%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET837-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:42:05 PM UTC 2026
% Result : Unsatisfiable 6.87s 1.96s
% Output : Refutation 8.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 22
% Syntax : Number of formulae : 115 ( 14 unt; 9 def)
% Number of atoms : 315 ( 23 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 373 ( 173 ~; 193 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 69 ( 0 sgn 69 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
( v_X = c_union(v_Y,v_Z,t_a)
| c_lessequals(v_Y,v_X,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
( v_X = c_union(v_Y,v_Z,t_a)
| c_lessequals(v_Z,v_X,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,negated_conjecture,
( c_lessequals(v_Y,v_x,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| v_X != c_union(v_Y,v_Z,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f4,negated_conjecture,
( c_lessequals(v_Z,v_x,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| v_X != c_union(v_Y,v_Z,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f5,negated_conjecture,
( ~ c_lessequals(v_X,v_x,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| v_X != c_union(v_Y,v_Z,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f6,negated_conjecture,
! [X0] :
( v_X = c_union(v_Y,v_Z,t_a)
| c_lessequals(v_X,X0,tc_set(t_a))
| ~ c_lessequals(v_Z,X0,tc_set(t_a))
| ~ c_lessequals(v_Y,X0,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,c_union(X3,X1,X2),X2)
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,c_union(X1,X3,X2),X2)
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_union(X1,X2,X3),X3)
| c_in(X0,X2,X3)
| c_in(X0,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).
fof(f10,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2)
| c_in(X0,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f11,axiom,
! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2)
| c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f12,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2)
| c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f13,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| ~ c_lessequals(X1,X0,tc_set(X2))
| X1 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f14,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2))
| X0 = X1 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,definition,
sF0 = c_union(v_Y,v_Z,t_a),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f16,plain,
c_union(v_Y,v_Z,t_a) = sF0,
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
sF1 = tc_set(t_a),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f18,plain,
tc_set(t_a) = sF1,
inference(reorient_equations,[],[f17]) ).
fof(f19,plain,
( v_X = sF0
| c_lessequals(v_Y,v_X,sF1) ),
inference(definition_folding,[],[f1,f18,f16]) ).
fof(f20,plain,
( v_X = sF0
| c_lessequals(v_Z,v_X,sF1) ),
inference(definition_folding,[],[f2,f18,f16]) ).
fof(f21,plain,
( c_lessequals(v_Y,v_x,sF1)
| ~ c_lessequals(v_Z,v_X,sF1)
| ~ c_lessequals(v_Y,v_X,sF1)
| v_X != sF0 ),
inference(definition_folding,[],[f3,f16,f18,f18,f18]) ).
fof(f22,plain,
( c_lessequals(v_Z,v_x,sF1)
| ~ c_lessequals(v_Z,v_X,sF1)
| ~ c_lessequals(v_Y,v_X,sF1)
| v_X != sF0 ),
inference(definition_folding,[],[f4,f16,f18,f18,f18]) ).
fof(f23,plain,
( ~ c_lessequals(v_X,v_x,sF1)
| ~ c_lessequals(v_Z,v_X,sF1)
| ~ c_lessequals(v_Y,v_X,sF1)
| v_X != sF0 ),
inference(definition_folding,[],[f5,f16,f18,f18,f18]) ).
fof(f24,plain,
! [X0] :
( v_X = sF0
| c_lessequals(v_X,X0,sF1)
| ~ c_lessequals(v_Z,X0,sF1)
| ~ c_lessequals(v_Y,X0,sF1) ),
inference(definition_folding,[],[f6,f18,f18,f18,f16]) ).
fof(f26,definition,
( spl2_1
<=> ! [X0] :
( c_lessequals(v_X,X0,sF1)
| ~ c_lessequals(v_Y,X0,sF1)
| ~ c_lessequals(v_Z,X0,sF1) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f27,plain,
( ! [X0] :
( c_lessequals(v_X,X0,sF1)
| ~ c_lessequals(v_Y,X0,sF1)
| ~ c_lessequals(v_Z,X0,sF1) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f29,definition,
( spl2_2
<=> v_X = sF0 ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f30,plain,
( v_X != sF0
| spl2_2 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f31,plain,
( v_X = sF0
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f32,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f24,f29,f26]) ).
