%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP198-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 07:28:21 AM UTC 2026
% Result : Unsatisfiable 2.11s 0.72s
% Output : CNFRefutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 52 unt; 0 def)
% Number of atoms : 60 ( 59 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 19 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 125 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_of_multiply,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_of_multiply) ).
cnf(c_1,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity_of_multiply]) ).
fof(right_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| multiply(VAR_0,VAR_1) != multiply(VAR_2,VAR_1) ),
file('theBenchmark.p',right_cancellation) ).
cnf(c_2,plain,
( A = C
| multiply(A,B) != multiply(C,B) ),
inference(clausify,[status(thm)],[right_cancellation]) ).
fof(left_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_1 = VAR_2
| multiply(VAR_0,VAR_1) != multiply(VAR_0,VAR_2) ),
file('theBenchmark.p',left_cancellation) ).
cnf(c_3,plain,
( B = C
| multiply(A,B) != multiply(A,C) ),
inference(clausify,[status(thm)],[left_cancellation]) ).
fof(condition,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,multiply(VAR_1,multiply(VAR_1,multiply(VAR_1,multiply(VAR_0,VAR_1))))) = multiply(VAR_1,multiply(VAR_1,multiply(VAR_1,multiply(VAR_1,multiply(VAR_0,VAR_0))))),
file('theBenchmark.p',condition) ).
cnf(c_4,plain,
multiply(A,multiply(B,multiply(B,multiply(B,multiply(A,B))))) = multiply(B,multiply(B,multiply(B,multiply(B,multiply(A,A))))),
inference(clausify,[status(thm)],[condition]) ).
fof(prove_this,axiom,
multiply(b,multiply(a,multiply(b,multiply(b,multiply(b,a))))) != multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))),
file('theBenchmark.p',prove_this) ).
cnf(c_5,plain,
multiply(b,multiply(a,multiply(b,multiply(b,multiply(b,a))))) != multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_32,plain,
multiply(multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,B))))),C) = multiply(B,multiply(multiply(A,multiply(A,multiply(A,multiply(B,A)))),C)),
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_33,plain,
multiply(A,multiply(multiply(A,multiply(A,multiply(A,multiply(B,B)))),C)) = multiply(B,multiply(multiply(A,multiply(A,multiply(A,multiply(B,A)))),C)),
inference(paramod,[status(thm)],[c_1,c_32]) ).
cnf(c_34,plain,
multiply(A,multiply(A,multiply(multiply(A,multiply(A,multiply(B,B))),C))) = multiply(B,multiply(multiply(A,multiply(A,multiply(A,multiply(B,A)))),C)),
inference(paramod,[status(thm)],[c_1,c_33]) ).
cnf(c_35,plain,
multiply(A,multiply(A,multiply(A,multiply(multiply(A,multiply(B,B)),C)))) = multiply(B,multiply(multiply(A,multiply(A,multiply(A,multiply(B,A)))),C)),
inference(paramod,[status(thm)],[c_1,c_34]) ).
cnf(c_36,plain,
multiply(A,multiply(A,multiply(A,multiply(A,multiply(multiply(B,B),C))))) = multiply(B,multiply(multiply(A,multiply(A,multiply(A,multiply(B,A)))),C)),
inference(paramod,[status(thm)],[c_1,c_35]) ).
cnf(c_37,plain,
multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,multiply(B,C)))))) = multiply(B,multiply(multiply(A,multiply(A,multiply(A,multiply(B,A)))),C)),
inference(paramod,[status(thm)],[c_1,c_36]) ).
cnf(c_38,plain,
multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,multiply(B,C)))))) = multiply(B,multiply(A,multiply(multiply(A,multiply(A,multiply(B,A))),C))),
inference(paramod,[status(thm)],[c_1,c_37]) ).
cnf(c_39,plain,
multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,multiply(B,C)))))) = multiply(B,multiply(A,multiply(A,multiply(multiply(A,multiply(B,A)),C)))),
inference(paramod,[status(thm)],[c_1,c_38]) ).
cnf(c_40,plain,
multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,multiply(B,C)))))) = multiply(B,multiply(A,multiply(A,multiply(A,multiply(multiply(B,A),C))))),
inference(paramod,[status(thm)],[c_1,c_39]) ).
cnf(c_41,plain,
multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,multiply(B,C)))))) = multiply(B,multiply(A,multiply(A,multiply(A,multiply(B,multiply(A,C)))))),
inference(paramod,[status(thm)],[c_1,c_40]) ).
cnf(c_6,plain,
multiply(A,multiply(B,multiply(B,multiply(B,multiply(A,multiply(B,C)))))) = multiply(B,multiply(B,multiply(B,multiply(B,multiply(A,multiply(A,C)))))),
inference(copy,[status(thm)],[c_41]) ).
