%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL009+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 : Theorem 40.71s 10.76s
% Output : Proof 40.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 7
% Syntax : Number of formulae : 73 ( 68 unt; 0 def)
% Number of atoms : 82 ( 81 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 9 ~; 3 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 120 ( 2 sgn 36 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,conjecture,
! [X0,X1,X2] :
( join(X0,X1) = X1
=> ( join(composition(X2,X0),composition(X2,X1)) = composition(X2,X1)
& join(composition(X0,X2),composition(X1,X2)) = composition(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f16_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( join(X0,X1) = X1
=> ( join(composition(X2,X0),composition(X2,X1)) = composition(X2,X1)
& join(composition(X0,X2),composition(X1,X2)) = composition(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [X0,X1,X2] :
( ( join(composition(X2,X0),composition(X2,X1)) != composition(X2,X1)
| join(composition(X0,X2),composition(X1,X2)) != composition(X1,X2) )
& join(X0,X1) = X1 ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
( ( join(composition(sk2,sk0),composition(sk2,sk1)) != composition(sk2,sk1)
| join(composition(sk0,sk2),composition(sk1,sk2)) != composition(sk1,sk2) )
& join(sk0,sk1) = sk1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f16_nnf]) ).
cnf(c17,plain,
( join(composition(sk2,sk0),composition(sk2,sk1)) != composition(sk2,sk1)
| join(composition(sk0,sk2),composition(sk1,sk2)) != composition(sk1,sk2) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t15,plain,
ifeq(join(composition(sk0,sk2),composition(sk1,sk2)),composition(sk1,sk2),ifeq(join(composition(sk2,sk0),composition(sk2,sk1)),composition(sk2,sk1),false,true),true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
fof(f6,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity) ).
fof(f6_nnf,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
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(t12,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t27,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(orient,[status(thm)],[t12]) ).
cnf(t98512,plain,
ifeq(composition(join(sk0,sk1),sk2),composition(sk1,sk2),ifeq(join(composition(sk2,sk0),composition(sk2,sk1)),composition(sk2,sk1),false,true),true) = true,
inference(step,[status(thm)],[t15,t27]) ).
fof(f0,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f0_nnf,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t6,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t46,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t98513,plain,
ifeq(composition(join(sk1,sk0),sk2),composition(sk1,sk2),ifeq(join(composition(sk2,sk0),composition(sk2,sk1)),composition(sk2,sk1),false,true),true) = true,
inference(step,[status(thm)],[t98512,t46]) ).
cnf(c16,plain,
join(sk0,sk1) = sk1,
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t2,plain,
join(sk0,sk1) = sk1,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t98511,plain,
join(sk1,sk0) = sk1,
inference(step,[status(thm)],[t2,t46]) ).
cnf(t86,plain,
join(sk1,sk0) = sk1,
inference(orient,[status(thm)],[t98511]) ).
cnf(t98514,plain,
ifeq(composition(sk1,sk2),composition(sk1,sk2),ifeq(join(composition(sk2,sk0),composition(sk2,sk1)),composition(sk2,sk1),false,true),true) = true,
inference(step,[status(thm)],[t98513,t86]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t24,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t98515,plain,
ifeq(join(composition(sk2,sk0),composition(sk2,sk1)),composition(sk2,sk1),false,true) = true,
inference(step,[status(thm)],[t98514,t24]) ).
cnf(t98516,plain,
ifeq(join(composition(sk2,sk1),composition(sk2,sk0)),composition(sk2,sk1),false,true) = true,
inference(step,[status(thm)],[t98515,t46]) ).
cnf(t100,plain,
ifeq(join(composition(sk2,sk1),composition(sk2,sk0)),composition(sk2,sk1),false,true) = true,
inference(orient,[status(thm)],[t98516]) ).
fof(f8,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
fof(f8_nnf,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
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(t9,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t63,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(orient,[status(thm)],[t9]) ).
