%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL031+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 08:25:01 AM UTC 2026
% Result : Theorem 48.17s 6.56s
% Output : CNFRefutation 48.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 70 ( 66 unt; 0 def)
% Number of atoms : 78 ( 77 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 5 ~; 0 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 112 ( 0 sgn 21 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('theBenchmark.p',maddux1_join_commutativity) ).
fof(maddux2_join_associativity,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('theBenchmark.p',maddux2_join_associativity) ).
fof(composition_associativity,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('theBenchmark.p',composition_associativity) ).
fof(composition_identity,axiom,
! [X0] : composition(X0,one) = X0,
file('theBenchmark.p',composition_identity) ).
fof(composition_distributivity,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('theBenchmark.p',composition_distributivity) ).
fof(converse_idempotence,axiom,
! [X0] : converse(converse(X0)) = X0,
file('theBenchmark.p',converse_idempotence) ).
fof(converse_additivity,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('theBenchmark.p',converse_additivity) ).
fof(converse_multiplicativity,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('theBenchmark.p',converse_multiplicativity) ).
fof(goals,conjecture,
! [X0,X1] :
( ( join(composition(converse(X1),X1),one) = one
& join(composition(converse(X0),X0),one) = one )
=> join(composition(converse(composition(X0,X1)),composition(X0,X1)),one) = one ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( ( join(composition(converse(X1),X1),one) = one
& join(composition(converse(X0),X0),one) = one )
=> join(composition(converse(composition(X0,X1)),composition(X0,X1)),one) = one ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_18,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_19,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_23,plain,
composition(composition(A,B),C) = composition(A,composition(B,C)),
inference(clausify,[status(thm)],[composition_associativity]) ).
cnf(c_24,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity]) ).
cnf(c_25,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity]) ).
cnf(c_26,plain,
join(composition(A,B),composition(C,B)) = composition(join(A,C),B),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_27,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence]) ).
cnf(c_28,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity]) ).
cnf(c_29,plain,
join(converse(A),converse(B)) = converse(join(A,B)),
inference(copy,[status(thm)],[c_28]) ).
cnf(c_30,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity]) ).
cnf(c_31,plain,
composition(converse(A),converse(B)) = converse(composition(B,A)),
inference(copy,[status(thm)],[c_30]) ).
fof(nnf_17,plain,
? [X0,X1] :
( join(composition(converse(composition(X0,X1)),composition(X0,X1)),one) != one
& join(composition(converse(X1),X1),one) = one
& join(composition(converse(X0),X0),one) = one ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( join(composition(converse(composition(sK0,sK1)),composition(sK0,sK1)),one) != one
& join(composition(converse(sK1),sK1),one) = one
& join(composition(converse(sK0),sK0),one) = one ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[nnf_17]) ).
cnf(c_43,negated_conjecture,
join(composition(converse(sK0),sK0),one) = one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_44,negated_conjecture,
join(one,composition(converse(sK0),sK0)) = one,
inference(paramod,[status(thm)],[c_18,c_43]) ).
cnf(c_45,negated_conjecture,
join(composition(converse(sK1),sK1),one) = one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_46,negated_conjecture,
join(one,composition(converse(sK1),sK1)) = one,
inference(paramod,[status(thm)],[c_18,c_45]) ).
cnf(c_47,negated_conjecture,
join(composition(converse(composition(sK0,sK1)),composition(sK0,sK1)),one) != one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_48,negated_conjecture,
join(one,composition(converse(composition(sK0,sK1)),composition(sK0,sK1))) != one,
inference(paramod,[status(thm)],[c_18,c_47]) ).
cnf(c_9033,plain,
composition(A,B) = composition(A,composition(one,B)),
inference(paramod,[status(thm)],[c_24,c_23]) ).
cnf(c_57,plain,
composition(A,composition(one,B)) = composition(A,B),
inference(copy,[status(thm)],[c_9033]) ).
cnf(c_9034,plain,
join(A,converse(B)) = converse(join(converse(A),B)),
inference(paramod,[status(thm)],[c_27,c_29]) ).
cnf(c_62,plain,
converse(join(converse(A),B)) = join(A,converse(B)),
inference(copy,[status(thm)],[c_9034]) ).
cnf(c_9035,plain,
composition(converse(composition(A,B)),C) = composition(converse(B),composition(converse(A),C)),
inference(paramod,[status(thm)],[c_31,c_23]) ).
cnf(c_64,plain,
composition(converse(A),composition(converse(B),C)) = composition(converse(composition(B,A)),C),
inference(copy,[status(thm)],[c_9035]) ).
cnf(c_65,plain,
join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(converse(B),C),converse(A)),
inference(paramod,[status(thm)],[c_31,c_26]) ).
cnf(c_9036,plain,
composition(A,converse(B)) = converse(composition(B,converse(A))),
inference(paramod,[status(thm)],[c_27,c_31]) ).
cnf(c_67,plain,
converse(composition(A,converse(B))) = composition(B,converse(A)),
inference(copy,[status(thm)],[c_9036]) ).
cnf(c_9037,plain,
composition(converse(A),B) = converse(composition(converse(B),A)),
inference(paramod,[status(thm)],[c_27,c_31]) ).
cnf(c_68,plain,
converse(composition(converse(A),B)) = composition(converse(B),A),
inference(copy,[status(thm)],[c_9037]) ).
