%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG004-1 : TPTP v9.3.1. Released v2.2.0.
% 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 06:49:06 AM UTC 2026
% Result : Unsatisfiable 2.61s 0.78s
% Output : CNFRefutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 24 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 22 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 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 : 76 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_0 = VAR_3
| multiply(VAR_3,VAR_1) != VAR_2
| multiply(VAR_0,VAR_1) != VAR_2 ),
file('theBenchmark.p',left_cancellation) ).
cnf(c_1,plain,
( A = D
| multiply(D,B) != C
| multiply(A,B) != C ),
inference(clausify,[status(thm)],[left_cancellation]) ).
fof(right_cancelaation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_1 = VAR_3
| multiply(VAR_0,VAR_3) != VAR_2
| multiply(VAR_0,VAR_1) != VAR_2 ),
file('theBenchmark.p',right_cancelaation) ).
cnf(c_2,plain,
( B = D
| multiply(A,D) != C
| multiply(A,B) != C ),
inference(clausify,[status(thm)],[right_cancelaation]) ).
fof(medial_law,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : multiply(multiply(VAR_0,VAR_1),multiply(VAR_2,VAR_3)) = multiply(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_3)),
file('theBenchmark.p',medial_law) ).
cnf(c_3,plain,
multiply(multiply(A,B),multiply(C,D)) = multiply(multiply(A,C),multiply(B,D)),
inference(clausify,[status(thm)],[medial_law]) ).
fof(prove_quotient_condition1,axiom,
multiply(b,b0) = multiply(a,a0),
file('theBenchmark.p',prove_quotient_condition1) ).
cnf(c_4,plain,
multiply(b,b0) = multiply(a,a0),
inference(clausify,[status(thm)],[prove_quotient_condition1]) ).
fof(prove_quotient_condition2,axiom,
multiply(d,b0) = multiply(c,a0),
file('theBenchmark.p',prove_quotient_condition2) ).
cnf(c_5,plain,
multiply(d,b0) = multiply(c,a0),
inference(clausify,[status(thm)],[prove_quotient_condition2]) ).
fof(prove_quotient_condition3,axiom,
multiply(b,d0) = multiply(a,c0),
file('theBenchmark.p',prove_quotient_condition3) ).
cnf(c_6,plain,
multiply(b,d0) = multiply(a,c0),
inference(clausify,[status(thm)],[prove_quotient_condition3]) ).
fof(prove_quotient_condition4,axiom,
multiply(d,d0) != multiply(c,c0),
file('theBenchmark.p',prove_quotient_condition4) ).
cnf(c_7,plain,
multiply(d,d0) != multiply(c,c0),
inference(clausify,[status(thm)],[prove_quotient_condition4]) ).
cnf(c_9,plain,
( multiply(B,D) = F
| multiply(multiply(A,C),F) != E
| multiply(multiply(A,B),multiply(C,D)) != E ),
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_10,plain,
multiply(multiply(multiply(A,B),multiply(C,D)),multiply(E,F)) = multiply(multiply(multiply(A,C),E),multiply(multiply(B,D),F)),
inference(paramod,[status(thm)],[c_3,c_3]) ).
cnf(c_791,plain,
multiply(multiply(a,a0),multiply(A,B)) = multiply(multiply(b,A),multiply(b0,B)),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_14,plain,
multiply(multiply(b,A),multiply(b0,B)) = multiply(multiply(a,a0),multiply(A,B)),
inference(copy,[status(thm)],[c_791]) ).
cnf(c_792,plain,
( multiply(D,E) = A
| multiply(A,multiply(B,C)) != multiply(multiply(D,B),multiply(E,C)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_793,plain,
multiply(multiply(c,c0),multiply(A,B)) != multiply(multiply(d,A),multiply(d0,B)),
inference(resolve,[status(thm)],[c_792,c_7]) ).
cnf(c_29,plain,
multiply(multiply(d,A),multiply(d0,B)) != multiply(multiply(c,c0),multiply(A,B)),
inference(copy,[status(thm)],[c_793]) ).
cnf(c_232,plain,
multiply(multiply(a,c0),multiply(b0,A)) = multiply(multiply(a,a0),multiply(d0,A)),
inference(paramod,[status(thm)],[c_6,c_14]) ).
cnf(c_794,plain,
multiply(multiply(c,a0),multiply(d0,A)) != multiply(multiply(c,c0),multiply(b0,A)),
inference(paramod,[status(thm)],[c_5,c_29]) ).
cnf(c_333,plain,
multiply(multiply(c,c0),multiply(b0,A)) != multiply(multiply(c,a0),multiply(d0,A)),
inference(copy,[status(thm)],[c_794]) ).
cnf(c_795,plain,
( multiply(multiply(E,F),V6) = D
| multiply(multiply(multiply(A,B),C),D) != multiply(multiply(multiply(A,E),C),multiply(multiply(B,F),V6)) ),
inference(resolve,[status(thm)],[c_9,c_10]) ).
cnf(c_796,plain,
multiply(multiply(c,a0),multiply(d0,A)) != multiply(multiply(c,c0),multiply(b0,A)),
inference(copy,[status(thm)],[c_333]) ).
cnf(c_797,plain,
multiply(multiply(multiply(A,B),C),multiply(multiply(c,c0),multiply(b0,D))) != multiply(multiply(multiply(A,c),C),multiply(multiply(B,a0),multiply(d0,D))),
inference(resolve,[status(thm)],[c_795,c_796]) ).
cnf(c_726,plain,
multiply(multiply(multiply(A,c),B),multiply(multiply(C,a0),multiply(d0,D))) != multiply(multiply(multiply(A,C),B),multiply(multiply(c,c0),multiply(b0,D))),
inference(copy,[status(thm)],[c_797]) ).
cnf(c_789,plain,
multiply(multiply(multiply(A,a),multiply(B,c0)),multiply(C,multiply(b0,D))) = multiply(multiply(multiply(A,B),C),multiply(multiply(a,a0),multiply(d0,D))),
inference(paramod,[status(thm)],[c_232,c_10]) ).
cnf(c_798,plain,
multiply(multiply(multiply(A,C),B),multiply(multiply(c,c0),multiply(b0,D))) != multiply(multiply(multiply(A,c),B),multiply(multiply(C,a0),multiply(d0,D))),
inference(copy,[status(thm)],[c_726]) ).
cnf(c_790,plain,
$false,
inference(resolve,[status(thm)],[c_789,c_798]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG004-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 21:00:05 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 2689930 was started by sandbox on n002,
% 0.09/0.36 % Sat Sep 26 21:00:05 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 2.61/0.78
% 2.61/0.78 % SZS status Unsatisfiable for theBenchmark
% 2.61/0.78
% 2.61/0.78 % Proof 1 at 0.33 (+ 0.08) seconds.
% 2.61/0.78 % Length of proof is 16.
% 2.61/0.78 % Level of proof is 4.
% 2.61/0.78 % Maximum clause weight is 97.000.
% 2.61/0.78 % Given clauses 41.
% 2.61/0.78
% 2.61/0.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------