%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT271-1 : 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 : n011.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 170.73s 23.71s
% Output : CNFRefutation 170.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 15 ( 2 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_Ia1_M_Ax1_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_4,VAR_0,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_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0) ).
cnf(c_677,plain,
( c_in(c_Pair(E,A,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_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0]) ).
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_3341,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_in(v_x,v_S,t_a),
file('theBenchmark.p',cls_conjecture_6) ).
cnf(c_3345,plain,
c_in(v_x,v_S,t_a),
inference(clausify,[status(thm)],[cls_conjecture_6]) ).
fof(cls_conjecture_7,axiom,
~ c_in(c_Pair(v_a,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('theBenchmark.p',cls_conjecture_7) ).
cnf(c_3346,plain,
~ c_in(c_Pair(v_a,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(clausify,[status(thm)],[cls_conjecture_7]) ).
cnf(c_13380,plain,
( c_in(c_Pair(B,v_x,t_a,t_a),A,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,c_Tarski_Ointerval(A,B,C,t_a),tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_677,c_3345]) ).
cnf(c_13381,plain,
c_in(c_Pair(v_a,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_13380,c_3341]) ).
cnf(c_13379,plain,
$false,
inference(resolve,[status(thm)],[c_3346,c_13381]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT271-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.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 20:22:30 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 2799718 was started by sandbox2 on n011,
% 0.08/0.36 % Fri Sep 25 20:22:30 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.43
% 0.12/0.43 % From the command line: assign(max_seconds, 300).
% 170.73/23.71
% 170.73/23.71 % given #500 (I,wt=19): 1037 c_append(A,B,C) != c_List_Olist_ONil | c_List_Olist_ONil = B. [copy(1036),flip(a),flip(b)].
% 170.73/23.71
% 170.73/23.71 % given #1000 (I,wt=17): 1846 -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_0,A) = c_0. [copy(1845),flip(b)].
% 170.73/23.71
% 170.73/23.71 % given #1500 (I,wt=20): 2579 -c_less(A,B,tc_set(C)) | c_lessequals(A,B,tc_set(C)) # tptp_name(cls_Set_OpsubsetE_1) # clausal_fof(1). [assumption].
% 170.73/23.71
% 170.73/23.71 % given #2000 (I,wt=9): 3091 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Opordered__semiring(A) # tptp_name(clsrel_Ring__and__Field_Oordered__ring__strict_24) # clausal_fof(1). [assumption].
% 170.73/23.71
% 170.73/23.71 % SZS status Unsatisfiable for theBenchmark
% 170.73/23.71
% 170.73/23.71 % Proof 1 at 6.11 (+ 0.55) seconds.
% 170.73/23.71 % Length of proof is 5.
% 170.73/23.71 % Level of proof is 1.
% 170.73/23.71 % Maximum clause weight is 33.000.
% 170.73/23.71 % Given clauses 2254.
% 170.73/23.71
% 170.73/23.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------