%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT274-2 : 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 : n013.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 0.15s 15.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of formulae : 70 ( 18 unt; 0 def)
% Number of atoms : 198 ( 22 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 206 ( 78 ~; 128 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-4 aty)
% Number of variables : 133 ( 10 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_0 = c_emptyset
| c_in(v_sko__4mk(VAR_3,VAR_0,v_r),VAR_0,t_a)
| c_in(v_sko__4mj(VAR_0,VAR_2,v_r),VAR_0,t_a)
| c_in(c_Pair(VAR_2,VAR_3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(VAR_0,VAR_1,tc_set(t_a)) ),
file('theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0) ).
cnf(c_1,plain,
( A = c_emptyset
| c_in(v_sko__4mk(D,A,v_r),A,t_a)
| c_in(v_sko__4mj(A,C,v_r),A,t_a)
| c_in(c_Pair(C,D,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(A,B,tc_set(t_a)) ),
inference(clausify,[status(thm)],[cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0]) ).
cnf(c_2,plain,
( c_emptyset = A
| c_in(v_sko__4mk(D,A,v_r),A,t_a)
| c_in(v_sko__4mj(A,C,v_r),A,t_a)
| c_in(c_Pair(C,D,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(A,B,tc_set(t_a)) ),
inference(copy,[status(thm)],[c_1]) ).
fof(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_1 = c_emptyset
| c_in(v_sko__4mj(VAR_1,VAR_3,v_r),VAR_1,t_a)
| c_in(c_Pair(VAR_3,VAR_0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(VAR_1,VAR_2,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(VAR_0,VAR_1,v_r),VAR_0,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_1) ).
cnf(c_3,plain,
( B = c_emptyset
| c_in(v_sko__4mj(B,D,v_r),B,t_a)
| c_in(c_Pair(D,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(B,C,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(A,B,v_r),A,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(clausify,[status(thm)],[cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_1]) ).
cnf(c_4,plain,
( c_emptyset = B
| c_in(v_sko__4mj(B,D,v_r),B,t_a)
| c_in(c_Pair(D,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(B,C,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(A,B,v_r),A,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(copy,[status(thm)],[c_3]) ).
fof(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_1 = c_emptyset
| c_in(v_sko__4mk(VAR_3,VAR_1,v_r),VAR_1,t_a)
| c_in(c_Pair(VAR_0,VAR_3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(VAR_1,VAR_2,tc_set(t_a))
| ~ c_in(c_Pair(VAR_0,v_sko__4mj(VAR_1,VAR_0,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_2) ).
cnf(c_5,plain,
( B = c_emptyset
| c_in(v_sko__4mk(D,B,v_r),B,t_a)
| c_in(c_Pair(A,D,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(B,C,tc_set(t_a))
| ~ c_in(c_Pair(A,v_sko__4mj(B,A,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(clausify,[status(thm)],[cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_2]) ).
cnf(c_6,plain,
( c_emptyset = B
| c_in(v_sko__4mk(D,B,v_r),B,t_a)
| c_in(c_Pair(A,D,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(B,C,tc_set(t_a))
| ~ c_in(c_Pair(A,v_sko__4mj(B,A,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(copy,[status(thm)],[c_5]) ).
fof(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_1 = c_emptyset
| c_in(c_Pair(VAR_0,VAR_2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(VAR_1,VAR_3,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(VAR_2,VAR_1,v_r),VAR_2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(VAR_0,v_sko__4mj(VAR_1,VAR_0,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_3) ).
cnf(c_7,plain,
( B = c_emptyset
| c_in(c_Pair(A,C,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(B,D,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(C,B,v_r),C,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(A,v_sko__4mj(B,A,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(clausify,[status(thm)],[cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_3]) ).
cnf(c_8,plain,
( c_emptyset = B
| c_in(c_Pair(A,C,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(B,D,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(C,B,v_r),C,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(A,v_sko__4mj(B,A,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(copy,[status(thm)],[c_7]) ).
