%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP199-1 : 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 : n018.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 7.62s 6.70s
% Output : CNFRefutation 7.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 38 unt; 0 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 9 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 12 !; 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(nilpotency,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,multiply(VAR_1,multiply(VAR_2,multiply(VAR_1,VAR_0)))) = multiply(VAR_1,multiply(VAR_0,multiply(VAR_2,multiply(VAR_0,VAR_1)))),
file('theBenchmark.p',nilpotency) ).
cnf(c_4,plain,
multiply(A,multiply(B,multiply(C,multiply(B,A)))) = multiply(B,multiply(A,multiply(C,multiply(A,B)))),
inference(clausify,[status(thm)],[nilpotency]) ).
fof(prove_quotient1,axiom,
multiply(b,b0) = multiply(a,a0),
file('theBenchmark.p',prove_quotient1) ).
cnf(c_5,plain,
multiply(b,b0) = multiply(a,a0),
inference(clausify,[status(thm)],[prove_quotient1]) ).
fof(prove_quotient2,axiom,
multiply(d,b0) = multiply(c,a0),
file('theBenchmark.p',prove_quotient2) ).
cnf(c_6,plain,
multiply(d,b0) = multiply(c,a0),
inference(clausify,[status(thm)],[prove_quotient2]) ).
fof(prove_quotient3,axiom,
multiply(b,d0) = multiply(a,c0),
file('theBenchmark.p',prove_quotient3) ).
cnf(c_7,plain,
multiply(b,d0) = multiply(a,c0),
inference(clausify,[status(thm)],[prove_quotient3]) ).
fof(prove_quotient4,axiom,
multiply(d,d0) != multiply(c,c0),
file('theBenchmark.p',prove_quotient4) ).
cnf(c_8,plain,
multiply(d,d0) != multiply(c,c0),
inference(clausify,[status(thm)],[prove_quotient4]) ).
cnf(c_1814,plain,
multiply(multiply(a,a0),A) = multiply(b,multiply(b0,A)),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_1815,plain,
multiply(a,multiply(a0,A)) = multiply(b,multiply(b0,A)),
inference(paramod,[status(thm)],[c_1,c_1814]) ).
cnf(c_16,plain,
multiply(b,multiply(b0,A)) = multiply(a,multiply(a0,A)),
inference(copy,[status(thm)],[c_1815]) ).
cnf(c_1816,plain,
multiply(multiply(c,a0),A) = multiply(d,multiply(b0,A)),
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_1817,plain,
multiply(c,multiply(a0,A)) = multiply(d,multiply(b0,A)),
inference(paramod,[status(thm)],[c_1,c_1816]) ).
cnf(c_18,plain,
multiply(d,multiply(b0,A)) = multiply(c,multiply(a0,A)),
inference(copy,[status(thm)],[c_1817]) ).
cnf(c_1818,plain,
multiply(multiply(a,c0),A) = multiply(b,multiply(d0,A)),
inference(paramod,[status(thm)],[c_7,c_1]) ).
cnf(c_1819,plain,
multiply(a,multiply(c0,A)) = multiply(b,multiply(d0,A)),
inference(paramod,[status(thm)],[c_1,c_1818]) ).
cnf(c_20,plain,
multiply(b,multiply(d0,A)) = multiply(a,multiply(c0,A)),
inference(copy,[status(thm)],[c_1819]) ).
cnf(c_1820,plain,
multiply(multiply(d,d0),A) != multiply(multiply(c,c0),A),
inference(resolve,[status(thm)],[c_2,c_8]) ).
cnf(c_1821,plain,
multiply(d,multiply(d0,A)) != multiply(multiply(c,c0),A),
inference(paramod,[status(thm)],[c_1,c_1820]) ).
cnf(c_23,plain,
multiply(d,multiply(d0,A)) != multiply(c,multiply(c0,A)),
inference(paramod,[status(thm)],[c_1,c_1821]) ).
cnf(c_1822,plain,
multiply(A,multiply(b0,multiply(a,multiply(a0,A)))) = multiply(b0,multiply(A,multiply(b,multiply(A,b0)))),
inference(paramod,[status(thm)],[c_16,c_4]) ).
cnf(c_39,plain,
multiply(b0,multiply(A,multiply(b,multiply(A,b0)))) = multiply(A,multiply(b0,multiply(a,multiply(a0,A)))),
inference(copy,[status(thm)],[c_1822]) ).
