%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP178-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 07:28:14 AM UTC 2026
% Result : Unsatisfiable 152.42s 41.84s
% Output : CNFRefutation 152.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 10
% Syntax : Number of formulae : 91 ( 91 unt; 0 def)
% Number of atoms : 91 ( 90 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 13 ( 13 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 100 ( 0 sgn 16 !; 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(associativity_of_glb,axiom,
! [VAR_0,VAR_1,VAR_2] : greatest_lower_bound(VAR_0,greatest_lower_bound(VAR_1,VAR_2)) = greatest_lower_bound(greatest_lower_bound(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_of_glb) ).
cnf(c_6,plain,
greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(greatest_lower_bound(A,B),C),
inference(clausify,[status(thm)],[associativity_of_glb]) ).
cnf(c_7,plain,
greatest_lower_bound(greatest_lower_bound(A,B),C) = greatest_lower_bound(A,greatest_lower_bound(B,C)),
inference(copy,[status(thm)],[c_6]) ).
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_glb2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(greatest_lower_bound(VAR_0,VAR_1),VAR_2) = greatest_lower_bound(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2)),
file('theBenchmark.p',monotony_glb2) ).
cnf(c_20,plain,
multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[monotony_glb2]) ).
cnf(c_21,plain,
greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B),
inference(copy,[status(thm)],[c_20]) ).
fof(p09b_3,axiom,
greatest_lower_bound(identity,c) = identity,
file('theBenchmark.p',p09b_3) ).
cnf(c_24,plain,
greatest_lower_bound(identity,c) = identity,
inference(clausify,[status(thm)],[p09b_3]) ).
fof(p09b_4,axiom,
greatest_lower_bound(a,b) = identity,
file('theBenchmark.p',p09b_4) ).
cnf(c_25,plain,
greatest_lower_bound(a,b) = identity,
inference(clausify,[status(thm)],[p09b_4]) ).
fof(prove_p09b,axiom,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('theBenchmark.p',prove_p09b) ).
cnf(c_26,plain,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
inference(clausify,[status(thm)],[prove_p09b]) ).
cnf(c_30295,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_30296,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_30295]) ).
cnf(c_27,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_30296]) ).
cnf(c_49,plain,
greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(A,B)),
inference(paramod,[status(thm)],[c_2,c_17]) ).
cnf(c_30297,plain,
greatest_lower_bound(multiply(inverse(A),B),identity) = multiply(inverse(A),greatest_lower_bound(B,A)),
inference(paramod,[status(thm)],[c_2,c_17]) ).
cnf(c_50,plain,
greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(B,A)),
inference(paramod,[status(thm)],[c_4,c_30297]) ).
cnf(c_59,plain,
greatest_lower_bound(A,multiply(B,A)) = multiply(greatest_lower_bound(identity,B),A),
inference(paramod,[status(thm)],[c_1,c_21]) ).
cnf(c_30298,plain,
greatest_lower_bound(multiply(A,B),identity) = multiply(greatest_lower_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_2,c_21]) ).
cnf(c_62,plain,
greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B),
inference(paramod,[status(thm)],[c_4,c_30298]) ).
cnf(c_79,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_27]) ).
cnf(c_80,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))) = C,
inference(paramod,[status(thm)],[c_3,c_27]) ).
cnf(c_89,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_27,c_27]) ).
cnf(c_90,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_89,c_79]) ).
cnf(c_95,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_90,c_2]) ).
cnf(c_98,plain,
greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(identity,B)),
inference(paramod,[status(thm)],[c_90,c_17]) ).
cnf(c_410,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_89,c_2]) ).
cnf(c_30299,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_89,c_90]) ).
cnf(c_30300,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_90,c_30299]) ).
cnf(c_416,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_30300]) ).
cnf(c_462,plain,
greatest_lower_bound(identity,multiply(A,inverse(B))) = multiply(greatest_lower_bound(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_410,c_21]) ).
