%------------------------------------------------------------------------------
% 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/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 : Unsatisfiable 35.26s 5.60s
% Output : CNFRefutation 35.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 71 ( 71 unt; 0 def)
% Number of atoms : 71 ( 70 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 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 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity_1,axiom,
! [VAR_0,VAR_1] : join(VAR_0,VAR_1) = join(VAR_1,VAR_0),
file('theBenchmark.p',maddux1_join_commutativity_1) ).
cnf(c_1,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity_1]) ).
fof(maddux2_join_associativity_2,axiom,
! [VAR_0,VAR_1,VAR_2] : join(VAR_0,join(VAR_1,VAR_2)) = join(join(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',maddux2_join_associativity_2) ).
cnf(c_2,plain,
join(A,join(B,C)) = join(join(A,B),C),
inference(clausify,[status(thm)],[maddux2_join_associativity_2]) ).
cnf(c_3,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(copy,[status(thm)],[c_2]) ).
fof(composition_associativity_5,axiom,
! [VAR_0,VAR_1,VAR_2] : composition(VAR_0,composition(VAR_1,VAR_2)) = composition(composition(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',composition_associativity_5) ).
cnf(c_7,plain,
composition(A,composition(B,C)) = composition(composition(A,B),C),
inference(clausify,[status(thm)],[composition_associativity_5]) ).
cnf(c_8,plain,
composition(composition(A,B),C) = composition(A,composition(B,C)),
inference(copy,[status(thm)],[c_7]) ).
fof(composition_identity_6,axiom,
! [VAR_0] : composition(VAR_0,one) = VAR_0,
file('theBenchmark.p',composition_identity_6) ).
cnf(c_9,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity_6]) ).
fof(composition_distributivity_7,axiom,
! [VAR_0,VAR_1,VAR_2] : composition(join(VAR_0,VAR_1),VAR_2) = join(composition(VAR_0,VAR_2),composition(VAR_1,VAR_2)),
file('theBenchmark.p',composition_distributivity_7) ).
cnf(c_10,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity_7]) ).
cnf(c_11,plain,
join(composition(A,B),composition(C,B)) = composition(join(A,C),B),
inference(copy,[status(thm)],[c_10]) ).
fof(converse_idempotence_8,axiom,
! [VAR_0] : converse(converse(VAR_0)) = VAR_0,
file('theBenchmark.p',converse_idempotence_8) ).
cnf(c_12,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence_8]) ).
fof(converse_additivity_9,axiom,
! [VAR_0,VAR_1] : converse(join(VAR_0,VAR_1)) = join(converse(VAR_0),converse(VAR_1)),
file('theBenchmark.p',converse_additivity_9) ).
cnf(c_13,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity_9]) ).
cnf(c_14,plain,
join(converse(A),converse(B)) = converse(join(A,B)),
inference(copy,[status(thm)],[c_13]) ).
fof(converse_multiplicativity_10,axiom,
! [VAR_0,VAR_1] : converse(composition(VAR_0,VAR_1)) = composition(converse(VAR_1),converse(VAR_0)),
file('theBenchmark.p',converse_multiplicativity_10) ).
cnf(c_15,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity_10]) ).
cnf(c_16,plain,
composition(converse(A),converse(B)) = converse(composition(B,A)),
inference(copy,[status(thm)],[c_15]) ).
fof(goals_17,axiom,
join(composition(converse(sk1),sk1),one) = one,
file('theBenchmark.p',goals_17) ).
cnf(c_29,plain,
join(composition(converse(sk1),sk1),one) = one,
inference(clausify,[status(thm)],[goals_17]) ).
cnf(c_30,plain,
join(one,composition(converse(sk1),sk1)) = one,
inference(paramod,[status(thm)],[c_1,c_29]) ).
fof(goals_18,axiom,
join(composition(converse(sk2),sk2),one) = one,
file('theBenchmark.p',goals_18) ).