cnf(c_9038,plain,
join(one,A) = join(one,join(composition(converse(sK1),sK1),A)),
inference(paramod,[status(thm)],[c_46,c_19]) ).
cnf(c_117,plain,
join(one,join(composition(converse(sK1),sK1),A)) = join(one,A),
inference(copy,[status(thm)],[c_9038]) ).
cnf(c_9039,plain,
converse(converse(A)) = composition(converse(one),A),
inference(paramod,[status(thm)],[c_24,c_68]) ).
cnf(c_9040,plain,
A = composition(converse(one),A),
inference(paramod,[status(thm)],[c_27,c_9039]) ).
cnf(c_553,plain,
composition(converse(one),A) = A,
inference(copy,[status(thm)],[c_9040]) ).
cnf(c_9041,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_553,c_24]) ).
cnf(c_559,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_9041]) ).
cnf(c_9042,plain,
join(A,composition(B,A)) = composition(join(converse(one),B),A),
inference(paramod,[status(thm)],[c_553,c_26]) ).
cnf(c_9043,plain,
join(A,composition(B,A)) = composition(join(one,B),A),
inference(paramod,[status(thm)],[c_559,c_9042]) ).
cnf(c_560,plain,
composition(join(one,A),B) = join(B,composition(A,B)),
inference(copy,[status(thm)],[c_9043]) ).
cnf(c_9044,plain,
composition(converse(one),composition(one,A)) = A,
inference(paramod,[status(thm)],[c_553,c_57]) ).
cnf(c_9045,plain,
composition(one,composition(one,A)) = A,
inference(paramod,[status(thm)],[c_559,c_9044]) ).
cnf(c_576,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_57,c_9045]) ).
cnf(c_9046,plain,
join(converse(converse(composition(A,B))),converse(composition(C,converse(A)))) = converse(composition(join(converse(B),C),converse(A))),
inference(paramod,[status(thm)],[c_65,c_29]) ).
cnf(c_9047,plain,
join(composition(A,B),converse(composition(C,converse(A)))) = converse(composition(join(converse(B),C),converse(A))),
inference(paramod,[status(thm)],[c_27,c_9046]) ).
cnf(c_9048,plain,
join(composition(A,B),composition(A,converse(C))) = converse(composition(join(converse(B),C),converse(A))),
inference(paramod,[status(thm)],[c_67,c_9047]) ).
cnf(c_9049,plain,
join(composition(A,B),composition(A,converse(C))) = composition(A,converse(join(converse(B),C))),
inference(paramod,[status(thm)],[c_67,c_9048]) ).
cnf(c_617,plain,
join(composition(A,B),composition(A,converse(C))) = composition(A,join(B,converse(C))),
inference(paramod,[status(thm)],[c_62,c_9049]) ).
cnf(c_9050,plain,
composition(one,A) = join(A,composition(composition(converse(sK0),sK0),A)),
inference(paramod,[status(thm)],[c_44,c_560]) ).
cnf(c_9051,plain,
A = join(A,composition(composition(converse(sK0),sK0),A)),
inference(paramod,[status(thm)],[c_576,c_9050]) ).
cnf(c_9052,plain,
A = join(A,composition(converse(sK0),composition(sK0,A))),
inference(paramod,[status(thm)],[c_23,c_9051]) ).
cnf(c_644,plain,
join(A,composition(converse(sK0),composition(sK0,A))) = A,
inference(copy,[status(thm)],[c_9052]) ).
cnf(c_9053,plain,
join(composition(A,B),composition(A,C)) = composition(A,join(B,converse(converse(C)))),
inference(paramod,[status(thm)],[c_27,c_617]) ).
cnf(c_3599,plain,
join(composition(A,B),composition(A,C)) = composition(A,join(B,C)),
inference(paramod,[status(thm)],[c_27,c_9053]) ).
cnf(c_4950,plain,
join(one,composition(converse(sK1),join(sK1,A))) = join(one,composition(converse(sK1),A)),
inference(paramod,[status(thm)],[c_3599,c_117]) ).
cnf(c_9054,plain,
join(one,composition(converse(sK1),sK1)) = join(one,composition(converse(sK1),composition(converse(sK0),composition(sK0,sK1)))),
inference(paramod,[status(thm)],[c_644,c_4950]) ).
cnf(c_9055,plain,
one = join(one,composition(converse(sK1),composition(converse(sK0),composition(sK0,sK1)))),
inference(paramod,[status(thm)],[c_46,c_9054]) ).
cnf(c_9056,plain,
one = join(one,composition(converse(composition(sK0,sK1)),composition(sK0,sK1))),
inference(paramod,[status(thm)],[c_64,c_9055]) ).
cnf(c_9057,plain,
join(one,composition(converse(composition(sK0,sK1)),composition(sK0,sK1))) = one,
inference(copy,[status(thm)],[c_9056]) ).
cnf(c_9032,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_48,c_9057]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL031+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n018.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 05:37:21 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 3837822 was started by sandbox2 on n018,
% 0.16/0.42 % Sat Sep 26 05:37:21 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 48.17/6.56
% 48.17/6.56 % SZS status Theorem for theBenchmark
% 48.17/6.56
% 48.17/6.56 % Proof 1 at 4.84 (+ 1.24) seconds.
% 48.17/6.56 % Length of proof is 42.
% 48.17/6.56 % Level of proof is 8.
% 48.17/6.56 % Maximum clause weight is 42.000.
% 48.17/6.56 % Given clauses 373.
% 48.17/6.56
% 48.17/6.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------