%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA024-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 06:51:09 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 11 unt; 0 def)
% Number of atoms : 38 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 19 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 37 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsrel_OrderedGroup_Opordered__ab__group__add_0,axiom,
! [VAR_0] :
( class_OrderedGroup_Oab__group__add(VAR_0)
| ~ class_OrderedGroup_Opordered__ab__group__add(VAR_0) ),
file('theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
cnf(c_1,plain,
( class_OrderedGroup_Oab__group__add(A)
| ~ class_OrderedGroup_Opordered__ab__group__add(A) ),
inference(clausify,[status(thm)],[clsrel_OrderedGroup_Opordered__ab__group__add_0]) ).
fof(cls_OrderedGroup_Ocompare__rls__10_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_1 = c_plus(c_minus(VAR_1,VAR_2,VAR_0),VAR_2,VAR_0)
| ~ class_OrderedGroup_Oab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Ocompare__rls__10_0) ).
cnf(c_2,plain,
( B = c_plus(c_minus(B,C,A),C,A)
| ~ class_OrderedGroup_Oab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Ocompare__rls__10_0]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_54,axiom,
! [VAR_0] :
( class_OrderedGroup_Opordered__ab__group__add(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
cnf(c_3,plain,
( class_OrderedGroup_Opordered__ab__group__add(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_54]) ).
cnf(c_4,plain,
( B = c_plus(c_minus(B,C,A),C,A)
| ~ class_OrderedGroup_Opordered__ab__group__add(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(cls_OrderedGroup_Ocompare__rls__9_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(VAR_1,c_minus(VAR_3,VAR_2,VAR_0),VAR_0)
| ~ c_lessequals(c_plus(VAR_1,VAR_2,VAR_0),VAR_3,VAR_0)
| ~ class_OrderedGroup_Opordered__ab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
cnf(c_5,plain,
( c_lessequals(B,c_minus(D,C,A),A)
| ~ c_lessequals(c_plus(B,C,A),D,A)
| ~ class_OrderedGroup_Opordered__ab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Ocompare__rls__9_1]) ).
fof(tfree_tcs,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('theBenchmark.p',tfree_tcs) ).
cnf(c_6,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(clausify,[status(thm)],[tfree_tcs]) ).
cnf(c_7,plain,
( B = c_plus(c_minus(B,C,A),C,A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(resolve,[status(thm)],[c_3,c_4]) ).
cnf(c_8,plain,
( ~ class_Ring__and__Field_Oordered__idom(C)
| c_lessequals(A,c_minus(D,B,C),C)
| ~ c_lessequals(c_plus(A,B,C),D,C) ),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_9,plain,
( c_lessequals(A,c_minus(C,B,t_b),t_b)
| ~ c_lessequals(c_plus(A,B,t_b),C,t_b) ),
inference(resolve,[status(thm)],[c_6,c_8]) ).
cnf(c_10,plain,
A = c_plus(c_minus(A,B,t_b),B,t_b),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_11,plain,
c_plus(c_minus(A,B,t_b),B,t_b) = A,
inference(copy,[status(thm)],[c_10]) ).
fof(cls_conjecture_3,axiom,
~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_12,plain,
~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] : c_lessequals(v_k(VAR_0),v_f(VAR_0),t_b),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_13,plain,
c_lessequals(v_k(A),v_f(A),t_b),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_17,plain,
~ c_lessequals(c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b),
inference(resolve,[status(thm)],[c_9,c_12]) ).
cnf(c_15,plain,
~ c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(paramod,[status(thm)],[c_11,c_17]) ).
cnf(c_16,plain,
$false,
inference(resolve,[status(thm)],[c_15,c_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA024-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n009.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 22:06:29 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 1234884 was started by sandbox2 on n009,
% 0.12/0.38 % Sat Sep 26 22:06:29 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 0.12/0.39
% 0.12/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.39
% 0.12/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.39 % Length of proof is 15.
% 0.12/0.39 % Level of proof is 6.
% 0.12/0.39 % Maximum clause weight is 14.000.
% 0.12/0.39 % Given clauses 3.
% 0.12/0.39
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------