%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP118-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 07:27:22 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of formulae : 32 ( 32 unt; 0 def)
% Number of atoms : 32 ( 31 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,multiply(multiply(VAR_0,multiply(multiply(VAR_0,VAR_1),VAR_2)),multiply(identity,multiply(VAR_2,VAR_2)))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,B),C)),multiply(identity,multiply(C,C)))) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(prove_order3,axiom,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('theBenchmark.p',prove_order3) ).
cnf(c_2,plain,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
inference(clausify,[status(thm)],[prove_order3]) ).
cnf(c_56,plain,
multiply(A,multiply(B,multiply(identity,multiply(multiply(identity,multiply(C,C)),multiply(identity,multiply(C,C)))))) = multiply(multiply(A,B),C),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,multiply(identity,multiply(multiply(identity,multiply(C,C)),multiply(identity,multiply(C,C)))))),
inference(copy,[status(thm)],[c_56]) ).
cnf(c_57,plain,
multiply(A,multiply(A,multiply(multiply(multiply(A,B),C),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(C,C)),multiply(identity,multiply(C,C)))),multiply(identity,multiply(multiply(identity,multiply(C,C)),multiply(identity,multiply(C,C))))))))) = B,
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_4,plain,
multiply(A,multiply(A,multiply(multiply(multiply(A,B),C),multiply(C,C)))) = B,
inference(paramod,[status(thm)],[c_1,c_57]) ).
cnf(c_58,plain,
multiply(A,multiply(multiply(multiply(A,multiply(A,B)),C),multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(C,C)),multiply(identity,multiply(C,C)))),multiply(identity,multiply(multiply(identity,multiply(C,C)),multiply(identity,multiply(C,C)))))))) = B,
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_5,plain,
multiply(A,multiply(multiply(multiply(A,multiply(A,B)),C),multiply(C,C))) = B,
inference(paramod,[status(thm)],[c_1,c_58]) ).
cnf(c_8,plain,
multiply(multiply(A,B),multiply(identity,C)) = multiply(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_59,plain,
multiply(a,multiply(b,multiply(identity,multiply(multiply(identity,multiply(c,c)),multiply(identity,multiply(c,c)))))) != multiply(a,multiply(b,c)),
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_9,plain,
multiply(a,multiply(b,multiply(identity,multiply(identity,multiply(multiply(c,c),multiply(c,c)))))) != multiply(a,multiply(b,c)),
inference(paramod,[status(thm)],[c_8,c_59]) ).
cnf(c_60,plain,
multiply(A,multiply(A,multiply(multiply(A,B),multiply(identity,identity)))) = B,
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_18,plain,
multiply(A,multiply(A,multiply(A,multiply(B,identity)))) = B,
inference(paramod,[status(thm)],[c_8,c_60]) ).
cnf(c_28,plain,
multiply(A,multiply(multiply(B,C),multiply(C,C))) = multiply(A,multiply(B,identity)),
inference(paramod,[status(thm)],[c_18,c_5]) ).
cnf(c_35,plain,
multiply(a,multiply(b,multiply(identity,multiply(identity,multiply(c,identity))))) != multiply(a,multiply(b,c)),
inference(paramod,[status(thm)],[c_28,c_9]) ).
cnf(c_61,plain,
multiply(A,multiply(multiply(B,multiply(identity,C)),multiply(identity,multiply(C,C)))) = multiply(A,multiply(B,identity)),
inference(paramod,[status(thm)],[c_8,c_28]) ).
cnf(c_62,plain,
multiply(A,multiply(B,multiply(multiply(identity,C),multiply(C,C)))) = multiply(A,multiply(B,identity)),
inference(paramod,[status(thm)],[c_8,c_61]) ).
cnf(c_39,plain,
multiply(A,multiply(B,multiply(identity,identity))) = multiply(A,multiply(B,identity)),
inference(paramod,[status(thm)],[c_28,c_62]) ).
cnf(c_44,plain,
multiply(A,multiply(A,multiply(A,identity))) = identity,
inference(paramod,[status(thm)],[c_39,c_18]) ).
cnf(c_47,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_44,c_18]) ).
cnf(c_63,plain,
multiply(A,multiply(identity,multiply(multiply(B,multiply(B,identity)),multiply(B,multiply(B,identity))))) = multiply(A,multiply(B,identity)),
inference(paramod,[status(thm)],[c_44,c_28]) ).
cnf(c_64,plain,
multiply(A,multiply(identity,multiply(multiply(B,B),multiply(B,multiply(B,identity))))) = multiply(A,multiply(B,identity)),
inference(paramod,[status(thm)],[c_47,c_63]) ).
cnf(c_65,plain,
multiply(A,multiply(identity,multiply(multiply(B,B),multiply(B,B)))) = multiply(A,multiply(B,identity)),
inference(paramod,[status(thm)],[c_47,c_64]) ).
cnf(c_66,plain,
multiply(A,multiply(identity,multiply(B,identity))) = multiply(A,multiply(B,identity)),
inference(paramod,[status(thm)],[c_28,c_65]) ).
cnf(c_67,plain,
multiply(A,multiply(identity,B)) = multiply(A,multiply(B,identity)),
inference(paramod,[status(thm)],[c_47,c_66]) ).
cnf(c_48,plain,
multiply(A,multiply(identity,B)) = multiply(A,B),
inference(paramod,[status(thm)],[c_47,c_67]) ).
cnf(c_68,plain,
multiply(a,multiply(b,multiply(identity,multiply(identity,c)))) != multiply(a,multiply(b,c)),
inference(paramod,[status(thm)],[c_47,c_35]) ).
cnf(c_69,plain,
multiply(a,multiply(b,multiply(identity,c))) != multiply(a,multiply(b,c)),
inference(paramod,[status(thm)],[c_48,c_68]) ).
cnf(c_70,plain,
multiply(a,multiply(b,c)) != multiply(a,multiply(b,c)),
inference(paramod,[status(thm)],[c_48,c_69]) ).
cnf(c_55,plain,
$false,
inference(copy,[status(thm)],[c_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP118-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:24:52 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 371535 was started by sandbox on n003,
% 0.09/0.36 % Fri Sep 25 14:24:52 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.13/0.38 % Length of proof is 15.
% 0.13/0.38 % Level of proof is 9.
% 0.13/0.38 % Maximum clause weight is 98.000.
% 0.13/0.38 % Given clauses 11.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------