%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL031-1 : 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 : n001.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 08:25:00 AM UTC 2026
% Result : Unsatisfiable 26.72s 3.85s
% Output : CNFRefutation 26.72s
% 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_14,axiom,
join(composition(converse(sk1),sk1),one) = one,
file('theBenchmark.p',goals_14) ).
cnf(c_23,plain,
join(composition(converse(sk1),sk1),one) = one,
inference(clausify,[status(thm)],[goals_14]) ).
cnf(c_24,plain,
join(one,composition(converse(sk1),sk1)) = one,
inference(paramod,[status(thm)],[c_1,c_23]) ).
fof(goals_15,axiom,
join(composition(converse(sk2),sk2),one) = one,
file('theBenchmark.p',goals_15) ).
cnf(c_25,plain,
join(composition(converse(sk2),sk2),one) = one,
inference(clausify,[status(thm)],[goals_15]) ).
cnf(c_26,plain,
join(one,composition(converse(sk2),sk2)) = one,
inference(paramod,[status(thm)],[c_1,c_25]) ).
fof(goals_16,axiom,
join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),one) != one,
file('theBenchmark.p',goals_16) ).
cnf(c_27,plain,
join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),one) != one,
inference(clausify,[status(thm)],[goals_16]) ).
cnf(c_28,plain,
join(one,composition(converse(composition(sk1,sk2)),composition(sk1,sk2))) != one,
inference(paramod,[status(thm)],[c_1,c_27]) ).
cnf(c_10094,plain,
composition(A,B) = composition(A,composition(one,B)),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_37,plain,
composition(A,composition(one,B)) = composition(A,B),
inference(copy,[status(thm)],[c_10094]) ).
cnf(c_10095,plain,
join(A,converse(B)) = converse(join(converse(A),B)),
inference(paramod,[status(thm)],[c_12,c_14]) ).
cnf(c_42,plain,
converse(join(converse(A),B)) = join(A,converse(B)),
inference(copy,[status(thm)],[c_10095]) ).
cnf(c_10096,plain,
composition(converse(composition(A,B)),C) = composition(converse(B),composition(converse(A),C)),
inference(paramod,[status(thm)],[c_16,c_8]) ).
cnf(c_44,plain,
composition(converse(A),composition(converse(B),C)) = composition(converse(composition(B,A)),C),
inference(copy,[status(thm)],[c_10096]) ).
cnf(c_45,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_10097,plain,
composition(A,converse(B)) = converse(composition(B,converse(A))),
inference(paramod,[status(thm)],[c_12,c_16]) ).
cnf(c_47,plain,
converse(composition(A,converse(B))) = composition(B,converse(A)),
inference(copy,[status(thm)],[c_10097]) ).
cnf(c_10098,plain,
composition(converse(A),B) = converse(composition(converse(B),A)),
inference(paramod,[status(thm)],[c_12,c_16]) ).
cnf(c_48,plain,
converse(composition(converse(A),B)) = composition(converse(B),A),
inference(copy,[status(thm)],[c_10098]) ).
cnf(c_10099,plain,
join(one,A) = join(one,join(composition(converse(sk2),sk2),A)),
inference(paramod,[status(thm)],[c_26,c_3]) ).
cnf(c_67,plain,
join(one,join(composition(converse(sk2),sk2),A)) = join(one,A),
inference(copy,[status(thm)],[c_10099]) ).
cnf(c_10100,plain,
converse(converse(A)) = composition(converse(one),A),
inference(paramod,[status(thm)],[c_9,c_48]) ).
cnf(c_10101,plain,
A = composition(converse(one),A),
inference(paramod,[status(thm)],[c_12,c_10100]) ).
cnf(c_423,plain,
composition(converse(one),A) = A,
inference(copy,[status(thm)],[c_10101]) ).
cnf(c_10102,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_423,c_9]) ).
cnf(c_429,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_10102]) ).
cnf(c_10103,plain,
join(A,composition(B,A)) = composition(join(converse(one),B),A),
inference(paramod,[status(thm)],[c_423,c_11]) ).
cnf(c_10104,plain,
join(A,composition(B,A)) = composition(join(one,B),A),
inference(paramod,[status(thm)],[c_429,c_10103]) ).
