%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP170-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 07:28:12 AM UTC 2026
% Result : Unsatisfiable 12.12s 1.96s
% Output : CNFRefutation 12.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 78 ( 78 unt; 0 def)
% Number of atoms : 78 ( 77 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 110 ( 8 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(symmetry_of_glb,axiom,
! [VAR_0,VAR_1] : greatest_lower_bound(VAR_0,VAR_1) = greatest_lower_bound(VAR_1,VAR_0),
file('theBenchmark.p',symmetry_of_glb) ).
cnf(c_4,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(B,A),
inference(clausify,[status(thm)],[symmetry_of_glb]) ).
fof(symmetry_of_lub,axiom,
! [VAR_0,VAR_1] : least_upper_bound(VAR_0,VAR_1) = least_upper_bound(VAR_1,VAR_0),
file('theBenchmark.p',symmetry_of_lub) ).
cnf(c_5,plain,
least_upper_bound(A,B) = least_upper_bound(B,A),
inference(clausify,[status(thm)],[symmetry_of_lub]) ).
fof(associativity_of_lub,axiom,
! [VAR_0,VAR_1,VAR_2] : least_upper_bound(VAR_0,least_upper_bound(VAR_1,VAR_2)) = least_upper_bound(least_upper_bound(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_of_lub) ).
cnf(c_8,plain,
least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(least_upper_bound(A,B),C),
inference(clausify,[status(thm)],[associativity_of_lub]) ).
cnf(c_9,plain,
least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(A,least_upper_bound(B,C)),
inference(copy,[status(thm)],[c_8]) ).
fof(lub_absorbtion,axiom,
! [VAR_0,VAR_1] : least_upper_bound(VAR_0,greatest_lower_bound(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',lub_absorbtion) ).
cnf(c_12,plain,
least_upper_bound(A,greatest_lower_bound(A,B)) = A,
inference(clausify,[status(thm)],[lub_absorbtion]) ).
fof(glb_absorbtion,axiom,
! [VAR_0,VAR_1] : greatest_lower_bound(VAR_0,least_upper_bound(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',glb_absorbtion) ).
cnf(c_13,plain,
greatest_lower_bound(A,least_upper_bound(A,B)) = A,
inference(clausify,[status(thm)],[glb_absorbtion]) ).
fof(monotony_lub1,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,least_upper_bound(VAR_1,VAR_2)) = least_upper_bound(multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_2)),
file('theBenchmark.p',monotony_lub1) ).
cnf(c_14,plain,
multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[monotony_lub1]) ).
cnf(c_15,plain,
least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)),
inference(copy,[status(thm)],[c_14]) ).
fof(monotony_glb1,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,greatest_lower_bound(VAR_1,VAR_2)) = greatest_lower_bound(multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_2)),
file('theBenchmark.p',monotony_glb1) ).
cnf(c_16,plain,
multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[monotony_glb1]) ).
cnf(c_17,plain,
greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)),
inference(copy,[status(thm)],[c_16]) ).
fof(monotony_lub2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(least_upper_bound(VAR_0,VAR_1),VAR_2) = least_upper_bound(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2)),
file('theBenchmark.p',monotony_lub2) ).
cnf(c_18,plain,
multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[monotony_lub2]) ).
cnf(c_19,plain,
least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B),
inference(copy,[status(thm)],[c_18]) ).
fof(p03d_1,axiom,
least_upper_bound(a,b) = b,
file('theBenchmark.p',p03d_1) ).
cnf(c_22,plain,
least_upper_bound(a,b) = b,
inference(clausify,[status(thm)],[p03d_1]) ).
cnf(c_23,plain,
least_upper_bound(b,a) = b,
inference(paramod,[status(thm)],[c_5,c_22]) ).
fof(p03d_2,axiom,
greatest_lower_bound(c,d) = c,
file('theBenchmark.p',p03d_2) ).
