%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT273-2 : 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 : n026.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 07:49:58 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 12 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 45 ( 22 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 27 ( 1 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_1,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_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Ab1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( c_in(c_Pair(VAR_0,VAR_5,VAR_2,VAR_2),VAR_3,tc_prod(VAR_2,VAR_2))
| ~ c_lessequals(VAR_1,c_Tarski_Ointerval(VAR_3,VAR_4,VAR_5,VAR_2),tc_set(VAR_2))
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Ab1_J_A_58_Ar_A_61_61_ATrue_0) ).
cnf(c_2,plain,
( c_in(c_Pair(A,F,C,C),D,tc_prod(C,C))
| ~ c_lessequals(B,c_Tarski_Ointerval(D,E,F,C),tc_set(C))
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Ab1_J_A_58_Ar_A_61_61_ATrue_0]) ).
fof(cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(c_Pair(VAR_1,VAR_2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mi(VAR_0,v_r,VAR_2),VAR_2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(VAR_2,v_A,t_a)
| ~ c_Tarski_OisLub(VAR_0,v_cl,VAR_1,t_a) ),
file('theBenchmark.p',cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_1) ).
cnf(c_3,plain,
( c_in(c_Pair(B,C,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mi(A,v_r,C),C,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(C,v_A,t_a)
| ~ c_Tarski_OisLub(A,v_cl,B,t_a) ),
inference(clausify,[status(thm)],[cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_1]) ).
fof(cls_conjecture_4,axiom,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_4,plain,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(v_sko__4mi(VAR_0,v_r,VAR_2),VAR_0,t_a)
| c_in(c_Pair(VAR_1,VAR_2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(VAR_2,v_A,t_a)
| ~ c_Tarski_OisLub(VAR_0,v_cl,VAR_1,t_a) ),
file('theBenchmark.p',cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_0) ).
cnf(c_5,plain,
( c_in(v_sko__4mi(A,v_r,C),A,t_a)
| c_in(c_Pair(B,C,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(C,v_A,t_a)
| ~ c_Tarski_OisLub(A,v_cl,B,t_a) ),
inference(clausify,[status(thm)],[cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_0]) ).
cnf(c_6,plain,
( c_in(v_sko__4mi(v_S,v_r,A),v_S,t_a)
| c_in(c_Pair(v_L,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(A,v_A,t_a) ),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_7,plain,
( c_in(c_Pair(v_L,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mi(v_S,v_r,A),A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(A,v_A,t_a) ),
inference(resolve,[status(thm)],[c_3,c_4]) ).
fof(cls_conjecture_1,axiom,
c_in(v_b,v_A,t_a),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_8,plain,
c_in(v_b,v_A,t_a),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_6,axiom,
~ c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('theBenchmark.p',cls_conjecture_6) ).
cnf(c_9,plain,
~ c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(clausify,[status(thm)],[cls_conjecture_6]) ).
cnf(c_10,plain,
( c_in(c_Pair(A,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(A,v_S,t_a) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_15,plain,
( c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_8,c_6]) ).
cnf(c_11,plain,
c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a),
inference(resolve,[status(thm)],[c_9,c_15]) ).
cnf(c_16,plain,
( c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_12,plain,
~ c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_16,c_9]) ).
cnf(c_17,plain,
c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_11,c_10]) ).
cnf(c_14,plain,
$false,
inference(resolve,[status(thm)],[c_12,c_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT273-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 20:25:56 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.35 % Process 3367163 was started by sandbox on n026,
% 0.12/0.35 % Fri Sep 25 20:25:56 2026
% 0.12/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.37
% 0.12/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.37
% 0.12/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.37 % Length of proof is 13.
% 0.12/0.37 % Level of proof is 3.
% 0.12/0.37 % Maximum clause weight is 27.000.
% 0.12/0.37 % Given clauses 6.
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------