cnf(c_31,plain,
join(composition(converse(sk2),sk2),one) = one,
inference(clausify,[status(thm)],[goals_18]) ).
cnf(c_32,plain,
join(one,composition(converse(sk2),sk2)) = one,
inference(paramod,[status(thm)],[c_1,c_31]) ).
fof(goals_19,axiom,
join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),one) != one,
file('theBenchmark.p',goals_19) ).
cnf(c_33,plain,
join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),one) != one,
inference(clausify,[status(thm)],[goals_19]) ).
cnf(c_34,plain,
join(one,composition(converse(composition(sk1,sk2)),composition(sk1,sk2))) != one,
inference(paramod,[status(thm)],[c_1,c_33]) ).
cnf(c_9019,plain,
composition(A,B) = composition(A,composition(one,B)),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_43,plain,
composition(A,composition(one,B)) = composition(A,B),
inference(copy,[status(thm)],[c_9019]) ).
cnf(c_9020,plain,
join(A,converse(B)) = converse(join(converse(A),B)),
inference(paramod,[status(thm)],[c_12,c_14]) ).
cnf(c_48,plain,
converse(join(converse(A),B)) = join(A,converse(B)),
inference(copy,[status(thm)],[c_9020]) ).
cnf(c_9021,plain,
composition(converse(composition(A,B)),C) = composition(converse(B),composition(converse(A),C)),
inference(paramod,[status(thm)],[c_16,c_8]) ).
cnf(c_50,plain,
composition(converse(A),composition(converse(B),C)) = composition(converse(composition(B,A)),C),
inference(copy,[status(thm)],[c_9021]) ).
cnf(c_51,plain,
join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(converse(B),C),converse(A)),
inference(paramod,[status(thm)],[c_16,c_11]) ).
cnf(c_9022,plain,
composition(A,converse(B)) = converse(composition(B,converse(A))),
inference(paramod,[status(thm)],[c_12,c_16]) ).
cnf(c_53,plain,
converse(composition(A,converse(B))) = composition(B,converse(A)),
inference(copy,[status(thm)],[c_9022]) ).
cnf(c_9023,plain,
composition(converse(A),B) = converse(composition(converse(B),A)),
inference(paramod,[status(thm)],[c_12,c_16]) ).
cnf(c_54,plain,
converse(composition(converse(A),B)) = composition(converse(B),A),
inference(copy,[status(thm)],[c_9023]) ).
cnf(c_9024,plain,
join(one,A) = join(one,join(composition(converse(sk2),sk2),A)),
inference(paramod,[status(thm)],[c_32,c_3]) ).
cnf(c_103,plain,
join(one,join(composition(converse(sk2),sk2),A)) = join(one,A),
inference(copy,[status(thm)],[c_9024]) ).
cnf(c_9025,plain,
converse(converse(A)) = composition(converse(one),A),
inference(paramod,[status(thm)],[c_9,c_54]) ).
cnf(c_9026,plain,
A = composition(converse(one),A),
inference(paramod,[status(thm)],[c_12,c_9025]) ).
cnf(c_539,plain,
composition(converse(one),A) = A,
inference(copy,[status(thm)],[c_9026]) ).
cnf(c_9027,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_539,c_9]) ).
cnf(c_545,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_9027]) ).
cnf(c_9028,plain,
join(A,composition(B,A)) = composition(join(converse(one),B),A),
inference(paramod,[status(thm)],[c_539,c_11]) ).
cnf(c_9029,plain,
join(A,composition(B,A)) = composition(join(one,B),A),
inference(paramod,[status(thm)],[c_545,c_9028]) ).
cnf(c_546,plain,
composition(join(one,A),B) = join(B,composition(A,B)),
inference(copy,[status(thm)],[c_9029]) ).
cnf(c_9030,plain,
composition(converse(one),composition(one,A)) = A,
inference(paramod,[status(thm)],[c_539,c_43]) ).