cnf(c_42,plain,
multiply(A,multiply(A,multiply(A,multiply(A,multiply(multiply(B,C),multiply(B,C)))))) = multiply(B,multiply(C,multiply(A,multiply(A,multiply(A,multiply(multiply(B,C),A)))))),
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_43,plain,
multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,multiply(C,multiply(B,C))))))) = multiply(B,multiply(C,multiply(A,multiply(A,multiply(A,multiply(multiply(B,C),A)))))),
inference(paramod,[status(thm)],[c_1,c_42]) ).
cnf(c_44,plain,
multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,multiply(C,multiply(B,C))))))) = multiply(B,multiply(C,multiply(A,multiply(A,multiply(A,multiply(B,multiply(C,A))))))),
inference(paramod,[status(thm)],[c_1,c_43]) ).
cnf(c_7,plain,
multiply(A,multiply(B,multiply(C,multiply(C,multiply(C,multiply(A,multiply(B,C))))))) = multiply(C,multiply(C,multiply(C,multiply(C,multiply(A,multiply(B,multiply(A,B))))))),
inference(copy,[status(thm)],[c_44]) ).
cnf(c_45,plain,
multiply(multiply(b,multiply(a,multiply(b,multiply(b,multiply(b,a))))),A) != multiply(multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))),A),
inference(resolve,[status(thm)],[c_2,c_5]) ).
cnf(c_46,plain,
multiply(b,multiply(multiply(a,multiply(b,multiply(b,multiply(b,a)))),A)) != multiply(multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))),A),
inference(paramod,[status(thm)],[c_1,c_45]) ).
cnf(c_47,plain,
multiply(b,multiply(a,multiply(multiply(b,multiply(b,multiply(b,a))),A))) != multiply(multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))),A),
inference(paramod,[status(thm)],[c_1,c_46]) ).
cnf(c_48,plain,
multiply(b,multiply(a,multiply(b,multiply(multiply(b,multiply(b,a)),A)))) != multiply(multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))),A),
inference(paramod,[status(thm)],[c_1,c_47]) ).
cnf(c_49,plain,
multiply(b,multiply(a,multiply(b,multiply(b,multiply(multiply(b,a),A))))) != multiply(multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))),A),
inference(paramod,[status(thm)],[c_1,c_48]) ).
cnf(c_50,plain,
multiply(b,multiply(a,multiply(b,multiply(b,multiply(b,multiply(a,A)))))) != multiply(multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))),A),
inference(paramod,[status(thm)],[c_1,c_49]) ).
cnf(c_51,plain,
multiply(b,multiply(a,multiply(b,multiply(b,multiply(b,multiply(a,A)))))) != multiply(a,multiply(multiply(a,multiply(b,multiply(b,multiply(b,b)))),A)),
inference(paramod,[status(thm)],[c_1,c_50]) ).
cnf(c_52,plain,
multiply(b,multiply(a,multiply(b,multiply(b,multiply(b,multiply(a,A)))))) != multiply(a,multiply(a,multiply(multiply(b,multiply(b,multiply(b,b))),A))),
inference(paramod,[status(thm)],[c_1,c_51]) ).
cnf(c_53,plain,
multiply(b,multiply(a,multiply(b,multiply(b,multiply(b,multiply(a,A)))))) != multiply(a,multiply(a,multiply(b,multiply(multiply(b,multiply(b,b)),A)))),
inference(paramod,[status(thm)],[c_1,c_52]) ).
cnf(c_54,plain,
multiply(b,multiply(a,multiply(b,multiply(b,multiply(b,multiply(a,A)))))) != multiply(a,multiply(a,multiply(b,multiply(b,multiply(multiply(b,b),A))))),
inference(paramod,[status(thm)],[c_1,c_53]) ).
cnf(c_10,plain,
multiply(b,multiply(a,multiply(b,multiply(b,multiply(b,multiply(a,A)))))) != multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,A)))))),
inference(paramod,[status(thm)],[c_1,c_54]) ).
cnf(c_21,plain,
multiply(A,multiply(B,multiply(B,multiply(B,multiply(B,multiply(A,B)))))) = multiply(B,multiply(B,multiply(B,multiply(B,multiply(A,multiply(B,A)))))),
inference(resolve,[status(thm)],[c_3,c_7]) ).
cnf(c_22,plain,
multiply(A,multiply(B,multiply(B,multiply(B,multiply(A,multiply(B,multiply(A,A))))))) = multiply(A,multiply(A,multiply(B,multiply(B,multiply(B,multiply(A,multiply(A,B))))))),
inference(paramod,[status(thm)],[c_7,c_6]) ).
cnf(c_55,plain,
multiply(multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,multiply(A,B)))))),C) = multiply(B,multiply(multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,A))))),C)),
inference(paramod,[status(thm)],[c_21,c_1]) ).
cnf(c_56,plain,
multiply(A,multiply(multiply(A,multiply(A,multiply(A,multiply(B,multiply(A,B))))),C)) = multiply(B,multiply(multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,A))))),C)),
inference(paramod,[status(thm)],[c_1,c_55]) ).
