%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA035-1 : 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 : n020.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 100.78s 14.45s
% Output : CNFRefutation 100.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 15 unt; 0 def)
% Number of atoms : 45 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 36 ( 21 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 50 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_103,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_109,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]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_20,axiom,
! [VAR_0] :
( class_Ring__and__Field_Osemiring(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_20) ).
cnf(c_152,plain,
( class_Ring__and__Field_Osemiring(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_20]) ).
fof(clsrel_Ring__and__Field_Osemiring_3,axiom,
! [VAR_0] :
( class_OrderedGroup_Osemigroup__mult(VAR_0)
| ~ class_Ring__and__Field_Osemiring(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Osemiring_3) ).
cnf(c_167,plain,
( class_OrderedGroup_Osemigroup__mult(A)
| ~ class_Ring__and__Field_Osemiring(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Osemiring_3]) ).
fof(cls_OrderedGroup_Omult__ac__1_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_Omult__ac__1_0) ).
cnf(c_363,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_Omult__ac__1_0]) ).
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_365,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]) ).
cnf(c_366,plain,
( c_times(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A) = c_HOL_Oabs(c_times(B,C,A),A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(copy,[status(thm)],[c_365]) ).
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_375,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_376,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_375]) ).
fof(tfree_tcs,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('theBenchmark.p',tfree_tcs) ).
cnf(c_377,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(clausify,[status(thm)],[tfree_tcs]) ).
cnf(c_514,plain,
( ~ class_Ring__and__Field_Oordered__idom(D)
| c_times(A,c_times(B,C,D),D) = c_times(B,c_times(A,C,D),D) ),
inference(resolve,[status(thm)],[c_109,c_103]) ).
cnf(c_700,plain,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Osemigroup__mult(A) ),
inference(resolve,[status(thm)],[c_167,c_152]) ).
cnf(c_3789,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(resolve,[status(thm)],[c_377,c_366]) ).
cnf(c_3799,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_514,c_377]) ).
cnf(c_3811,plain,
class_OrderedGroup_Osemigroup__mult(t_b),
inference(resolve,[status(thm)],[c_700,c_377]) ).
cnf(c_11902,plain,
c_times(c_times(A,B,t_b),C,t_b) = c_times(A,c_times(B,C,t_b),t_b),
inference(resolve,[status(thm)],[c_3811,c_363]) ).
cnf(c_11957,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_11902,c_376]) ).
cnf(c_11903,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_11902,c_11957]) ).
cnf(c_11958,plain,
c_times(A,c_HOL_Oabs(c_times(B,C,t_b),t_b),t_b) = c_times(c_HOL_Oabs(B,t_b),c_times(A,c_HOL_Oabs(C,t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_3789,c_3799]) ).
cnf(c_11952,plain,
c_times(c_HOL_Oabs(A,t_b),c_times(B,c_HOL_Oabs(C,t_b),t_b),t_b) = c_times(B,c_HOL_Oabs(c_times(A,C,t_b),t_b),t_b),
inference(copy,[status(thm)],[c_11958]) ).
cnf(c_11959,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_11952,c_11903]) ).
cnf(c_11956,plain,
$false,
inference(copy,[status(thm)],[c_11959]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA035-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n020.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 22:09:05 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2613422 was started by sandbox on n020,
% 0.11/0.37 % Sat Sep 26 22:09:05 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.44
% 0.11/0.44 % From the command line: assign(max_seconds, 300).
% 100.78/14.45
% 100.78/14.45 % given #500 (I,wt=9): 881 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oorder(A) # tptp_name(clsrel_Ring__and__Field_Oordered__semidom_38) # clausal_fof(1). [assumption].
% 100.78/14.45
% 100.78/14.45 % given #1000 (I,wt=7): 1381 class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) # tptp_name(clsarity_IntDef__Oint_30) # clausal_fof(1). [assumption].
% 100.78/14.45
% 100.78/14.45 % given #1500 (I,wt=18): 2058 -c_Parity_Oeven(c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_Parity_Oeven(A,tc_IntDef_Oint) # tptp_name(cls_Parity_Oeven__neg_0) # clausal_fof(1). [assumption].
% 100.78/14.45
% 100.78/14.45 % given #2000 (I,wt=15): 2789 c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) = c_0 # tptp_name(cls_List_Onibble_Osize__15_0) # clausal_fof(1). [assumption].
% 100.78/14.45
% 100.78/14.45 % given #2500 (I,wt=18): 3522 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(129,a,115,b)].
% 100.78/14.45
% 100.78/14.45 % SZS status Unsatisfiable for theBenchmark
% 100.78/14.45
% 100.78/14.45 % Proof 1 at 5.11 (+ 0.46) seconds.
% 100.78/14.45 % Length of proof is 19.
% 100.78/14.45 % Level of proof is 5.
% 100.78/14.45 % Maximum clause weight is 61.000.
% 100.78/14.45 % Given clauses 2714.
% 100.78/14.45
% 100.78/14.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------