%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA016-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 06:51:07 AM UTC 2026
% Result : Unsatisfiable 0.16s 5.41s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 53 ( 29 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 19 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 40 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsrel_Ring__and__Field_Oordered__field_0,axiom,
! [VAR_0] :
( class_Ring__and__Field_Ofield(VAR_0)
| ~ class_Ring__and__Field_Oordered__field(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
cnf(c_1,plain,
( class_Ring__and__Field_Ofield(A)
| ~ class_Ring__and__Field_Oordered__field(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_0]) ).
fof(tfree_tcs,axiom,
class_Ring__and__Field_Oordered__field(t_a),
file('theBenchmark.p',tfree_tcs) ).
cnf(c_2,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(clausify,[status(thm)],[tfree_tcs]) ).
fof(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0,axiom,
! [VAR_0,VAR_1] :
( c_times(c_1,VAR_1,VAR_0) = VAR_1
| ~ class_OrderedGroup_Omonoid__mult(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
cnf(c_3,plain,
( c_times(c_1,B,A) = B
| ~ class_OrderedGroup_Omonoid__mult(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0]) ).
fof(clsrel_Ring__and__Field_Ofield_12,axiom,
! [VAR_0] :
( class_OrderedGroup_Omonoid__mult(VAR_0)
| ~ class_Ring__and__Field_Ofield(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Ofield_12) ).
cnf(c_4,plain,
( class_OrderedGroup_Omonoid__mult(A)
| ~ class_Ring__and__Field_Ofield(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Ofield_12]) ).
fof(clsrel_Ring__and__Field_Ofield_21,axiom,
! [VAR_0] :
( class_OrderedGroup_Osemigroup__mult(VAR_0)
| ~ class_Ring__and__Field_Ofield(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Ofield_21) ).
cnf(c_5,plain,
( class_OrderedGroup_Osemigroup__mult(A)
| ~ class_Ring__and__Field_Ofield(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Ofield_21]) ).
fof(cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_times(c_times(VAR_1,VAR_2,VAR_0),VAR_3,VAR_0) = c_times(VAR_1,c_times(VAR_2,VAR_3,VAR_0),VAR_0)
| ~ class_OrderedGroup_Osemigroup__mult(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0) ).
cnf(c_6,plain,
( c_times(c_times(B,C,A),D,A) = c_times(B,c_times(C,D,A),A)
| ~ class_OrderedGroup_Osemigroup__mult(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0]) ).
cnf(c_7,plain,
class_Ring__and__Field_Ofield(t_a),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_8,plain,
( c_times(c_times(B,C,A),D,A) = c_times(B,c_times(C,D,A),A)
| ~ class_Ring__and__Field_Ofield(A) ),
inference(resolve,[status(thm)],[c_5,c_6]) ).
fof(cls_Ring__and__Field_Oright__inverse_0,axiom,
! [VAR_0,VAR_1] :
( c_times(VAR_1,c_HOL_Oinverse(VAR_1,VAR_0),VAR_0) = c_1
| VAR_1 = c_0
| ~ class_Ring__and__Field_Ofield(VAR_0) ),
file('theBenchmark.p',cls_Ring__and__Field_Oright__inverse_0) ).
cnf(c_9,plain,
( c_times(B,c_HOL_Oinverse(B,A),A) = c_1
| B = c_0
| ~ class_Ring__and__Field_Ofield(A) ),
inference(clausify,[status(thm)],[cls_Ring__and__Field_Oright__inverse_0]) ).
cnf(c_10,plain,
( ~ class_Ring__and__Field_Ofield(B)
| c_times(c_1,A,B) = A ),
inference(resolve,[status(thm)],[c_3,c_4]) ).
cnf(c_11,plain,
c_times(c_1,A,t_a) = A,
inference(resolve,[status(thm)],[c_10,c_7]) ).
cnf(c_12,plain,
( c_times(A,c_HOL_Oinverse(A,t_a),t_a) = c_1
| A = c_0 ),
inference(resolve,[status(thm)],[c_9,c_7]) ).
cnf(c_13,plain,
( c_times(A,c_HOL_Oinverse(A,t_a),t_a) = c_1
| c_0 = A ),
inference(copy,[status(thm)],[c_12]) ).
cnf(c_14,plain,
c_times(c_times(A,B,t_a),C,t_a) = c_times(A,c_times(B,C,t_a),t_a),
inference(resolve,[status(thm)],[c_7,c_8]) ).
fof(cls_conjecture_0,axiom,
v_c != c_0,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_15,plain,
v_c != c_0,
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_2,axiom,
v_g(v_x) != c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_16,plain,
v_g(v_x) != c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_17,plain,
c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a) != v_g(v_x),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_23,plain,
( c_times(c_1,B,t_a) = c_times(A,c_times(c_HOL_Oinverse(A,t_a),B,t_a),t_a)
| c_0 = A ),
inference(paramod,[status(thm)],[c_13,c_14]) ).
cnf(c_24,plain,
( B = c_times(A,c_times(c_HOL_Oinverse(A,t_a),B,t_a),t_a)
| c_0 = A ),
inference(paramod,[status(thm)],[c_11,c_23]) ).
cnf(c_20,plain,
( c_times(A,c_times(c_HOL_Oinverse(A,t_a),B,t_a),t_a) = B
| c_0 = A ),
inference(copy,[status(thm)],[c_24]) ).
cnf(c_25,plain,
c_0 = v_c,
inference(resolve,[status(thm)],[c_20,c_17]) ).
cnf(c_26,plain,
v_c = c_0,
inference(copy,[status(thm)],[c_25]) ).
cnf(c_22,plain,
$false,
inference(resolve,[status(thm)],[c_15,c_26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA016-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.39 % Computer : n010.cluster.edu
% 0.13/5.39 % Model : x86_64 x86_64
% 0.13/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.39 % Memory : 8046.5625MB
% 0.13/5.39 % OS : Linux 6.8.0-71-generic
% 0.13/5.39 % CPULimit : 300
% 0.13/5.39 % WCLimit : 300
% 0.13/5.39 % DateTime : Sat Sep 26 22:05:21 UTC 2026
% 0.13/5.39 % CPUTime :
% 0.13/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/5.39 % Process 121336 was started by sandbox on n010,
% 0.13/5.39 % Sat Sep 26 22:05:21 2026
% 0.13/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/5.40
% 0.16/5.40 % From the command line: assign(max_seconds, 300).
% 0.16/5.41
% 0.16/5.41 % SZS status Unsatisfiable for theBenchmark
% 0.16/5.41
% 0.16/5.41 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/5.41 % Length of proof is 19.
% 0.16/5.41 % Level of proof is 5.
% 0.16/5.41 % Maximum clause weight is 15.000.
% 0.16/5.41 % Given clauses 7.
% 0.16/5.41
% 0.16/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------