fof(f34,definition,
( spl2_3
<=> c_lessequals(v_Y,v_X,sF1) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f35,plain,
( c_lessequals(v_Y,v_X,sF1)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f36,plain,
( ~ c_lessequals(v_Y,v_X,sF1)
| spl2_3 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f38,definition,
( spl2_4
<=> c_lessequals(v_Z,v_X,sF1) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f39,plain,
( c_lessequals(v_Z,v_X,sF1)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f40,plain,
( ~ c_lessequals(v_Z,v_X,sF1)
| spl2_4 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f42,definition,
( spl2_5
<=> c_lessequals(v_X,v_x,sF1) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f44,plain,
( ~ c_lessequals(v_X,v_x,sF1)
| spl2_5 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f45,plain,
( ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| ~ spl2_5 ),
inference(avatar_split_clause,[],[f23,f42,f38,f34,f29]) ).
fof(f47,definition,
( spl2_6
<=> c_lessequals(v_Z,v_x,sF1) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f49,plain,
( c_lessequals(v_Z,v_x,sF1)
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,plain,
( ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| spl2_6 ),
inference(avatar_split_clause,[],[f22,f47,f38,f34,f29]) ).
fof(f52,definition,
( spl2_7
<=> c_lessequals(v_Y,v_x,sF1) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f54,plain,
( c_lessequals(v_Y,v_x,sF1)
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,plain,
( ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| spl2_7 ),
inference(avatar_split_clause,[],[f21,f52,f38,f34,f29]) ).
fof(f56,plain,
( spl2_4
| spl2_2 ),
inference(avatar_split_clause,[],[f20,f29,f38]) ).
fof(f57,plain,
( spl2_3
| spl2_2 ),
inference(avatar_split_clause,[],[f19,f29,f34]) ).
fof(f58,plain,
( v_X = c_union(v_Y,v_Z,t_a)
| ~ spl2_2 ),
inference(backward_demodulation,[],[f16,f31]) ).
fof(f59,plain,
( ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| spl2_3 ),
inference(forward_demodulation,[],[f36,f18]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_union(X1,X2,X3),X3),X2,X3)
| c_lessequals(X0,c_union(X1,X2,X3),tc_set(X3)) ),
inference(resolution,[],[f7,f12]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_union(X1,X2,X3),X3),X1,X3)
| c_lessequals(X0,c_union(X1,X2,X3),tc_set(X3)) ),
inference(resolution,[],[f8,f12]) ).
fof(f69,plain,
( ! [X0] :
( c_in(X0,v_Z,t_a)
| ~ c_in(X0,v_X,t_a)
| c_in(X0,v_Y,t_a) )
| ~ spl2_2 ),
inference(superposition,[],[f9,f58]) ).
fof(f73,plain,
! [X2,X0,X1] :
( c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2))
| c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2)) ),
inference(resolution,[],[f62,f11]) ).
fof(f80,plain,
! [X2,X0,X1] : c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2)),
inference(duplicate_literal_removal,[],[f73]) ).
fof(f83,plain,
( c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ spl2_2 ),
inference(superposition,[],[f80,f58]) ).
fof(f95,plain,
! [X2,X0,X1] :
( c_lessequals(X0,c_union(X0,X1,X2),tc_set(X2))
| c_lessequals(X0,c_union(X0,X1,X2),tc_set(X2)) ),
inference(resolution,[],[f64,f11]) ).
fof(f102,plain,
! [X2,X0,X1] : c_lessequals(X0,c_union(X0,X1,X2),tc_set(X2)),
inference(duplicate_literal_removal,[],[f95]) ).
fof(f105,plain,
( c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ spl2_2 ),
inference(superposition,[],[f102,f58]) ).
fof(f106,plain,
( $false
| ~ spl2_2
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f105,f59]) ).
fof(f107,plain,
( ~ spl2_2
| spl2_3 ),
inference(avatar_contradiction_clause,[],[f106]) ).