cnf(c_30301,plain,
greatest_lower_bound(identity,multiply(inverse(a),b)) = multiply(inverse(a),identity),
inference(paramod,[status(thm)],[c_25,c_49]) ).
cnf(c_558,plain,
greatest_lower_bound(identity,multiply(inverse(a),b)) = inverse(a),
inference(paramod,[status(thm)],[c_90,c_30301]) ).
cnf(c_30302,plain,
multiply(inverse(inverse(A)),greatest_lower_bound(identity,multiply(inverse(A),B))) = greatest_lower_bound(A,B),
inference(paramod,[status(thm)],[c_49,c_27]) ).
cnf(c_30303,plain,
multiply(A,greatest_lower_bound(identity,multiply(inverse(A),B))) = greatest_lower_bound(A,B),
inference(paramod,[status(thm)],[c_416,c_30302]) ).
cnf(c_559,plain,
greatest_lower_bound(A,B) = multiply(A,greatest_lower_bound(identity,multiply(inverse(A),B))),
inference(copy,[status(thm)],[c_30303]) ).
cnf(c_560,plain,
greatest_lower_bound(identity,A) = multiply(inverse(B),greatest_lower_bound(B,multiply(B,A))),
inference(paramod,[status(thm)],[c_27,c_49]) ).
cnf(c_30304,plain,
multiply(inverse(multiply(A,B)),multiply(A,identity)) = inverse(B),
inference(paramod,[status(thm)],[c_410,c_80]) ).
cnf(c_1311,plain,
multiply(inverse(multiply(A,B)),A) = inverse(B),
inference(paramod,[status(thm)],[c_90,c_30304]) ).
cnf(c_1839,plain,
greatest_lower_bound(inverse(A),B) = multiply(inverse(A),greatest_lower_bound(identity,multiply(A,B))),
inference(paramod,[status(thm)],[c_27,c_98]) ).
cnf(c_30305,plain,
inverse(a) = multiply(greatest_lower_bound(inverse(a),inverse(b)),b),
inference(paramod,[status(thm)],[c_558,c_62]) ).
cnf(c_30306,plain,
inverse(a) = multiply(multiply(inverse(a),greatest_lower_bound(identity,multiply(a,inverse(b)))),b),
inference(paramod,[status(thm)],[c_1839,c_30305]) ).
cnf(c_30307,plain,
inverse(a) = multiply(inverse(a),multiply(greatest_lower_bound(identity,multiply(a,inverse(b))),b)),
inference(paramod,[status(thm)],[c_3,c_30306]) ).
cnf(c_3260,plain,
multiply(inverse(a),multiply(greatest_lower_bound(identity,multiply(a,inverse(b))),b)) = inverse(a),
inference(copy,[status(thm)],[c_30307]) ).
cnf(c_30308,plain,
multiply(inverse(A),inverse(B)) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_27,c_1311]) ).
cnf(c_3457,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(copy,[status(thm)],[c_30308]) ).
cnf(c_30309,plain,
greatest_lower_bound(identity,multiply(b,inverse(a))) = multiply(identity,inverse(a)),
inference(paramod,[status(thm)],[c_25,c_462]) ).
cnf(c_27133,plain,
greatest_lower_bound(identity,multiply(b,inverse(a))) = inverse(a),
inference(paramod,[status(thm)],[c_1,c_30309]) ).
cnf(c_30310,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(b,inverse(a))),identity)) = multiply(inverse(multiply(b,inverse(a))),inverse(a)),
inference(paramod,[status(thm)],[c_27133,c_50]) ).
cnf(c_30311,plain,
greatest_lower_bound(identity,multiply(multiply(inverse(inverse(a)),inverse(b)),identity)) = multiply(inverse(multiply(b,inverse(a))),inverse(a)),
inference(paramod,[status(thm)],[c_3457,c_30310]) ).
cnf(c_30312,plain,
greatest_lower_bound(identity,multiply(multiply(a,inverse(b)),identity)) = multiply(inverse(multiply(b,inverse(a))),inverse(a)),
inference(paramod,[status(thm)],[c_416,c_30311]) ).
