%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA035-2 : 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 : n017.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 06:51:11 AM UTC 2026
% Result : Unsatisfiable 0.15s 5.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 19 unt; 0 def)
% Number of atoms : 35 ( 21 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 16 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 40 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Ring__and__Field_Oabs__mult_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_HOL_Oabs(c_times(VAR_1,VAR_2,VAR_0),VAR_0) = c_times(c_HOL_Oabs(VAR_1,VAR_0),c_HOL_Oabs(VAR_2,VAR_0),VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
cnf(c_1,plain,
( c_HOL_Oabs(c_times(B,C,A),A) = c_times(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[cls_Ring__and__Field_Oabs__mult_0]) ).
fof(tfree_tcs,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('theBenchmark.p',tfree_tcs) ).
cnf(c_2,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(clausify,[status(thm)],[tfree_tcs]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_17,axiom,
! [VAR_0] :
( class_OrderedGroup_Oab__semigroup__mult(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
cnf(c_3,plain,
( class_OrderedGroup_Oab__semigroup__mult(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_17]) ).
fof(cls_OrderedGroup_Omult__ac__3_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_times(VAR_1,c_times(VAR_2,VAR_3,VAR_0),VAR_0) = c_times(VAR_2,c_times(VAR_1,VAR_3,VAR_0),VAR_0)
| ~ class_OrderedGroup_Oab__semigroup__mult(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Omult__ac__3_0) ).
cnf(c_4,plain,
( c_times(B,c_times(C,D,A),A) = c_times(C,c_times(B,D,A),A)
| ~ class_OrderedGroup_Oab__semigroup__mult(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Omult__ac__3_0]) ).
cnf(c_5,plain,
class_OrderedGroup_Oab__semigroup__mult(t_b),
inference(resolve,[status(thm)],[c_3,c_2]) ).
fof(cls_OrderedGroup_Omult__ac__2_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_times(VAR_1,VAR_2,VAR_0) = c_times(VAR_2,VAR_1,VAR_0)
| ~ class_OrderedGroup_Oab__semigroup__mult(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Omult__ac__2_0) ).
cnf(c_6,plain,
( c_times(B,C,A) = c_times(C,B,A)
| ~ class_OrderedGroup_Oab__semigroup__mult(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Omult__ac__2_0]) ).
cnf(c_7,plain,
c_times(A,B,t_b) = c_times(B,A,t_b),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_8,plain,
c_times(A,c_times(B,C,t_b),t_b) = c_times(B,c_times(A,C,t_b),t_b),
inference(resolve,[status(thm)],[c_4,c_5]) ).
fof(cls_conjecture_4,axiom,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) != c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_9,plain,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) != c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
cnf(c_10,plain,
c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) != c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(copy,[status(thm)],[c_9]) ).
cnf(c_11,plain,
c_HOL_Oabs(c_times(A,B,t_b),t_b) = c_times(c_HOL_Oabs(A,t_b),c_HOL_Oabs(B,t_b),t_b),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_12,plain,
c_times(c_HOL_Oabs(A,t_b),c_HOL_Oabs(B,t_b),t_b) = c_HOL_Oabs(c_times(A,B,t_b),t_b),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_37,plain,
c_times(A,c_times(B,C,t_b),t_b) = c_times(c_times(A,C,t_b),B,t_b),
inference(paramod,[status(thm)],[c_8,c_7]) ).
cnf(c_13,plain,
c_times(c_times(A,B,t_b),C,t_b) = c_times(A,c_times(C,B,t_b),t_b),
inference(copy,[status(thm)],[c_37]) ).
cnf(c_22,plain,
c_times(c_times(A,B,t_b),C,t_b) = c_times(A,c_times(B,C,t_b),t_b),
inference(paramod,[status(thm)],[c_7,c_13]) ).
cnf(c_38,plain,
c_times(v_c,c_times(c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) != c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_13,c_10]) ).
cnf(c_39,plain,
c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) != c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_7,c_38]) ).
cnf(c_26,plain,
c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) != c_times(v_c,c_times(v_ca,c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_22,c_39]) ).
cnf(c_40,plain,
c_times(v_c,c_times(v_ca,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) != c_times(v_c,c_times(v_ca,c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_8,c_26]) ).
cnf(c_41,plain,
c_times(v_c,c_times(v_ca,c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) != c_times(v_c,c_times(v_ca,c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_12,c_40]) ).
cnf(c_36,plain,
$false,
inference(copy,[status(thm)],[c_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA035-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n017.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sat Sep 26 22:04:10 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.38 % Process 1756190 was started by sandbox on n017,
% 0.09/5.38 % Sat Sep 26 22:04:10 2026
% 0.09/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.38
% 0.09/5.38 % From the command line: assign(max_seconds, 300).
% 0.15/5.40
% 0.15/5.40 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.40
% 0.15/5.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/5.40 % Length of proof is 16.
% 0.15/5.40 % Level of proof is 6.
% 0.15/5.40 % Maximum clause weight is 31.000.
% 0.15/5.40 % Given clauses 6.
% 0.15/5.40
% 0.15/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------