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_9,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_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_10,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_A_Ia1_M_Ax1_J_A_58_Ar_59_A_Ix1_M_Ab1_J_A_58_Ar_A_124_93_A_61_61_62_Ax1_A_58_Ainterval_Ar_Aa1_Ab1_A_61_61_ATrue_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( c_in(VAR_0,c_Tarski_Ointerval(VAR_3,VAR_4,VAR_1,VAR_2),VAR_2)
| ~ c_in(c_Pair(VAR_4,VAR_0,VAR_2,VAR_2),VAR_3,tc_prod(VAR_2,VAR_2))
| ~ c_in(c_Pair(VAR_0,VAR_1,VAR_2,VAR_2),VAR_3,tc_prod(VAR_2,VAR_2)) ),
file('theBenchmark.p',cls_Tarski_O_91_124_A_Ia1_M_Ax1_J_A_58_Ar_59_A_Ix1_M_Ab1_J_A_58_Ar_A_124_93_A_61_61_62_Ax1_A_58_Ainterval_Ar_Aa1_Ab1_A_61_61_ATrue_0) ).
cnf(c_11,plain,
( c_in(A,c_Tarski_Ointerval(D,E,B,C),C)
| ~ c_in(c_Pair(E,A,C,C),D,tc_prod(C,C))
| ~ c_in(c_Pair(A,B,C,C),D,tc_prod(C,C)) ),
inference(clausify,[status(thm)],[cls_Tarski_O_91_124_A_Ia1_M_Ax1_J_A_58_Ar_59_A_Ix1_M_Ab1_J_A_58_Ar_A_124_93_A_61_61_62_Ax1_A_58_Ainterval_Ar_Aa1_Ab1_A_61_61_ATrue_0]) ).
fof(cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Ay1_A_58_AS1_A_124_93_A_61_61_62_A_Iy1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(c_Pair(VAR_2,VAR_1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(VAR_2,VAR_0,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_Ay1_A_58_AS1_A_124_93_A_61_61_62_A_Iy1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0) ).
cnf(c_12,plain,
( c_in(c_Pair(C,B,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(C,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_Ay1_A_58_AS1_A_124_93_A_61_61_62_A_Iy1_M_AL1_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_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_13,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]) ).
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_14,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_1,axiom,
c_in(v_b,v_A,t_a),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_15,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_16,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_3,axiom,
v_S != c_emptyset,
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_17,plain,
v_S != c_emptyset,
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_4,axiom,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_18,plain,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_6,axiom,
~ c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),
file('theBenchmark.p',cls_conjecture_6) ).
cnf(c_19,plain,
~ c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),
inference(clausify,[status(thm)],[cls_conjecture_6]) ).
cnf(c_21,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_16,c_10]) ).
cnf(c_22,plain,
( c_in(c_Pair(v_a,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(A,v_S,t_a) ),
inference(resolve,[status(thm)],[c_16,c_9]) ).
cnf(c_225,plain,
( c_emptyset = v_S
| c_in(c_Pair(A,B,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mk(B,v_S,v_r),B,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(A,v_sko__4mj(v_S,A,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_16,c_8]) ).
cnf(c_226,plain,
( v_S = c_emptyset
| c_in(c_Pair(A,B,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mk(B,v_S,v_r),B,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(A,v_sko__4mj(v_S,A,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(copy,[status(thm)],[c_225]) ).
cnf(c_23,plain,
( c_in(c_Pair(A,B,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mk(B,v_S,v_r),B,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(A,v_sko__4mj(v_S,A,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_17,c_226]) ).
cnf(c_227,plain,
( c_emptyset = v_S
| c_in(v_sko__4mk(B,v_S,v_r),v_S,t_a)
| c_in(c_Pair(A,B,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(A,v_sko__4mj(v_S,A,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_16,c_6]) ).
cnf(c_228,plain,
( v_S = c_emptyset
| c_in(v_sko__4mk(B,v_S,v_r),v_S,t_a)
| c_in(c_Pair(A,B,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(A,v_sko__4mj(v_S,A,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(copy,[status(thm)],[c_227]) ).
cnf(c_24,plain,
( c_in(v_sko__4mk(B,v_S,v_r),v_S,t_a)
| c_in(c_Pair(A,B,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(A,v_sko__4mj(v_S,A,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_17,c_228]) ).
cnf(c_229,plain,
( c_emptyset = v_S
| c_in(v_sko__4mj(v_S,B,v_r),v_S,t_a)
| c_in(c_Pair(B,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mk(A,v_S,v_r),A,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_230,plain,
( v_S = c_emptyset
| c_in(v_sko__4mj(v_S,B,v_r),v_S,t_a)
| c_in(c_Pair(B,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mk(A,v_S,v_r),A,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(copy,[status(thm)],[c_229]) ).
cnf(c_25,plain,
( c_in(v_sko__4mj(v_S,B,v_r),v_S,t_a)
| c_in(c_Pair(B,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mk(A,v_S,v_r),A,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_17,c_230]) ).