cnf(c_30313,plain,
greatest_lower_bound(identity,multiply(a,inverse(b))) = multiply(inverse(multiply(b,inverse(a))),inverse(a)),
inference(paramod,[status(thm)],[c_90,c_30312]) ).
cnf(c_30314,plain,
greatest_lower_bound(identity,multiply(a,inverse(b))) = multiply(multiply(inverse(inverse(a)),inverse(b)),inverse(a)),
inference(paramod,[status(thm)],[c_3457,c_30313]) ).
cnf(c_30315,plain,
greatest_lower_bound(identity,multiply(a,inverse(b))) = multiply(multiply(a,inverse(b)),inverse(a)),
inference(paramod,[status(thm)],[c_416,c_30314]) ).
cnf(c_27195,plain,
greatest_lower_bound(identity,multiply(a,inverse(b))) = multiply(a,multiply(inverse(b),inverse(a))),
inference(paramod,[status(thm)],[c_3,c_30315]) ).
cnf(c_30316,plain,
greatest_lower_bound(A,multiply(multiply(b,inverse(a)),A)) = multiply(inverse(a),A),
inference(paramod,[status(thm)],[c_27133,c_59]) ).
cnf(c_27196,plain,
greatest_lower_bound(A,multiply(b,multiply(inverse(a),A))) = multiply(inverse(a),A),
inference(paramod,[status(thm)],[c_3,c_30316]) ).
cnf(c_30317,plain,
multiply(inverse(a),multiply(multiply(a,multiply(inverse(b),inverse(a))),b)) = inverse(a),
inference(paramod,[status(thm)],[c_27195,c_3260]) ).
cnf(c_30318,plain,
multiply(inverse(a),multiply(a,multiply(multiply(inverse(b),inverse(a)),b))) = inverse(a),
inference(paramod,[status(thm)],[c_3,c_30317]) ).
cnf(c_30319,plain,
multiply(inverse(a),multiply(a,multiply(inverse(b),multiply(inverse(a),b)))) = inverse(a),
inference(paramod,[status(thm)],[c_3,c_30318]) ).
cnf(c_27200,plain,
multiply(inverse(b),multiply(inverse(a),b)) = inverse(a),
inference(paramod,[status(thm)],[c_27,c_30319]) ).
cnf(c_30320,plain,
multiply(inverse(inverse(b)),inverse(a)) = multiply(inverse(a),b),
inference(paramod,[status(thm)],[c_27200,c_27]) ).
cnf(c_30321,plain,
multiply(b,inverse(a)) = multiply(inverse(a),b),
inference(paramod,[status(thm)],[c_416,c_30320]) ).
cnf(c_27205,plain,
multiply(inverse(a),b) = multiply(b,inverse(a)),
inference(copy,[status(thm)],[c_30321]) ).
cnf(c_30322,plain,
multiply(multiply(b,inverse(a)),A) = multiply(inverse(a),multiply(b,A)),
inference(paramod,[status(thm)],[c_27205,c_3]) ).
cnf(c_30323,plain,
multiply(b,multiply(inverse(a),A)) = multiply(inverse(a),multiply(b,A)),
inference(paramod,[status(thm)],[c_3,c_30322]) ).
cnf(c_27253,plain,
multiply(inverse(a),multiply(b,A)) = multiply(b,multiply(inverse(a),A)),
inference(copy,[status(thm)],[c_30323]) ).
cnf(c_30324,plain,
multiply(a,greatest_lower_bound(identity,multiply(inverse(a),multiply(b,c)))) != greatest_lower_bound(a,c),
inference(paramod,[status(thm)],[c_559,c_26]) ).
cnf(c_30325,plain,
multiply(a,greatest_lower_bound(identity,multiply(b,multiply(inverse(a),c)))) != greatest_lower_bound(a,c),
inference(paramod,[status(thm)],[c_27253,c_30324]) ).
