%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG439-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 06:50:12 AM UTC 2026
% Result : Unsatisfiable 10.66s 12.00s
% Output : CNFRefutation 10.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 11 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 6 ( 2 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_1,axiom,
( v_c = v_y
| c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = v_y ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_1101,plain,
( v_c = v_y
| c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = v_y ),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_1102,plain,
( v_y = v_c
| c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = v_y ),
inference(copy,[status(thm)],[c_1101]) ).
fof(cls_conjecture_0,axiom,
( c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) != v_y
| v_c != v_y ),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1103,plain,
( c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) != v_y
| v_c != v_y ),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_1104,plain,
( c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) != v_y
| v_y != v_c ),
inference(copy,[status(thm)],[c_1103]) ).
fof(cls_mpoly__base__conv_I2_J_0,axiom,
! [VAR_0,VAR_1] : VAR_0 = c_Polynomial_Opoly(c_Polynomial_OpCons(VAR_0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),VAR_1,tc_Complex_Ocomplex),
file('theBenchmark.p',cls_mpoly__base__conv_I2_J_0) ).
cnf(c_1105,plain,
A = c_Polynomial_Opoly(c_Polynomial_OpCons(A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_mpoly__base__conv_I2_J_0]) ).
cnf(c_1106,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = A,
inference(copy,[status(thm)],[c_1105]) ).
cnf(c_1982,plain,
( v_c != v_y
| v_y != v_c ),
inference(paramod,[status(thm)],[c_1106,c_1104]) ).
cnf(c_1983,plain,
( v_y != v_c
| v_y != v_c ),
inference(copy,[status(thm)],[c_1982]) ).
cnf(c_1980,plain,
v_y != v_c,
inference(copy,[status(thm)],[c_1983]) ).
cnf(c_1984,plain,
( v_y = v_c
| v_c = v_y ),
inference(paramod,[status(thm)],[c_1106,c_1102]) ).
cnf(c_1985,plain,
( v_y = v_c
| v_y = v_c ),
inference(copy,[status(thm)],[c_1984]) ).
cnf(c_1986,plain,
v_y = v_c,
inference(copy,[status(thm)],[c_1985]) ).
cnf(c_1981,plain,
$false,
inference(resolve,[status(thm)],[c_1980,c_1986]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG439-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/10.51 % Computer : n008.cluster.edu
% 0.12/10.51 % Model : x86_64 x86_64
% 0.12/10.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.51 % Memory : 8046.5625MB
% 0.12/10.51 % OS : Linux 6.8.0-71-generic
% 0.12/10.51 % CPULimit : 300
% 0.12/10.51 % WCLimit : 300
% 0.12/10.51 % DateTime : Sat Sep 26 22:02:22 UTC 2026
% 0.12/10.51 % CPUTime :
% 0.12/10.51 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/10.51 % Process 453153 was started by sandbox2 on n008,
% 0.12/10.51 % Sat Sep 26 22:02:22 2026
% 0.12/10.51 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/10.56
% 0.12/10.56 % From the command line: assign(max_seconds, 300).
% 10.66/12.00
% 10.66/12.00 % SZS status Unsatisfiable for theBenchmark
% 10.66/12.00
% 10.66/12.00 % Proof 1 at 1.41 (+ 0.02) seconds.
% 10.66/12.00 % Length of proof is 8.
% 10.66/12.00 % Level of proof is 3.
% 10.66/12.00 % Maximum clause weight is 39.000.
% 10.66/12.00 % Given clauses 0.
% 10.66/12.00
% 10.66/12.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------