cnf(c_9031,plain,
composition(one,composition(one,A)) = A,
inference(paramod,[status(thm)],[c_545,c_9030]) ).
cnf(c_562,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_43,c_9031]) ).
cnf(c_9032,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_51,c_14]) ).
cnf(c_9033,plain,
join(composition(A,B),converse(composition(C,converse(A)))) = converse(composition(join(converse(B),C),converse(A))),
inference(paramod,[status(thm)],[c_12,c_9032]) ).
cnf(c_9034,plain,
join(composition(A,B),composition(A,converse(C))) = converse(composition(join(converse(B),C),converse(A))),
inference(paramod,[status(thm)],[c_53,c_9033]) ).
cnf(c_9035,plain,
join(composition(A,B),composition(A,converse(C))) = composition(A,converse(join(converse(B),C))),
inference(paramod,[status(thm)],[c_53,c_9034]) ).
cnf(c_603,plain,
join(composition(A,B),composition(A,converse(C))) = composition(A,join(B,converse(C))),
inference(paramod,[status(thm)],[c_48,c_9035]) ).
cnf(c_9036,plain,
composition(one,A) = join(A,composition(composition(converse(sk1),sk1),A)),
inference(paramod,[status(thm)],[c_30,c_546]) ).
cnf(c_9037,plain,
A = join(A,composition(composition(converse(sk1),sk1),A)),
inference(paramod,[status(thm)],[c_562,c_9036]) ).
cnf(c_9038,plain,
A = join(A,composition(converse(sk1),composition(sk1,A))),
inference(paramod,[status(thm)],[c_8,c_9037]) ).
cnf(c_630,plain,
join(A,composition(converse(sk1),composition(sk1,A))) = A,
inference(copy,[status(thm)],[c_9038]) ).
cnf(c_9039,plain,
join(composition(A,B),composition(A,C)) = composition(A,join(B,converse(converse(C)))),
inference(paramod,[status(thm)],[c_12,c_603]) ).
cnf(c_3585,plain,
join(composition(A,B),composition(A,C)) = composition(A,join(B,C)),
inference(paramod,[status(thm)],[c_12,c_9039]) ).
cnf(c_4936,plain,
join(one,composition(converse(sk2),join(sk2,A))) = join(one,composition(converse(sk2),A)),
inference(paramod,[status(thm)],[c_3585,c_103]) ).
cnf(c_9040,plain,
join(one,composition(converse(sk2),sk2)) = join(one,composition(converse(sk2),composition(converse(sk1),composition(sk1,sk2)))),
inference(paramod,[status(thm)],[c_630,c_4936]) ).
cnf(c_9041,plain,
one = join(one,composition(converse(sk2),composition(converse(sk1),composition(sk1,sk2)))),
inference(paramod,[status(thm)],[c_32,c_9040]) ).
cnf(c_9042,plain,
one = join(one,composition(converse(composition(sk1,sk2)),composition(sk1,sk2))),
inference(paramod,[status(thm)],[c_50,c_9041]) ).
cnf(c_9043,plain,
join(one,composition(converse(composition(sk1,sk2)),composition(sk1,sk2))) = one,
inference(copy,[status(thm)],[c_9042]) ).
cnf(c_9018,plain,
$false,
inference(resolve,[status(thm)],[c_34,c_9043]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL031-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.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
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 05:35:14 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3472216 was started by sandbox on n009,
% 0.08/0.36 % Sat Sep 26 05:35:14 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 35.26/5.60
% 35.26/5.60 % SZS status Unsatisfiable for theBenchmark
% 35.26/5.60
% 35.26/5.60 % Proof 1 at 3.89 (+ 0.92) seconds.
% 35.26/5.60 % Length of proof is 35.
% 35.26/5.60 % Level of proof is 7.
% 35.26/5.60 % Maximum clause weight is 42.000.
% 35.26/5.60 % Given clauses 373.
% 35.26/5.60
% 35.26/5.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------