cnf(c_24,plain,
greatest_lower_bound(c,d) = c,
inference(clausify,[status(thm)],[p03d_2]) ).
fof(prove_p03d,axiom,
least_upper_bound(multiply(a,c),multiply(b,d)) != multiply(b,d),
file('theBenchmark.p',prove_p03d) ).
cnf(c_25,plain,
least_upper_bound(multiply(a,c),multiply(b,d)) != multiply(b,d),
inference(clausify,[status(thm)],[prove_p03d]) ).
cnf(c_26,plain,
least_upper_bound(multiply(b,d),multiply(a,c)) != multiply(b,d),
inference(paramod,[status(thm)],[c_5,c_25]) ).
cnf(c_3066,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_3067,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_3066]) ).
cnf(c_27,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_3067]) ).
cnf(c_38,plain,
least_upper_bound(A,greatest_lower_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_4,c_12]) ).
cnf(c_42,plain,
greatest_lower_bound(A,least_upper_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_13]) ).
cnf(c_46,plain,
least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)),
inference(paramod,[status(thm)],[c_2,c_15]) ).
cnf(c_3068,plain,
least_upper_bound(multiply(inverse(A),B),identity) = multiply(inverse(A),least_upper_bound(B,A)),
inference(paramod,[status(thm)],[c_2,c_15]) ).
cnf(c_47,plain,
least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(B,A)),
inference(paramod,[status(thm)],[c_5,c_3068]) ).
cnf(c_57,plain,
least_upper_bound(multiply(A,B),multiply(C,multiply(D,B))) = multiply(least_upper_bound(A,multiply(C,D)),B),
inference(paramod,[status(thm)],[c_3,c_19]) ).
cnf(c_3069,plain,
least_upper_bound(b,A) = least_upper_bound(b,least_upper_bound(a,A)),
inference(paramod,[status(thm)],[c_23,c_9]) ).
cnf(c_66,plain,
least_upper_bound(b,least_upper_bound(a,A)) = least_upper_bound(b,A),
inference(copy,[status(thm)],[c_3069]) ).
cnf(c_71,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_27]) ).
cnf(c_81,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_27,c_27]) ).
cnf(c_82,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_81,c_71]) ).
cnf(c_91,plain,
greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(identity,B)),
inference(paramod,[status(thm)],[c_82,c_17]) ).
cnf(c_3070,plain,
least_upper_bound(d,c) = d,
inference(paramod,[status(thm)],[c_24,c_38]) ).
cnf(c_96,plain,
least_upper_bound(c,d) = d,
inference(paramod,[status(thm)],[c_5,c_3070]) ).
cnf(c_3071,plain,
least_upper_bound(b,a) = least_upper_bound(b,greatest_lower_bound(a,A)),
inference(paramod,[status(thm)],[c_12,c_66]) ).
cnf(c_3072,plain,
b = least_upper_bound(b,greatest_lower_bound(a,A)),
inference(paramod,[status(thm)],[c_23,c_3071]) ).
cnf(c_201,plain,
least_upper_bound(b,greatest_lower_bound(a,A)) = b,
inference(copy,[status(thm)],[c_3072]) ).
cnf(c_297,plain,
least_upper_bound(identity,A) = multiply(inverse(B),least_upper_bound(B,multiply(B,A))),
inference(paramod,[status(thm)],[c_27,c_46]) ).
cnf(c_3073,plain,
least_upper_bound(identity,multiply(inverse(d),c)) = multiply(inverse(d),d),
inference(paramod,[status(thm)],[c_96,c_47]) ).
cnf(c_328,plain,
least_upper_bound(identity,multiply(inverse(d),c)) = identity,
inference(paramod,[status(thm)],[c_2,c_3073]) ).
cnf(c_3074,plain,
least_upper_bound(multiply(identity,A),multiply(multiply(inverse(d),c),A)) = multiply(identity,A),
inference(paramod,[status(thm)],[c_328,c_19]) ).
