5,sF4),
inference(step,[status(thm)],[t8750,t31]) ).
cnf(t8752,plain,
sF6 = join(sF4,sF5),
inference(step,[status(thm)],[t8751,t71]) ).
cnf(t381,plain,
join(sF4,sF5) = sF6,
inference(orient,[status(thm)],[t8752]) ).
cnf(t8753,plain,
ifeq(sF6,sF5,false,true) = true,
inference(step,[status(thm)],[t331,t381]) ).
cnf(t382,plain,
ifeq(sF6,sF5,false,true) = true,
inference(rw,[status(thm)],[t8753]) ).
cnf(t22,axiom,
sF7 = ifeq(join(composition(sk3,sk1),composition(sk3,sk2)),composition(sk3,sk2),false,true),
introduced(definition) ).
cnf(t8759,plain,
sF7 = ifeq(join(composition(sk3,sk2),composition(sk3,sk1)),composition(sk3,sk2),false,true),
inference(step,[status(thm)],[t22,t71]) ).
cnf(t8760,plain,
sF7 = ifeq(join(composition(sk3,sF0),composition(sk3,sk1)),composition(sk3,sk2),false,true),
inference(step,[status(thm)],[t8759,t27]) ).
cnf(t8761,plain,
sF7 = ifeq(join(sF5,composition(sk3,sk1)),composition(sk3,sk2),false,true),
inference(step,[status(thm)],[t8760,t32]) ).
cnf(t8762,plain,
sF7 = ifeq(join(sF5,sF4),composition(sk3,sk2),false,true),
inference(step,[status(thm)],[t8761,t31]) ).
cnf(t8763,plain,
sF7 = ifeq(join(sF4,sF5),composition(sk3,sk2),false,true),
inference(step,[status(thm)],[t8762,t71]) ).
cnf(t8764,plain,
sF7 = ifeq(sF6,composition(sk3,sk2),false,true),
inference(step,[status(thm)],[t8763,t381]) ).
cnf(t8765,plain,
sF7 = ifeq(sF6,composition(sk3,sF0),false,true),
inference(step,[status(thm)],[t8764,t27]) ).
cnf(t8766,plain,
sF7 = ifeq(sF6,sF5,false,true),
inference(step,[status(thm)],[t8765,t32]) ).
cnf(t399,plain,
ifeq(sF6,sF5,false,true) = sF7,
inference(orient,[status(thm)],[t8766]) ).
cnf(t8818,plain,
sF7 = true,
inference(step,[status(thm)],[t382,t399]) ).
cnf(t616,plain,
true = sF7,
inference(orient,[status(thm)],[t8818]) ).
cnf(t8819,plain,
ifeq(sF6,sF5,false,sF7) = sF7,
inference(step,[status(thm)],[t399,t616]) ).
cnf(t617,plain,
ifeq(sF6,sF5,false,sF7) = sF7,
inference(rw,[status(thm)],[t8819]) ).
cnf(t743,plain,
ifeq(sF6,sF5,false,sF7) = sF7,
inference(orient,[status(thm)],[t617]) ).
cnf(t8561,plain,
ifeq(sF5,sF5,false,sF7) = sF7,
inference(rw,[status(thm)],[t743]) ).
cnf(t9136,plain,
false = sF7,
inference(step,[status(thm)],[t8561,t35]) ).
cnf(t8697,plain,
false = sF7,
inference(orient,[status(thm)],[t9136]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(g0_0,plain,
sF7 != false,
inference(rw,[status(thm)],[goal_0,t616]) ).
cnf(g0_1,plain,
sF7 != sF7,
inference(rw,[status(thm)],[g0_0,t8697]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL009-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/10.40 % Computer : n010.cluster.edu
% 0.12/10.40 % Model : x86_64 x86_64
% 0.12/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.40 % Memory : 8046.5625MB
% 0.12/10.40 % OS : Linux 6.8.0-71-generic
% 0.12/10.40 % CPULimit : 300
% 0.12/10.40 % WCLimit : 300
% 0.12/10.40 % DateTime : Thu Sep 24 07:08:45 UTC 2026
% 0.12/10.40 % CPUTime :
% 0.12/10.40 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 13.99/12.19 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.99/12.19 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------