fof(f108,plain,
( c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ spl2_3 ),
inference(forward_demodulation,[],[f35,f18]) ).
fof(f109,plain,
( ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| spl2_4 ),
inference(forward_demodulation,[],[f40,f18]) ).
fof(f110,plain,
( $false
| ~ spl2_2
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f109,f83]) ).
fof(f111,plain,
( ~ spl2_2
| spl2_4 ),
inference(avatar_contradiction_clause,[],[f110]) ).
fof(f112,plain,
( c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ spl2_4 ),
inference(forward_demodulation,[],[f39,f18]) ).
fof(f113,plain,
( ~ c_lessequals(v_X,v_x,tc_set(t_a))
| spl2_5 ),
inference(forward_demodulation,[],[f44,f18]) ).
fof(f114,plain,
( c_lessequals(v_Z,v_x,tc_set(t_a))
| ~ spl2_6 ),
inference(forward_demodulation,[],[f49,f18]) ).
fof(f115,plain,
( c_lessequals(v_Y,v_x,tc_set(t_a))
| ~ spl2_7 ),
inference(forward_demodulation,[],[f54,f18]) ).
fof(f116,plain,
( ! [X0] :
( c_in(X0,v_x,t_a)
| ~ c_in(X0,v_Y,t_a) )
| ~ spl2_7 ),
inference(resolution,[],[f115,f10]) ).
fof(f127,plain,
( ! [X0] :
( c_in(X0,v_x,t_a)
| ~ c_in(X0,v_Z,t_a) )
| ~ spl2_6 ),
inference(resolution,[],[f114,f10]) ).
fof(f138,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x,t_a),v_Z,t_a)
| c_lessequals(X0,v_x,tc_set(t_a)) )
| ~ spl2_6 ),
inference(resolution,[],[f127,f12]) ).
fof(f141,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x,t_a),v_Y,t_a)
| c_lessequals(X0,v_x,tc_set(t_a)) )
| ~ spl2_7 ),
inference(resolution,[],[f116,f12]) ).
fof(f158,plain,
( ! [X0] :
( c_lessequals(X0,v_x,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X0,v_x,t_a),v_X,t_a)
| c_in(c_Main_OsubsetI__1(X0,v_x,t_a),v_Y,t_a) )
| ~ spl2_2
| ~ spl2_6 ),
inference(resolution,[],[f138,f69]) ).
fof(f160,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x,t_a),v_X,t_a)
| c_lessequals(X0,v_x,tc_set(t_a)) )
| ~ spl2_2
| ~ spl2_6
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f158,f141]) ).
fof(f161,plain,
( c_lessequals(v_X,v_x,tc_set(t_a))
| c_lessequals(v_X,v_x,tc_set(t_a))
| ~ spl2_2
| ~ spl2_6
| ~ spl2_7 ),
inference(resolution,[],[f160,f11]) ).
fof(f164,plain,
( c_lessequals(v_X,v_x,tc_set(t_a))
| ~ spl2_2
| ~ spl2_6
| ~ spl2_7 ),
inference(duplicate_literal_removal,[],[f161]) ).
fof(f165,plain,
( $false
| ~ spl2_2
| spl2_5
| ~ spl2_6
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f164,f113]) ).
fof(f166,plain,
( ~ spl2_2
| spl2_5
| ~ spl2_6
| ~ spl2_7 ),
inference(avatar_contradiction_clause,[],[f165]) ).
fof(f167,plain,
( ! [X0] :
( c_lessequals(v_X,X0,tc_set(t_a))
| ~ c_lessequals(v_Y,X0,sF1)
| ~ c_lessequals(v_Z,X0,sF1) )
| ~ spl2_1 ),
inference(forward_demodulation,[],[f27,f18]) ).
fof(f168,plain,
( ! [X0] :
( ~ c_lessequals(v_Y,X0,tc_set(t_a))
| c_lessequals(v_X,X0,tc_set(t_a))
| ~ c_lessequals(v_Z,X0,sF1) )
| ~ spl2_1 ),
inference(forward_demodulation,[],[f167,f18]) ).
