%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LAT274-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 : Tue Sep 29 11:48:09 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 23
% Syntax : Number of formulae : 100 ( 17 unt; 8 def)
% Number of atoms : 293 ( 21 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 324 ( 131 ~; 185 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-4 aty)
% Number of variables : 110 ( 0 sgn 110 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(t_a))
| c_in(c_Pair(X2,X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(X0,X2,v_r),X0,t_a)
| c_in(v_sko__4mk(X3,X0,v_r),X0,t_a)
| X0 = c_emptyset ),
file('/export/starexec/sandbox2/benchmark/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) ).
fof(f2,plain,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(t_a))
| c_in(c_Pair(X2,X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(X0,X2,v_r),X0,t_a)
| c_in(v_sko__4mk(X3,X0,v_r),X0,t_a)
| c_emptyset = X0 ),
inference(reorient_equations,[],[f1]) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(v_sko__4mk(X0,X1,v_r),X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X1,X2,tc_set(t_a))
| c_in(c_Pair(X3,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(X1,X3,v_r),X1,t_a)
| X1 = c_emptyset ),
file('/export/starexec/sandbox2/benchmark/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) ).
fof(f4,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(v_sko__4mk(X0,X1,v_r),X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X1,X2,tc_set(t_a))
| c_in(c_Pair(X3,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(X1,X3,v_r),X1,t_a)
| c_emptyset = X1 ),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,v_sko__4mj(X1,X0,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X1,X2,tc_set(t_a))
| c_in(c_Pair(X0,X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(X3,X1,v_r),X1,t_a)
| X1 = c_emptyset ),
file('/export/starexec/sandbox2/benchmark/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) ).
fof(f6,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,v_sko__4mj(X1,X0,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X1,X2,tc_set(t_a))
| c_in(c_Pair(X0,X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(X3,X1,v_r),X1,t_a)
| c_emptyset = X1 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(X0,v_sko__4mj(X1,X0,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mk(X2,X1,v_r),X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X1,X3,tc_set(t_a))
| c_in(c_Pair(X0,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| X1 = c_emptyset ),
file('/export/starexec/sandbox2/benchmark/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) ).
fof(f8,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_Pair(v_sko__4mk(X2,X1,v_r),X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,v_sko__4mj(X1,X0,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X1,X3,tc_set(t_a))
| c_in(c_Pair(X0,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_emptyset = X1 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_lessequals(X1,c_Tarski_Ointerval(X3,X4,X5,X2),tc_set(X2))
| ~ c_in(X0,X1,X2)
| c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox2/benchmark/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) ).
fof(f10,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_lessequals(X1,c_Tarski_Ointerval(X3,X4,X5,X2),tc_set(X2))
| ~ c_in(X0,X1,X2)
| c_in(c_Pair(X0,X5,X2,X2),X3,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox2/benchmark/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) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))
| c_in(X0,c_Tarski_Ointerval(X3,X4,X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/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) ).
fof(f12,axiom,
! [X2,X0,X1] :
( ~ c_Tarski_OisLub(X0,v_cl,X1,t_a)
| ~ c_in(X2,X0,t_a)
| c_in(c_Pair(X2,X1,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/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) ).
fof(f13,axiom,
! [X2,X0,X1] :
( ~ c_Tarski_OisLub(X0,v_cl,X1,t_a)
| ~ c_in(X2,v_A,t_a)
| c_in(c_Pair(X1,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(X0,v_r,X2),X0,t_a) ),
file('/export/starexec/sandbox2/benchmark/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) ).
fof(f14,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Pair(v_sko__4mi(X0,v_r,X2),X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X2,v_A,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,X1,t_a)
| c_in(c_Pair(X1,X2,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/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) ).
fof(f15,negated_conjecture,
c_in(v_b,v_A,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f16,negated_conjecture,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f17,negated_conjecture,
v_S != c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f18,plain,
c_emptyset != v_S,
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f20,negated_conjecture,
~ c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f21,plain,
! [X0] :
( c_in(c_Pair(X0,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X0,v_S,t_a) ),
inference(resolution,[],[f12,f19]) ).
fof(f22,plain,
! [X0] :
( c_in(c_Pair(v_a,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X0,v_S,t_a) ),
inference(resolution,[],[f9,f16]) ).
fof(f23,plain,
! [X0] :
( c_in(c_Pair(X0,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X0,v_S,t_a) ),
inference(resolution,[],[f10,f16]) ).
fof(f24,plain,
! [X0] :
( c_in(c_Pair(v_L,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X0,v_A,t_a)
| c_in(v_sko__4mi(v_S,v_r,X0),v_S,t_a) ),
inference(resolution,[],[f13,f19]) ).