cnf(c_3075,plain,
least_upper_bound(A,multiply(multiply(inverse(d),c),A)) = multiply(identity,A),
inference(paramod,[status(thm)],[c_1,c_3074]) ).
cnf(c_3076,plain,
least_upper_bound(A,multiply(inverse(d),multiply(c,A))) = multiply(identity,A),
inference(paramod,[status(thm)],[c_3,c_3075]) ).
cnf(c_351,plain,
least_upper_bound(A,multiply(inverse(d),multiply(c,A))) = A,
inference(paramod,[status(thm)],[c_1,c_3076]) ).
cnf(c_473,plain,
least_upper_bound(b,multiply(a,greatest_lower_bound(identity,A))) = b,
inference(paramod,[status(thm)],[c_91,c_201]) ).
cnf(c_3077,plain,
least_upper_bound(multiply(A,B),multiply(C,identity)) = multiply(least_upper_bound(A,multiply(C,inverse(B))),B),
inference(paramod,[status(thm)],[c_2,c_57]) ).
cnf(c_651,plain,
least_upper_bound(multiply(A,B),C) = multiply(least_upper_bound(A,multiply(C,inverse(B))),B),
inference(paramod,[status(thm)],[c_82,c_3077]) ).
cnf(c_3078,plain,
multiply(least_upper_bound(b,multiply(multiply(a,c),inverse(d))),d) != multiply(b,d),
inference(paramod,[status(thm)],[c_651,c_26]) ).
cnf(c_657,plain,
multiply(least_upper_bound(b,multiply(a,multiply(c,inverse(d)))),d) != multiply(b,d),
inference(paramod,[status(thm)],[c_3,c_3078]) ).
cnf(c_836,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_81,c_2]) ).
cnf(c_3079,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_81,c_82]) ).
cnf(c_3080,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_82,c_3079]) ).
cnf(c_838,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_3080]) ).
cnf(c_3081,plain,
least_upper_bound(identity,multiply(c,inverse(d))) = multiply(inverse(inverse(d)),inverse(d)),
inference(paramod,[status(thm)],[c_351,c_297]) ).
cnf(c_3082,plain,
least_upper_bound(identity,multiply(c,inverse(d))) = multiply(d,inverse(d)),
inference(paramod,[status(thm)],[c_838,c_3081]) ).
cnf(c_3020,plain,
least_upper_bound(identity,multiply(c,inverse(d))) = identity,
inference(paramod,[status(thm)],[c_836,c_3082]) ).
cnf(c_3083,plain,
greatest_lower_bound(multiply(c,inverse(d)),identity) = multiply(c,inverse(d)),
inference(paramod,[status(thm)],[c_3020,c_42]) ).
cnf(c_3022,plain,
greatest_lower_bound(identity,multiply(c,inverse(d))) = multiply(c,inverse(d)),
inference(paramod,[status(thm)],[c_4,c_3083]) ).
cnf(c_3049,plain,
least_upper_bound(b,multiply(a,multiply(c,inverse(d)))) = b,
inference(paramod,[status(thm)],[c_3022,c_473]) ).
cnf(c_3084,plain,
multiply(b,d) != multiply(b,d),
inference(paramod,[status(thm)],[c_3049,c_657]) ).
cnf(c_3065,plain,
$false,
inference(copy,[status(thm)],[c_3084]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP170-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:31:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1217295 was started by sandbox2 on n007,
% 0.09/0.37 % Fri Sep 25 14:31:54 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 12.12/1.96
% 12.12/1.96 % SZS status Unsatisfiable for theBenchmark
% 12.12/1.96
% 12.12/1.96 % Proof 1 at 1.17 (+ 0.34) seconds.
% 12.12/1.96 % Length of proof is 45.
% 12.12/1.96 % Level of proof is 8.
% 12.12/1.96 % Maximum clause weight is 28.000.
% 12.12/1.96 % Given clauses 305.
% 12.12/1.96
% 12.12/1.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------