fof(f169,plain,
( ! [X0] :
( c_lessequals(v_X,X0,tc_set(t_a))
| ~ c_lessequals(v_Y,X0,tc_set(t_a))
| ~ c_lessequals(v_Z,X0,tc_set(t_a)) )
| ~ spl2_1 ),
inference(forward_demodulation,[],[f168,f18]) ).
fof(f172,plain,
! [X0] :
( c_in(X0,v_Z,t_a)
| ~ c_in(X0,sF0,t_a)
| c_in(X0,v_Y,t_a) ),
inference(superposition,[],[f9,f16]) ).
fof(f175,plain,
c_lessequals(v_Z,sF0,tc_set(t_a)),
inference(superposition,[],[f80,f16]) ).
fof(f176,plain,
c_lessequals(v_Y,sF0,tc_set(t_a)),
inference(superposition,[],[f102,f16]) ).
fof(f184,plain,
( ! [X0] :
( c_in(X0,v_X,t_a)
| ~ c_in(X0,v_Y,t_a) )
| ~ spl2_3 ),
inference(resolution,[],[f108,f10]) ).
fof(f186,plain,
( ! [X0] :
( c_in(X0,v_X,t_a)
| ~ c_in(X0,v_Z,t_a) )
| ~ spl2_4 ),
inference(resolution,[],[f112,f10]) ).
fof(f188,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_X,t_a),v_Z,t_a)
| c_lessequals(X0,v_X,tc_set(t_a)) )
| ~ spl2_4 ),
inference(resolution,[],[f186,f12]) ).
fof(f191,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_X,t_a),v_Y,t_a)
| c_lessequals(X0,v_X,tc_set(t_a)) )
| ~ spl2_3 ),
inference(resolution,[],[f184,f12]) ).
fof(f266,plain,
( ! [X0] :
( c_lessequals(X0,v_X,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X0,v_X,t_a),sF0,t_a)
| c_in(c_Main_OsubsetI__1(X0,v_X,t_a),v_Y,t_a) )
| ~ spl2_4 ),
inference(resolution,[],[f188,f172]) ).
fof(f268,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_X,t_a),sF0,t_a)
| c_lessequals(X0,v_X,tc_set(t_a)) )
| ~ spl2_3
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f266,f191]) ).
fof(f269,plain,
( c_lessequals(sF0,v_X,tc_set(t_a))
| c_lessequals(sF0,v_X,tc_set(t_a))
| ~ spl2_3
| ~ spl2_4 ),
inference(resolution,[],[f268,f11]) ).
fof(f272,plain,
( c_lessequals(sF0,v_X,tc_set(t_a))
| ~ spl2_3
| ~ spl2_4 ),
inference(duplicate_literal_removal,[],[f269]) ).
fof(f274,plain,
( ~ c_lessequals(v_X,sF0,tc_set(t_a))
| v_X = sF0
| ~ spl2_3
| ~ spl2_4 ),
inference(resolution,[],[f272,f14]) ).
fof(f275,plain,
( ~ c_lessequals(v_X,sF0,tc_set(t_a))
| spl2_2
| ~ spl2_3
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f274,f30]) ).
fof(f276,plain,
( ~ c_lessequals(v_Y,sF0,tc_set(t_a))
| ~ c_lessequals(v_Z,sF0,tc_set(t_a))
| ~ spl2_1
| spl2_2
| ~ spl2_3
| ~ spl2_4 ),
inference(resolution,[],[f275,f169]) ).
fof(f277,plain,
( ~ c_lessequals(v_Z,sF0,tc_set(t_a))
| ~ spl2_1
| spl2_2
| ~ spl2_3
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f276,f176]) ).
fof(f278,plain,
( $false
| ~ spl2_1
| spl2_2
| ~ spl2_3
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f277,f175]) ).
fof(f279,plain,
( ~ spl2_1
| spl2_2
| ~ spl2_3
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f278]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f32]) ).
cnf(s2,plain,
( ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| ~ spl2_5 ),
inference(sat_conversion,[],[f45]) ).