fof(f44,plain,
! [X0,X1] :
( c_in(c_Pair(X0,X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,X0,v_r),v_S,t_a)
| c_in(v_sko__4mk(X1,v_S,v_r),v_S,t_a)
| c_emptyset = v_S ),
inference(resolution,[],[f2,f16]) ).
fof(f45,plain,
! [X0,X1] :
( c_in(c_Pair(X0,X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,X0,v_r),v_S,t_a)
| c_in(v_sko__4mk(X1,v_S,v_r),v_S,t_a) ),
inference(forward_subsumption_resolution,[],[f44,f18]) ).
fof(f47,plain,
! [X0,X1] :
( ~ c_in(v_b,v_A,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,X1,t_a)
| c_in(c_Pair(X1,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_sko__4mi(X0,v_r,v_b),v_S,t_a) ),
inference(resolution,[],[f14,f23]) ).
fof(f48,plain,
! [X0,X1] :
( ~ c_in(v_sko__4mi(X0,v_r,v_b),v_S,t_a)
| c_in(c_Pair(X1,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(X0,v_cl,X1,t_a) ),
inference(forward_subsumption_resolution,[],[f47,f15]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ c_in(v_sko__4mk(v_L,X0,v_r),v_S,t_a)
| c_in(c_Pair(X2,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(X0,X2,v_r),X0,t_a)
| c_emptyset = X0
| ~ c_lessequals(X0,X1,tc_set(t_a)) ),
inference(resolution,[],[f4,f21]) ).
fof(f73,plain,
! [X2,X0,X1] :
( ~ c_in(v_sko__4mj(X0,v_a,v_r),v_S,t_a)
| c_in(c_Pair(v_a,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(X2,X0,v_r),X0,t_a)
| c_emptyset = X0
| ~ c_lessequals(X0,X1,tc_set(t_a)) ),
inference(resolution,[],[f6,f22]) ).
fof(f75,plain,
! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,v_sko__4mj(X1,X0,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X1,X2,tc_set(t_a))
| c_in(c_Pair(X0,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_emptyset = X1
| ~ c_in(v_sko__4mk(v_L,X1,v_r),v_S,t_a) ),
inference(resolution,[],[f8,f21]) ).
fof(f98,plain,
! [X2,X0,X1] :
( ~ c_in(c_Pair(X1,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(X1,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,X0,v_r),v_S,t_a)
| c_in(X1,c_Tarski_Ointerval(v_r,X0,X2,t_a),t_a) ),
inference(resolution,[],[f45,f11]) ).
fof(f143,definition,
( spl0_19
<=> c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f144,plain,
( ~ c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| spl0_19 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f145,plain,
( c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f158,plain,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(t_a))
| c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_emptyset = X0
| ~ c_in(v_sko__4mk(v_L,X0,v_r),v_S,t_a)
| ~ c_in(v_sko__4mj(X0,v_a,v_r),v_S,t_a) ),
inference(resolution,[],[f75,f22]) ).
fof(f169,definition,
( spl0_24
<=> c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f170,plain,
( ~ c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| spl0_24 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f171,plain,
( c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f173,definition,
( spl0_25
<=> ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(t_a))
| ~ c_in(v_sko__4mj(X0,v_a,v_r),v_S,t_a)
| ~ c_in(v_sko__4mk(v_L,X0,v_r),v_S,t_a)
| c_emptyset = X0 ) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f174,plain,
( ! [X0,X1] :
( ~ c_in(v_sko__4mk(v_L,X0,v_r),v_S,t_a)
| ~ c_in(v_sko__4mj(X0,v_a,v_r),v_S,t_a)
| ~ c_lessequals(X0,X1,tc_set(t_a))
| c_emptyset = X0 )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f175,plain,
( spl0_24
| spl0_25 ),
inference(avatar_split_clause,[],[f158,f173,f169]) ).
fof(f190,definition,
( spl0_27
<=> c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f191,plain,
( ~ c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| spl0_27 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f192,plain,
( c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f213,plain,
( ! [X0] :
( ~ c_in(c_Pair(v_L,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_L,c_Tarski_Ointerval(v_r,v_a,X0,t_a),t_a) )
| ~ spl0_24 ),
inference(resolution,[],[f171,f11]) ).
fof(f228,definition,
( spl0_32
<=> ! [X0] :
( c_in(v_sko__4mj(v_S,X0,v_r),v_S,t_a)
| c_in(v_L,c_Tarski_Ointerval(v_r,X0,v_b,t_a),t_a) ) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f229,plain,
( ! [X0] :
( c_in(v_L,c_Tarski_Ointerval(v_r,X0,v_b,t_a),t_a)
| c_in(v_sko__4mj(v_S,X0,v_r),v_S,t_a) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f232,plain,
( ! [X0,X1] :
( c_in(c_Pair(X0,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,X0,v_r),v_S,t_a)
| c_emptyset = v_S
| ~ c_lessequals(v_S,X1,tc_set(t_a)) )
| ~ spl0_19 ),
inference(resolution,[],[f145,f57]) ).