cnf(c_430,plain,
composition(join(one,A),B) = join(B,composition(A,B)),
inference(copy,[status(thm)],[c_10104]) ).
cnf(c_10105,plain,
composition(converse(one),composition(one,A)) = A,
inference(paramod,[status(thm)],[c_423,c_37]) ).
cnf(c_10106,plain,
composition(one,composition(one,A)) = A,
inference(paramod,[status(thm)],[c_429,c_10105]) ).
cnf(c_434,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_37,c_10106]) ).
cnf(c_10107,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_45,c_14]) ).
cnf(c_10108,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_10107]) ).
cnf(c_10109,plain,
join(composition(A,B),composition(A,converse(C))) = converse(composition(join(converse(B),C),converse(A))),
inference(paramod,[status(thm)],[c_47,c_10108]) ).
cnf(c_10110,plain,
join(composition(A,B),composition(A,converse(C))) = composition(A,converse(join(converse(B),C))),
inference(paramod,[status(thm)],[c_47,c_10109]) ).
cnf(c_460,plain,
join(composition(A,B),composition(A,converse(C))) = composition(A,join(B,converse(C))),
inference(paramod,[status(thm)],[c_42,c_10110]) ).
cnf(c_10111,plain,
composition(one,A) = join(A,composition(composition(converse(sk1),sk1),A)),
inference(paramod,[status(thm)],[c_24,c_430]) ).
cnf(c_10112,plain,
A = join(A,composition(composition(converse(sk1),sk1),A)),
inference(paramod,[status(thm)],[c_434,c_10111]) ).
cnf(c_10113,plain,
A = join(A,composition(converse(sk1),composition(sk1,A))),
inference(paramod,[status(thm)],[c_8,c_10112]) ).
cnf(c_479,plain,
join(A,composition(converse(sk1),composition(sk1,A))) = A,
inference(copy,[status(thm)],[c_10113]) ).
cnf(c_10114,plain,
join(composition(A,B),composition(A,C)) = composition(A,join(B,converse(converse(C)))),
inference(paramod,[status(thm)],[c_12,c_460]) ).
cnf(c_6160,plain,
join(composition(A,B),composition(A,C)) = composition(A,join(B,C)),
inference(paramod,[status(thm)],[c_12,c_10114]) ).
cnf(c_6445,plain,
join(one,composition(converse(sk2),join(sk2,A))) = join(one,composition(converse(sk2),A)),
inference(paramod,[status(thm)],[c_6160,c_67]) ).
cnf(c_10115,plain,
join(one,composition(converse(sk2),sk2)) = join(one,composition(converse(sk2),composition(converse(sk1),composition(sk1,sk2)))),
inference(paramod,[status(thm)],[c_479,c_6445]) ).
cnf(c_10116,plain,
one = join(one,composition(converse(sk2),composition(converse(sk1),composition(sk1,sk2)))),
inference(paramod,[status(thm)],[c_26,c_10115]) ).
cnf(c_10117,plain,
one = join(one,composition(converse(composition(sk1,sk2)),composition(sk1,sk2))),
inference(paramod,[status(thm)],[c_44,c_10116]) ).
cnf(c_10118,plain,
join(one,composition(converse(composition(sk1,sk2)),composition(sk1,sk2))) = one,
inference(copy,[status(thm)],[c_10117]) ).
cnf(c_10093,plain,
$false,
inference(resolve,[status(thm)],[c_28,c_10118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL031-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 % Computer : n001.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Sat Sep 26 05:41:11 UTC 2026
% 0.18/0.42 % CPUTime :
% 0.18/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.43 % Process 1017990 was started by sandbox on n001,
% 0.18/0.43 % Sat Sep 26 05:41:11 2026
% 0.18/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.43
% 0.18/0.43 % From the command line: assign(max_seconds, 300).
% 26.72/3.85
% 26.72/3.85 % SZS status Unsatisfiable for theBenchmark
% 26.72/3.85
% 26.72/3.85 % Proof 1 at 2.64 (+ 0.74) seconds.
% 26.72/3.85 % Length of proof is 35.
% 26.72/3.85 % Level of proof is 7.
% 26.72/3.85 % Maximum clause weight is 42.000.
% 26.72/3.85 % Given clauses 404.
% 26.72/3.85
% 26.72/3.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------