cnf(s3,plain,
( ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| spl2_6 ),
inference(sat_conversion,[],[f50]) ).
cnf(s4,plain,
( ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| spl2_7 ),
inference(sat_conversion,[],[f55]) ).
cnf(s5,plain,
( spl2_2
| spl2_4 ),
inference(sat_conversion,[],[f56]) ).
cnf(s6,plain,
( spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f57]) ).
cnf(s8,plain,
( ~ spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f107]) ).
cnf(s9,plain,
( ~ spl2_2
| spl2_4 ),
inference(sat_conversion,[],[f111]) ).
cnf(s13,plain,
( ~ spl2_2
| spl2_5
| ~ spl2_6
| ~ spl2_7 ),
inference(sat_conversion,[],[f166]) ).
cnf(s19,plain,
( ~ spl2_1
| spl2_2
| ~ spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f279]) ).
cnf(s20,plain,
( ~ spl2_3
| ~ spl2_2
| ~ spl2_4 ),
inference(rat,[],[s13,s2,s3,s4]) ).
cnf(s21,plain,
~ spl2_2,
inference(rat,[],[s20,s8,s9]) ).
cnf(s22,plain,
spl2_3,
inference(rat,[],[s6,s21]) ).
cnf(s23,plain,
spl2_4,
inference(rat,[],[s5,s21]) ).
cnf(s24,plain,
spl2_1,
inference(rat,[],[s1,s21]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s19,s23,s21,s22,s24]) ).
fof(f280,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET837-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 03:02:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.87/1.96 % (4168932)Input is clausal, will run a generic CNF schedule.
% 6.87/1.96 % (4168943)dis-21_1_sil=8000:lcm=predicate:random_seed=2429269201:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 6.87/1.96 % (4168937)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2018453003:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.87/1.96 % (4168939)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=512633628:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.87/1.96 % (4168941)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2444493755:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.87/1.96 % (4168940)lrs+10_1_sil=8000:sp=occurrence:random_seed=1421411805:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.87/1.96 % (4168938)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1353061102:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.87/1.96 % (4168942)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3178658590:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.87/1.96 % (4168940)Refutation not found, incomplete strategy
% 6.87/1.96 % (4168940)------------------------------
% 6.87/1.96 % (4168940)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.87/1.96 % (4168940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.96 % (4168940)CaDiCaL version: 2.1.3
% 6.87/1.96 % (4168940)Termination reason: Refutation not found, incomplete strategy
% 6.87/1.96 % (4168940)Time elapsed: 0.001 s
% 6.87/1.96 % (4168940)Peak memory usage: 88 MB
% 6.87/1.96 % (4168941)Refutation not found, incomplete strategy
% 6.87/1.96 % (4168941)------------------------------
% 6.87/1.96 % (4168941)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.87/1.96 % (4168941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.96 % (4168941)CaDiCaL version: 2.1.3
% 6.87/1.96 % (4168941)Termination reason: Refutation not found, incomplete strategy
% 6.87/1.96 % (4168941)Time elapsed: 0.002 s
% 6.87/1.96 % (4168941)Peak memory usage: 88 MB
% 6.87/1.96 % (4168941)Instructions burned: 1 (million)
% 6.87/1.96 % (4168943)Instruction limit reached!
% 6.87/1.96 % (4168943)------------------------------
% 6.87/1.96 % (4168943)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.87/1.96 % (4168943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.96 % (4168943)CaDiCaL version: 2.1.3
% 6.87/1.96 % (4168943)Termination reason: Instruction limit
% 6.87/1.96 % (4168943)Termination phase: Saturation
% 6.87/1.96 % (4168943)Time elapsed: 0.037 s
% 6.87/1.96 % (4168943)Peak memory usage: 88 MB
% 6.87/1.96 % (4168943)Instructions burned: 119 (million)
% 6.87/1.96 % (4168942)Instruction limit reached!