cnf(c_57,plain,
multiply(A,multiply(A,multiply(multiply(A,multiply(A,multiply(B,multiply(A,B)))),C))) = multiply(B,multiply(multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,A))))),C)),
inference(paramod,[status(thm)],[c_1,c_56]) ).
cnf(c_58,plain,
multiply(A,multiply(A,multiply(A,multiply(multiply(A,multiply(B,multiply(A,B))),C)))) = multiply(B,multiply(multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,A))))),C)),
inference(paramod,[status(thm)],[c_1,c_57]) ).
cnf(c_59,plain,
multiply(A,multiply(A,multiply(A,multiply(A,multiply(multiply(B,multiply(A,B)),C))))) = multiply(B,multiply(multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,A))))),C)),
inference(paramod,[status(thm)],[c_1,c_58]) ).
cnf(c_60,plain,
multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,multiply(multiply(A,B),C)))))) = multiply(B,multiply(multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,A))))),C)),
inference(paramod,[status(thm)],[c_1,c_59]) ).
cnf(c_61,plain,
multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,multiply(A,multiply(B,C))))))) = multiply(B,multiply(multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,A))))),C)),
inference(paramod,[status(thm)],[c_1,c_60]) ).
cnf(c_62,plain,
multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,multiply(A,multiply(B,C))))))) = multiply(B,multiply(A,multiply(multiply(A,multiply(A,multiply(A,multiply(B,A)))),C))),
inference(paramod,[status(thm)],[c_1,c_61]) ).
cnf(c_63,plain,
multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,multiply(A,multiply(B,C))))))) = multiply(B,multiply(A,multiply(A,multiply(multiply(A,multiply(A,multiply(B,A))),C)))),
inference(paramod,[status(thm)],[c_1,c_62]) ).
cnf(c_64,plain,
multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,multiply(A,multiply(B,C))))))) = multiply(B,multiply(A,multiply(A,multiply(A,multiply(multiply(A,multiply(B,A)),C))))),
inference(paramod,[status(thm)],[c_1,c_63]) ).
cnf(c_65,plain,
multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,multiply(A,multiply(B,C))))))) = multiply(B,multiply(A,multiply(A,multiply(A,multiply(A,multiply(multiply(B,A),C)))))),
inference(paramod,[status(thm)],[c_1,c_64]) ).
cnf(c_66,plain,
multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,multiply(A,multiply(B,C))))))) = multiply(B,multiply(A,multiply(A,multiply(A,multiply(A,multiply(B,multiply(A,C))))))),
inference(paramod,[status(thm)],[c_1,c_65]) ).
cnf(c_24,plain,
multiply(A,multiply(B,multiply(B,multiply(B,multiply(B,multiply(A,multiply(B,C))))))) = multiply(B,multiply(B,multiply(B,multiply(B,multiply(A,multiply(B,multiply(A,C))))))),
inference(copy,[status(thm)],[c_66]) ).
cnf(c_26,plain,
multiply(b,multiply(a,multiply(b,multiply(b,multiply(b,multiply(a,multiply(a,b))))))) != multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(a,multiply(b,a))))))),
inference(paramod,[status(thm)],[c_21,c_10]) ).
cnf(c_67,plain,
multiply(A,multiply(A,multiply(A,multiply(B,multiply(A,multiply(B,B)))))) = multiply(B,multiply(A,multiply(A,multiply(A,multiply(B,multiply(B,A)))))),
inference(resolve,[status(thm)],[c_3,c_22]) ).
cnf(c_27,plain,
multiply(A,multiply(B,multiply(B,multiply(B,multiply(A,multiply(A,B)))))) = multiply(B,multiply(B,multiply(B,multiply(A,multiply(B,multiply(A,A)))))),
inference(copy,[status(thm)],[c_67]) ).
cnf(c_68,plain,
multiply(b,multiply(b,multiply(b,multiply(b,multiply(a,multiply(b,multiply(a,a))))))) != multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(a,multiply(b,a))))))),
inference(paramod,[status(thm)],[c_27,c_26]) ).
cnf(c_31,plain,
$false,
inference(resolve,[status(thm)],[c_24,c_68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP198-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n010.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 14:37:44 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 978035 was started by sandbox2 on n010,
% 0.17/0.43 % Fri Sep 25 14:37:44 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.43
% 0.17/0.43 % From the command line: assign(max_seconds, 300).
% 2.11/0.72
% 2.11/0.72 % SZS status Unsatisfiable for theBenchmark
% 2.11/0.72
% 2.11/0.72 % Proof 1 at 0.14 (+ 0.02) seconds.
% 2.11/0.72 % Length of proof is 14.
% 2.11/0.72 % Level of proof is 4.
% 2.11/0.72 % Maximum clause weight is 95.000.
% 2.11/0.72 % Given clauses 24.
% 2.11/0.72
% 2.11/0.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------