fof(f9,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
fof(f9_nnf,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
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(t8,plain,
composition(converse(X1),converse(X2)) = converse(composition(X2,X1)),
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t30,plain,
composition(converse(X1),converse(X2)) = converse(composition(X2,X1)),
inference(orient,[status(thm)],[t8]) ).
fof(f7,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f7_nnf,plain,
! [X0] : converse(converse(X0)) = X0,
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X0] : converse(converse(X0)) = X0,
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(t23,plain,
converse(converse(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t32,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(cp,[status(thm)],[t30,t23]) ).
cnf(t163,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(orient,[status(thm)],[t32]) ).
cnf(t167,plain,
converse(join(composition(converse(X1),X2),X3)) = join(composition(converse(X2),X1),converse(X3)),
inference(cp,[status(thm)],[t63,t163]) ).
cnf(t89620,plain,
converse(join(composition(converse(X1),X2),X3)) = join(composition(converse(X2),X1),converse(X3)),
inference(orient,[status(thm)],[t167]) ).
cnf(t34,plain,
composition(join(X1,converse(X2)),converse(X3)) = join(composition(X1,converse(X3)),converse(composition(X3,X2))),
inference(cp,[status(thm)],[t27,t30]) ).
cnf(t2194,plain,
join(composition(X1,converse(X2)),converse(composition(X2,X3))) = composition(join(X1,converse(X3)),converse(X2)),
inference(orient,[status(thm)],[t34]) ).
cnf(t89629,plain,
join(composition(converse(converse(X1)),X2),converse(converse(composition(X1,X3)))) = converse(composition(join(converse(X2),converse(X3)),converse(X1))),
inference(cp,[status(thm)],[t89620,t2194]) ).
cnf(t100403,plain,
join(composition(X1,X2),converse(converse(composition(X1,X3)))) = converse(composition(join(converse(X2),converse(X3)),converse(X1))),
inference(step,[status(thm)],[t89629,t23]) ).
cnf(t100404,plain,
join(composition(X1,X2),composition(X1,X3)) = converse(composition(join(converse(X2),converse(X3)),converse(X1))),
inference(step,[status(thm)],[t100403,t23]) ).
cnf(t31,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(cp,[status(thm)],[t30,t23]) ).
cnf(t153,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(orient,[status(thm)],[t31]) ).
cnf(t100405,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,converse(join(converse(X2),converse(X3)))),
inference(step,[status(thm)],[t100404,t153]) ).
cnf(t65,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(cp,[status(thm)],[t63,t23]) ).
cnf(t272,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(orient,[status(thm)],[t65]) ).
cnf(t100406,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,converse(converse(X3)))),
inference(step,[status(thm)],[t100405,t272]) ).
cnf(t100407,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(step,[status(thm)],[t100406,t23]) ).
cnf(t98188,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(orient,[status(thm)],[t100407]) ).
cnf(t100408,plain,
ifeq(composition(sk2,join(sk1,sk0)),composition(sk2,sk1),false,true) = true,
inference(step,[status(thm)],[t100,t98188]) ).
cnf(t100409,plain,
ifeq(composition(sk2,sk1),composition(sk2,sk1),false,true) = true,
inference(step,[status(thm)],[t100408,t86]) ).
cnf(t100410,plain,
false = true,
inference(step,[status(thm)],[t100409,t24]) ).
cnf(t98508,plain,
false = true,
inference(rw,[status(thm)],[t100410]) ).
cnf(t98509,plain,
false = true,
inference(orient,[status(thm)],[t98508]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t98509]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL009+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.57 % Computer : n010.cluster.edu
% 0.09/5.57 % Model : x86_64 x86_64
% 0.09/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.57 % Memory : 8046.5625MB
% 0.09/5.57 % OS : Linux 6.8.0-71-generic
% 0.09/5.57 % CPULimit : 300
% 0.09/5.57 % WCLimit : 300
% 0.09/5.57 % DateTime : Thu Sep 24 07:08:40 UTC 2026
% 0.09/5.57 % CPUTime :
% 0.09/5.57 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 40.71/10.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 40.71/10.76 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------