fof(f233,plain,
( ! [X0,X1] :
( c_in(c_Pair(X0,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,X0,v_r),v_S,t_a)
| ~ c_lessequals(v_S,X1,tc_set(t_a)) )
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f232,f18]) ).
fof(f235,definition,
( spl0_33
<=> ! [X1] : ~ c_lessequals(v_S,X1,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f236,plain,
( ! [X1] : ~ c_lessequals(v_S,X1,tc_set(t_a))
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f238,definition,
( spl0_34
<=> ! [X0] :
( c_in(c_Pair(X0,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,X0,v_r),v_S,t_a) ) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f239,plain,
( ! [X0] :
( c_in(c_Pair(X0,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,X0,v_r),v_S,t_a) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f240,plain,
( spl0_33
| spl0_34
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f233,f143,f238,f235]) ).
fof(f241,plain,
( ~ c_in(v_b,v_A,t_a)
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| spl0_27 ),
inference(resolution,[],[f191,f24]) ).
fof(f244,plain,
( c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| spl0_27 ),
inference(forward_subsumption_resolution,[],[f241,f15]) ).
fof(f245,plain,
( ! [X0] :
( c_in(c_Pair(X0,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(v_S,v_cl,X0,t_a) )
| spl0_27 ),
inference(resolution,[],[f244,f48]) ).
fof(f258,plain,
( ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| spl0_27 ),
inference(resolution,[],[f245,f191]) ).
fof(f261,plain,
( $false
| spl0_27 ),
inference(forward_subsumption_resolution,[],[f258,f19]) ).
fof(f262,plain,
spl0_27,
inference(avatar_contradiction_clause,[],[f261]) ).
fof(f270,plain,
( ! [X0] :
( c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,X0,v_r),v_S,t_a)
| c_in(v_L,c_Tarski_Ointerval(v_r,X0,v_b,t_a),t_a) )
| ~ spl0_27 ),
inference(resolution,[],[f192,f98]) ).
fof(f276,plain,
( c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a)
| ~ spl0_32 ),
inference(resolution,[],[f229,f20]) ).
fof(f277,plain,
( ! [X0,X1] :
( c_in(c_Pair(v_a,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(X0,v_S,v_r),v_S,t_a)
| c_emptyset = v_S
| ~ c_lessequals(v_S,X1,tc_set(t_a)) )
| ~ spl0_32 ),
inference(resolution,[],[f276,f73]) ).
fof(f278,plain,
( ! [X0,X1] :
( c_in(c_Pair(v_a,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(X0,v_S,v_r),v_S,t_a)
| ~ c_lessequals(v_S,X1,tc_set(t_a)) )
| ~ spl0_32 ),
inference(forward_subsumption_resolution,[],[f277,f18]) ).
fof(f280,definition,
( spl0_36
<=> ! [X0] :
( c_in(c_Pair(v_a,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(X0,v_S,v_r),v_S,t_a) ) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f281,plain,
( ! [X0] :
( c_in(c_Pair(v_a,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(X0,v_S,v_r),v_S,t_a) )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f282,plain,
( spl0_33
| spl0_36
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f278,f228,f280,f235]) ).
fof(f283,plain,
( spl0_32
| spl0_19
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f270,f190,f143,f228]) ).
fof(f287,plain,
( $false
| ~ spl0_33 ),
inference(resolution,[],[f236,f16]) ).
fof(f288,plain,
~ spl0_33,
inference(avatar_contradiction_clause,[],[f287]) ).
fof(f302,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| ~ spl0_24
| ~ spl0_27 ),
inference(resolution,[],[f213,f192]) ).
fof(f307,plain,
( $false
| ~ spl0_24
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f302,f20]) ).
fof(f308,plain,
( ~ spl0_24
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f307]) ).
fof(f310,plain,
( c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a)
| spl0_24
| ~ spl0_34 ),
inference(resolution,[],[f170,f239]) ).
fof(f316,plain,
( ! [X0] :
( ~ c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a)
| ~ c_lessequals(v_S,X0,tc_set(t_a))
| c_emptyset = v_S )
| ~ spl0_19
| ~ spl0_25 ),
inference(resolution,[],[f174,f145]) ).
fof(f317,plain,
( ! [X0] :
( ~ c_lessequals(v_S,X0,tc_set(t_a))
| c_emptyset = v_S )
| ~ spl0_19
| spl0_24
| ~ spl0_25
| ~ spl0_34 ),
inference(forward_subsumption_resolution,[],[f316,f310]) ).
