%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT270-2 : 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 : 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 07:49:57 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.38s
% Output : CNFRefutation 0.08s
% 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 : 9 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
c_in(v_a,v_A,t_a),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
c_in(v_a,v_A,t_a),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
c_in(v_b,v_A,t_a),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_2,plain,
c_in(v_b,v_A,t_a),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
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_3,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_6,axiom,
~ c_lessequals(v_S,v_A,tc_set(t_a)),
file('theBenchmark.p',cls_conjecture_6) ).
cnf(c_4,plain,
~ c_lessequals(v_S,v_A,tc_set(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_6]) ).
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_5,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_9,plain,
( c_lessequals(B,v_A,tc_set(t_a))
| ~ c_lessequals(B,c_Tarski_Ointerval(v_r,A,v_b,t_a),tc_set(t_a))
| ~ c_in(A,v_A,t_a) ),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_10,plain,
( c_lessequals(A,v_A,tc_set(t_a))
| ~ c_lessequals(A,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_9,c_1]) ).
cnf(c_7,plain,
c_lessequals(v_S,v_A,tc_set(t_a)),
inference(resolve,[status(thm)],[c_10,c_3]) ).
cnf(c_8,plain,
$false,
inference(resolve,[status(thm)],[c_7,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT270-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 20:23:20 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3698927 was started by sandbox on n020,
% 0.08/0.36 % Fri Sep 25 20:23:20 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.38
% 0.08/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.38 % Length of proof is 7.
% 0.08/0.38 % Level of proof is 2.
% 0.08/0.38 % Maximum clause weight is 22.000.
% 0.08/0.38 % Given clauses 5.
% 0.08/0.38
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------