cnf(c_231,plain,
( c_emptyset = v_S
| c_in(v_sko__4mk(B,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,A,v_r),v_S,t_a)
| c_in(c_Pair(A,B,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_16,c_2]) ).
cnf(c_232,plain,
( v_S = c_emptyset
| c_in(v_sko__4mk(B,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,A,v_r),v_S,t_a)
| c_in(c_Pair(A,B,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(copy,[status(thm)],[c_231]) ).
cnf(c_26,plain,
( c_in(v_sko__4mk(B,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,A,v_r),v_S,t_a)
| c_in(c_Pair(A,B,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_17,c_232]) ).
cnf(c_27,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_18,c_14]) ).
cnf(c_28,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_18,c_13]) ).
cnf(c_29,plain,
( c_in(c_Pair(A,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(A,v_S,t_a) ),
inference(resolve,[status(thm)],[c_18,c_12]) ).
cnf(c_30,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_28,c_15]) ).
cnf(c_35,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))
| 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_30,c_21]) ).
cnf(c_233,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_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_b,v_A,t_a) ),
inference(resolve,[status(thm)],[c_27,c_35]) ).
cnf(c_234,plain,
( c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_b,v_A,t_a) ),
inference(copy,[status(thm)],[c_233]) ).
cnf(c_83,plain,
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_15,c_234]) ).
cnf(c_235,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,A,v_b,t_a),t_a)
| ~ c_in(c_Pair(A,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_11,c_83]) ).
cnf(c_87,plain,
~ c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_235,c_19]) ).
cnf(c_97,plain,
( c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolve,[status(thm)],[c_87,c_26]) ).
cnf(c_110,plain,
( c_in(c_Pair(v_a,v_sko__4mj(v_S,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) ),
inference(resolve,[status(thm)],[c_97,c_22]) ).
cnf(c_138,plain,
( c_in(v_sko__4mk(A,v_S,v_r),v_S,t_a)
| c_in(c_Pair(v_a,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) ),
inference(resolve,[status(thm)],[c_110,c_24]) ).
cnf(c_236,plain,
( c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) ),
inference(factor,[status(thm)],[c_138]) ).
cnf(c_143,plain,
c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a),
inference(resolve,[status(thm)],[c_87,c_236]) ).
cnf(c_144,plain,
c_in(c_Pair(v_sko__4mk(v_L,v_S,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_143,c_29]) ).
cnf(c_203,plain,
( c_in(v_sko__4mj(v_S,A,v_r),v_S,t_a)
| c_in(c_Pair(A,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_144,c_25]) ).
cnf(c_237,plain,
( c_in(c_Pair(A,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(A,v_sko__4mj(v_S,A,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_23,c_144]) ).
cnf(c_207,plain,
~ c_in(c_Pair(v_a,v_sko__4mj(v_S,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_237,c_87]) ).
cnf(c_209,plain,
c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a),
inference(resolve,[status(thm)],[c_203,c_87]) ).
cnf(c_238,plain,
c_in(c_Pair(v_a,v_sko__4mj(v_S,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_209,c_22]) ).
cnf(c_224,plain,
$false,
inference(resolve,[status(thm)],[c_207,c_238]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT274-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/15.39 % Computer : n013.cluster.edu
% 0.10/15.39 % Model : x86_64 x86_64
% 0.10/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.39 % Memory : 8046.5625MB
% 0.10/15.39 % OS : Linux 6.8.0-71-generic
% 0.10/15.40 % CPULimit : 300
% 0.10/15.40 % WCLimit : 300
% 0.10/15.40 % DateTime : Fri Sep 25 20:22:38 UTC 2026
% 0.15/15.40 % CPUTime :
% 0.15/15.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/15.40 % Process 1117806 was started by sandbox2 on n013,
% 0.15/15.40 % Fri Sep 25 20:22:38 2026
% 0.15/15.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/15.40
% 0.15/15.40 % From the command line: assign(max_seconds, 300).
% 0.15/15.44
% 0.15/15.44 % SZS status Unsatisfiable for theBenchmark
% 0.15/15.44
% 0.15/15.44 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.15/15.44 % Length of proof is 41.
% 0.15/15.44 % Level of proof is 13.
% 0.15/15.44 % Maximum clause weight is 59.000.
% 0.15/15.44 % Given clauses 57.
% 0.15/15.44
% 0.15/15.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------