fof(f318,plain,
( ! [X0] : ~ c_lessequals(v_S,X0,tc_set(t_a))
| ~ spl0_19
| spl0_24
| ~ spl0_25
| ~ spl0_34 ),
inference(forward_subsumption_resolution,[],[f317,f18]) ).
fof(f319,plain,
( spl0_33
| ~ spl0_19
| spl0_24
| ~ spl0_25
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f318,f238,f173,f169,f143,f235]) ).
fof(f322,plain,
( c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| spl0_24
| ~ spl0_36 ),
inference(resolution,[],[f281,f170]) ).
fof(f332,plain,
( $false
| spl0_19
| spl0_24
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[],[f322,f144]) ).
fof(f333,plain,
( spl0_19
| spl0_24
| ~ spl0_36 ),
inference(avatar_contradiction_clause,[],[f332]) ).
cnf(s13,plain,
( spl0_24
| spl0_25 ),
inference(sat_conversion,[],[f175]) ).
cnf(s22,plain,
( ~ spl0_19
| spl0_33
| spl0_34 ),
inference(sat_conversion,[],[f240]) ).
cnf(s23,plain,
spl0_27,
inference(sat_conversion,[],[f262]) ).
cnf(s26,plain,
( ~ spl0_32
| spl0_33
| spl0_36 ),
inference(sat_conversion,[],[f282]) ).
cnf(s27,plain,
( spl0_19
| ~ spl0_27
| spl0_32 ),
inference(sat_conversion,[],[f283]) ).
cnf(s29,plain,
~ spl0_33,
inference(sat_conversion,[],[f288]) ).
cnf(s31,plain,
( ~ spl0_24
| ~ spl0_27 ),
inference(sat_conversion,[],[f308]) ).
cnf(s33,plain,
( ~ spl0_19
| spl0_24
| ~ spl0_25
| spl0_33
| ~ spl0_34 ),
inference(sat_conversion,[],[f319]) ).
cnf(s34,plain,
( spl0_19
| spl0_24
| ~ spl0_36 ),
inference(sat_conversion,[],[f333]) ).
cnf(s36,plain,
( ~ spl0_32
| spl0_36 ),
inference(rat,[],[s26,s29]) ).
cnf(s37,plain,
~ spl0_24,
inference(rat,[],[s31,s23]) ).
cnf(s38,plain,
( ~ spl0_19
| spl0_34 ),
inference(rat,[],[s22,s29]) ).
cnf(s41,plain,
spl0_25,
inference(rat,[],[s13,s37]) ).
cnf(s42,plain,
~ spl0_19,
inference(rat,[],[s38,s33,s37,s29,s41]) ).
cnf(s43,plain,
~ spl0_36,
inference(rat,[],[s34,s37,s42]) ).
cnf(s44,plain,
spl0_32,
inference(rat,[],[s27,s23,s42]) ).
cnf(s46,plain,
$false,
inference(rat,[],[s36,s43,s44]) ).
fof(f334,plain,
$false,
inference(avatar_sat_refutation,[],[s46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT274-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n020.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 14:10:35 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.41 Running first-order model finding
% 0.13/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.47 % (3415010)Will run a generic schedule for satisfiability detection.
% 0.18/0.47 % (3415015)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2631210329_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.47 % TRYING [1]
% 0.18/0.47 % TRYING [2]
% 0.18/0.47 % (3415016)% WARNING: option uhcvi not known.
% 0.18/0.47 % (3415016)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2721499921:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.47 % (3415018)dis+10_1_sil=32000:sp=arity:random_seed=3197610502:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.47 % (3415020)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3056804675:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.47 % (3415017)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1016490362:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.47 % (3415019)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=788245878:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.47 % (3415021)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3790091473:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.47 % TRYING [3]
% 0.18/0.47 % (3415018) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3415010-3415018"...
% 0.18/0.47 % (3415018)...printing done.
% 0.18/0.47 % (3415018)Refutation found. Thanks to Tanya!
% 0.18/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.48 % (3415018)------------------------------
% 0.18/0.48 % (3415018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.48 % (3415018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.48 % (3415018)CaDiCaL version: 2.1.3
% 0.18/0.48 % (3415018)Termination reason: Refutation
% 0.18/0.48 % (3415018)Time elapsed: 0.012 s
% 0.18/0.48 % (3415018)Peak memory usage: 12 MB
% 0.18/0.48 % (3415018)Instructions burned: 16 (million)
% 0.18/0.48 % (3415010)Success in time 0.05 s
% 0.18/0.48 % Vampire exiting
%------------------------------------------------------------------------------