%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT270-1 : 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 : n006.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 07:49:57 AM UTC 2026
% Result : Unsatisfiable 39.81s 6.26s
% Output : CNFRefutation 39.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 10 unt; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 6 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_6,axiom,
~ c_lessequals(v_S,v_A,tc_set(t_a)),
file('theBenchmark.p',cls_conjecture_6) ).
cnf(c_1358,plain,
~ c_lessequals(v_S,v_A,tc_set(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_6]) ).
fof(cls_conjecture_2,axiom,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_1362,plain,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
c_in(v_b,v_A,t_a),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_1363,plain,
c_in(v_b,v_A,t_a),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
c_in(v_a,v_A,t_a),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1364,plain,
c_in(v_a,v_A,t_a),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_2,v_A,tc_set(t_a))
| ~ c_lessequals(VAR_2,c_Tarski_Ointerval(v_r,VAR_1,VAR_0,t_a),tc_set(t_a))
| ~ c_in(VAR_1,v_A,t_a)
| ~ c_in(VAR_0,v_A,t_a) ),
file('theBenchmark.p',cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0) ).
cnf(c_3930,plain,
( c_lessequals(C,v_A,tc_set(t_a))
| ~ c_lessequals(C,c_Tarski_Ointerval(v_r,B,A,t_a),tc_set(t_a))
| ~ c_in(B,v_A,t_a)
| ~ c_in(A,v_A,t_a) ),
inference(clausify,[status(thm)],[cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0]) ).
cnf(c_14329,plain,
( c_lessequals(v_S,v_A,tc_set(t_a))
| ~ c_in(v_a,v_A,t_a)
| ~ c_in(v_b,v_A,t_a) ),
inference(resolve,[status(thm)],[c_3930,c_1362]) ).
cnf(c_14330,plain,
( c_lessequals(v_S,v_A,tc_set(t_a))
| ~ c_in(v_a,v_A,t_a) ),
inference(resolve,[status(thm)],[c_1363,c_14329]) ).
cnf(c_14331,plain,
c_lessequals(v_S,v_A,tc_set(t_a)),
inference(resolve,[status(thm)],[c_1364,c_14330]) ).
cnf(c_14328,plain,
$false,
inference(resolve,[status(thm)],[c_1358,c_14331]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT270-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 20:22:15 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.36 % Process 3638089 was started by sandbox on n006,
% 0.14/0.36 % Fri Sep 25 20:22:15 2026
% 0.14/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.44
% 0.14/0.44 % From the command line: assign(max_seconds, 300).
% 39.81/6.26
% 39.81/6.26 % given #500 (I,wt=9): 1395 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A) # tptp_name(clsrel_Ring__and__Field_Osemiring__0__cancel_5) # clausal_fof(1). [assumption].
% 39.81/6.26
% 39.81/6.26 % given #1000 (I,wt=9): 1895 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ominus(A) # tptp_name(clsrel_Ring__and__Field_Ocomm__ring_13) # clausal_fof(1). [assumption].
% 39.81/6.26
% 39.81/6.26 % given #1500 (I,wt=28): 2555 -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Ofield(A) | c_times(c_0,c_divide(B,c_0,A),A) = c_0 # tptp_name(cls_Ring__and__Field_Otimes__divide__self__right_0) # clausal_fof(1). [assumption].
% 39.81/6.26
% 39.81/6.26 % given #2000 (I,wt=63): 3424 -c_in(c_Pair(c_List_Olist_OCons(A,B,C),c_List_Olist_OCons(D,E,C),tc_List_Olist(C),tc_List_Olist(C)),c_List_Olexord(F,C),tc_prod(tc_List_Olist(C),tc_List_Olist(C))) | c_in(c_Pair(A,D,C,C),F,tc_prod(C,C)) | c_in(c_Pair(B,E,tc_List_Olist(C),tc_List_Olist(C)),c_List_Olexord(F,C),tc_prod(tc_List_Olist(C),tc_List_Olist(C))) # tptp_name(cls_List_Olexord__cons__cons_1) # clausal_fof(1). [assumption].
% 39.81/6.26
% 39.81/6.26 % SZS status Unsatisfiable for theBenchmark
% 39.81/6.26
% 39.81/6.26 % Proof 1 at 5.43 (+ 0.31) seconds.
% 39.81/6.26 % Length of proof is 6.
% 39.81/6.26 % Level of proof is 1.
% 39.81/6.26 % Maximum clause weight is 32.000.
% 39.81/6.26 % Given clauses 2321.
% 39.81/6.26
% 39.81/6.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------