%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP170-2 : 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 : 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 07:28:12 AM UTC 2026
% Result : Unsatisfiable 2.39s 0.75s
% Output : CNFRefutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 42 unt; 0 def)
% Number of atoms : 42 ( 41 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 14 !; 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(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(p03b_1,axiom,
greatest_lower_bound(a,b) = a,
file('theBenchmark.p',p03b_1) ).
cnf(c_22,plain,
greatest_lower_bound(a,b) = a,
inference(clausify,[status(thm)],[p03b_1]) ).
fof(p03b_2,axiom,
greatest_lower_bound(c,d) = c,
file('theBenchmark.p',p03b_2) ).
cnf(c_23,plain,
greatest_lower_bound(c,d) = c,
inference(clausify,[status(thm)],[p03b_2]) ).
fof(prove_p03b,axiom,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
file('theBenchmark.p',prove_p03b) ).
cnf(c_24,plain,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
inference(clausify,[status(thm)],[prove_p03b]) ).
cnf(c_1686,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_1687,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_1686]) ).
cnf(c_25,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_1687]) ).
cnf(c_47,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_57,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_1688,plain,
greatest_lower_bound(c,A) = greatest_lower_bound(c,greatest_lower_bound(d,A)),
inference(paramod,[status(thm)],[c_23,c_7]) ).
cnf(c_66,plain,
greatest_lower_bound(c,greatest_lower_bound(d,A)) = greatest_lower_bound(c,A),
inference(copy,[status(thm)],[c_1688]) ).
cnf(c_79,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_25,c_25]) ).
cnf(c_199,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_79,c_25]) ).
cnf(c_220,plain,
greatest_lower_bound(multiply(A,B),C) = multiply(A,greatest_lower_bound(B,multiply(inverse(A),C))),
inference(paramod,[status(thm)],[c_199,c_17]) ).
cnf(c_242,plain,
multiply(a,greatest_lower_bound(c,multiply(inverse(a),multiply(b,d)))) != multiply(a,c),
inference(paramod,[status(thm)],[c_220,c_24]) ).
cnf(c_1689,plain,
greatest_lower_bound(identity,multiply(inverse(a),b)) = multiply(inverse(a),a),
inference(paramod,[status(thm)],[c_22,c_47]) ).
cnf(c_417,plain,
greatest_lower_bound(identity,multiply(inverse(a),b)) = identity,
inference(paramod,[status(thm)],[c_2,c_1689]) ).
cnf(c_1690,plain,
greatest_lower_bound(A,multiply(multiply(inverse(a),b),A)) = multiply(identity,A),
inference(paramod,[status(thm)],[c_417,c_57]) ).
cnf(c_1691,plain,
greatest_lower_bound(A,multiply(inverse(a),multiply(b,A))) = multiply(identity,A),
inference(paramod,[status(thm)],[c_3,c_1690]) ).
cnf(c_808,plain,
greatest_lower_bound(A,multiply(inverse(a),multiply(b,A))) = A,
inference(paramod,[status(thm)],[c_1,c_1691]) ).
cnf(c_1692,plain,
greatest_lower_bound(c,d) = greatest_lower_bound(c,multiply(inverse(a),multiply(b,d))),
inference(paramod,[status(thm)],[c_808,c_66]) ).
cnf(c_1693,plain,
c = greatest_lower_bound(c,multiply(inverse(a),multiply(b,d))),
inference(paramod,[status(thm)],[c_23,c_1692]) ).
cnf(c_1678,plain,
greatest_lower_bound(c,multiply(inverse(a),multiply(b,d))) = c,
inference(copy,[status(thm)],[c_1693]) ).
cnf(c_1694,plain,
multiply(a,c) != multiply(a,c),
inference(paramod,[status(thm)],[c_1678,c_242]) ).
cnf(c_1685,plain,
$false,
inference(copy,[status(thm)],[c_1694]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP170-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 14:33:30 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1819323 was started by sandbox on n009,
% 0.09/0.37 % Fri Sep 25 14:33:30 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 2.39/0.75
% 2.39/0.75 % SZS status Unsatisfiable for theBenchmark
% 2.39/0.75
% 2.39/0.75 % Proof 1 at 0.27 (+ 0.10) seconds.
% 2.39/0.75 % Length of proof is 24.
% 2.39/0.75 % Level of proof is 6.
% 2.39/0.75 % Maximum clause weight is 14.000.
% 2.39/0.75 % Given clauses 157.
% 2.39/0.75
% 2.39/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------