cnf(c_1823,plain,
multiply(A,multiply(d0,multiply(a,multiply(c0,A)))) = multiply(d0,multiply(A,multiply(b,multiply(A,d0)))),
inference(paramod,[status(thm)],[c_20,c_4]) ).
cnf(c_47,plain,
multiply(d0,multiply(A,multiply(b,multiply(A,d0)))) = multiply(A,multiply(d0,multiply(a,multiply(c0,A)))),
inference(copy,[status(thm)],[c_1823]) ).
cnf(c_1824,plain,
multiply(b,multiply(b0,multiply(d0,multiply(b,multiply(d0,b0))))) = multiply(a,multiply(c0,multiply(b0,multiply(a,multiply(a0,d0))))),
inference(paramod,[status(thm)],[c_39,c_20]) ).
cnf(c_1825,plain,
multiply(b,multiply(b0,multiply(d0,multiply(a,multiply(c0,b0))))) = multiply(a,multiply(c0,multiply(b0,multiply(a,multiply(a0,d0))))),
inference(paramod,[status(thm)],[c_20,c_1824]) ).
cnf(c_130,plain,
multiply(a,multiply(a0,multiply(d0,multiply(a,multiply(c0,b0))))) = multiply(a,multiply(c0,multiply(b0,multiply(a,multiply(a0,d0))))),
inference(paramod,[status(thm)],[c_16,c_1825]) ).
cnf(c_1826,plain,
multiply(d,multiply(d0,multiply(b0,multiply(b,multiply(b0,d0))))) = multiply(c,multiply(a0,multiply(d0,multiply(a,multiply(c0,b0))))),
inference(paramod,[status(thm)],[c_47,c_18]) ).
cnf(c_1827,plain,
multiply(d,multiply(d0,multiply(b0,multiply(a,multiply(a0,d0))))) = multiply(c,multiply(a0,multiply(d0,multiply(a,multiply(c0,b0))))),
inference(paramod,[status(thm)],[c_16,c_1826]) ).
cnf(c_225,plain,
multiply(c,multiply(a0,multiply(d0,multiply(a,multiply(c0,b0))))) = multiply(d,multiply(d0,multiply(b0,multiply(a,multiply(a0,d0))))),
inference(copy,[status(thm)],[c_1827]) ).
cnf(c_1803,plain,
multiply(a0,multiply(d0,multiply(a,multiply(c0,b0)))) = multiply(c0,multiply(b0,multiply(a,multiply(a0,d0)))),
inference(resolve,[status(thm)],[c_3,c_130]) ).
cnf(c_1828,plain,
multiply(c,multiply(c0,multiply(b0,multiply(a,multiply(a0,d0))))) = multiply(d,multiply(d0,multiply(b0,multiply(a,multiply(a0,d0))))),
inference(paramod,[status(thm)],[c_1803,c_225]) ).
cnf(c_1829,plain,
multiply(d,multiply(d0,multiply(b0,multiply(a,multiply(a0,d0))))) = multiply(c,multiply(c0,multiply(b0,multiply(a,multiply(a0,d0))))),
inference(copy,[status(thm)],[c_1828]) ).
cnf(c_1813,plain,
$false,
inference(resolve,[status(thm)],[c_23,c_1829]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP199-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.43 % Computer : n018.cluster.edu
% 0.16/5.43 % Model : x86_64 x86_64
% 0.16/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.43 % Memory : 8046.5625MB
% 0.16/5.43 % OS : Linux 6.8.0-71-generic
% 0.16/5.43 % CPULimit : 300
% 0.16/5.43 % WCLimit : 300
% 0.16/5.43 % DateTime : Fri Sep 25 14:39:26 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.43 % Process 2189401 was started by sandbox2 on n018,
% 0.16/5.43 % Fri Sep 25 14:39:26 2026
% 0.16/5.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.44
% 0.16/5.44 % From the command line: assign(max_seconds, 300).
% 7.62/6.70
% 7.62/6.70 % SZS status Unsatisfiable for theBenchmark
% 7.62/6.70
% 7.62/6.70 % Proof 1 at 1.11 (+ 0.14) seconds.
% 7.62/6.70 % Length of proof is 18.
% 7.62/6.70 % Level of proof is 5.
% 7.62/6.70 % Maximum clause weight is 53.000.
% 7.62/6.70 % Given clauses 97.
% 7.62/6.70
% 7.62/6.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------