cnf(c_28579,plain,
greatest_lower_bound(a,c) != multiply(a,greatest_lower_bound(identity,multiply(b,multiply(inverse(a),c)))),
inference(copy,[status(thm)],[c_30325]) ).
cnf(c_28768,plain,
greatest_lower_bound(a,c) != multiply(a,multiply(inverse(A),greatest_lower_bound(A,multiply(A,multiply(b,multiply(inverse(a),c)))))),
inference(paramod,[status(thm)],[c_560,c_28579]) ).
cnf(c_28852,plain,
greatest_lower_bound(a,c) != multiply(a,multiply(inverse(greatest_lower_bound(A,B)),greatest_lower_bound(A,greatest_lower_bound(B,multiply(greatest_lower_bound(A,B),multiply(b,multiply(inverse(a),c))))))),
inference(paramod,[status(thm)],[c_7,c_28768]) ).
cnf(c_30326,plain,
greatest_lower_bound(a,c) != multiply(a,multiply(inverse(identity),greatest_lower_bound(identity,greatest_lower_bound(c,multiply(greatest_lower_bound(identity,c),multiply(b,multiply(inverse(a),c))))))),
inference(paramod,[status(thm)],[c_24,c_28852]) ).
cnf(c_30327,plain,
greatest_lower_bound(a,c) != multiply(a,multiply(identity,greatest_lower_bound(identity,greatest_lower_bound(c,multiply(greatest_lower_bound(identity,c),multiply(b,multiply(inverse(a),c))))))),
inference(paramod,[status(thm)],[c_95,c_30326]) ).
cnf(c_30328,plain,
greatest_lower_bound(a,c) != multiply(a,multiply(identity,greatest_lower_bound(identity,greatest_lower_bound(c,multiply(identity,multiply(b,multiply(inverse(a),c))))))),
inference(paramod,[status(thm)],[c_24,c_30327]) ).
cnf(c_30329,plain,
greatest_lower_bound(a,c) != multiply(a,multiply(identity,greatest_lower_bound(identity,greatest_lower_bound(c,multiply(b,multiply(inverse(a),c)))))),
inference(paramod,[status(thm)],[c_1,c_30328]) ).
cnf(c_30330,plain,
greatest_lower_bound(a,c) != multiply(a,multiply(identity,greatest_lower_bound(identity,multiply(inverse(a),c)))),
inference(paramod,[status(thm)],[c_27196,c_30329]) ).
cnf(c_30293,plain,
greatest_lower_bound(a,c) != multiply(a,greatest_lower_bound(identity,multiply(inverse(a),c))),
inference(paramod,[status(thm)],[c_1,c_30330]) ).
cnf(c_30294,plain,
$false,
inference(resolve,[status(thm)],[c_30293,c_559]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP178-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:37:19 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 3511488 was started by sandbox on n002,
% 0.08/0.36 % Fri Sep 25 14:37:19 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 152.42/41.84
% 152.42/41.84 % given #500 (T,wt=10): 971 least_upper_bound(identity,multiply(greatest_lower_bound(A,inverse(B)),B)) = identity. [para(38(a,1),54(a,1,1)),rewrite([2(2)]),flip(a)].
% 152.42/41.84
% 152.42/41.84 % given #1000 (T,wt=11): 2740 greatest_lower_bound(A,multiply(c,least_upper_bound(B,least_upper_bound(A,C)))) = A. [para(31(a,1),280(a,1,2,2))].
% 152.42/41.84
% 152.42/41.84 % SZS status Unsatisfiable for theBenchmark
% 152.42/41.84
% 152.42/41.84 % Proof 1 at 15.47 (+ 3.96) seconds.
% 152.42/41.84 % Length of proof is 45.
% 152.42/41.84 % Level of proof is 14.
% 152.42/41.84 % Maximum clause weight is 25.000.
% 152.42/41.84 % Given clauses 1391.
% 152.42/41.84
% 152.42/41.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------