% 6.87/1.96 % (4168942)------------------------------
% 6.87/1.96 % (4168942)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.87/1.96 % (4168942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.96 % (4168942)CaDiCaL version: 2.1.3
% 6.87/1.96 % (4168942)Termination reason: Instruction limit
% 6.87/1.96 % (4168942)Termination phase: Saturation
% 6.87/1.96 % (4168942)Time elapsed: 0.114 s
% 6.87/1.96 % (4168942)Peak memory usage: 89 MB
% 6.87/1.96 % (4168942)Instructions burned: 181 (million)
% 6.87/1.96 % (4168951)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=219726040:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 6.87/1.96 % (4168951)Refutation not found, incomplete strategy
% 6.87/1.96 % (4168951)------------------------------
% 6.87/1.96 % (4168951)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.87/1.96 % (4168951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.96 % (4168951)CaDiCaL version: 2.1.3
% 6.87/1.96 % (4168951)Termination reason: Refutation not found, incomplete strategy
% 6.87/1.96 % (4168951)Time elapsed: 0.002 s
% 6.87/1.96 % (4168951)Peak memory usage: 88 MB
% 6.87/1.96 % (4168951)Instructions burned: 4 (million)
% 6.87/1.96 % (4168940)------------------------------
% 6.87/1.96 % (4168940)------------------------------
% 6.87/1.96 % (4168941)------------------------------
% 6.87/1.96 % (4168941)------------------------------
% 6.87/1.96 % (4168951)------------------------------
% 6.87/1.96 % (4168951)------------------------------
% 6.87/1.96 % (4168952)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3603675622:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 6.87/1.96 % (4168952)Instruction limit reached!
% 6.87/1.96 % (4168952)------------------------------
% 6.87/1.96 % (4168952)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.87/1.96 % (4168952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.96 % (4168952)CaDiCaL version: 2.1.3
% 6.87/1.96 % (4168952)Termination reason: Instruction limit
% 6.87/1.96 % (4168952)Termination phase: Saturation
% 6.87/1.96 % (4168952)Time elapsed: 0.103 s
% 6.87/1.96 % (4168952)Peak memory usage: 90 MB
% 6.87/1.96 % (4168952)Instructions burned: 189 (million)
% 6.87/1.96 % (4168954)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1014445830:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 6.87/1.96 % (4168955)lrs+10_64_to=lpo:sil=8000:random_seed=2187898153:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 6.87/1.96 % (4168954)Refutation not found, incomplete strategy
% 6.87/1.96 % (4168954)------------------------------
% 6.87/1.96 % (4168954)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.87/1.96 % (4168954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.96 % (4168954)CaDiCaL version: 2.1.3
% 6.87/1.96 % (4168954)Termination reason: Refutation not found, incomplete strategy
% 6.87/1.96 % (4168954)Time elapsed: 0.004 s
% 6.87/1.96 % (4168954)Peak memory usage: 88 MB
% 6.87/1.96 % (4168954)Instructions burned: 3 (million)
% 6.87/1.96 % (4168957)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2711674454:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 6.87/1.96 % (4168957)Instruction limit reached!
% 6.87/1.96 % (4168957)------------------------------
% 6.87/1.96 % (4168957)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.87/1.96 % (4168957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.96 % (4168957)CaDiCaL version: 2.1.3
% 6.87/1.96 % (4168957)Termination reason: Instruction limit
% 6.87/1.96 % (4168957)Termination phase: Saturation
% 6.87/1.96 % (4168957)Time elapsed: 0.069 s
% 6.87/1.96 % (4168957)Peak memory usage: 89 MB
% 6.87/1.96 % (4168957)Instructions burned: 195 (million)
% 6.87/1.96 % (4168955)Instruction limit reached!
% 6.87/1.96 % (4168955)------------------------------
% 6.87/1.96 % (4168955)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.87/1.96 % (4168955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.96 % (4168955)CaDiCaL version: 2.1.3
% 6.87/1.96 % (4168955)Termination reason: Instruction limit
% 6.87/1.96 % (4168955)Termination phase: Saturation
% 6.87/1.96 % (4168955)Time elapsed: 0.081 s
% 6.87/1.96 % (4168955)Peak memory usage: 89 MB
% 6.87/1.96 % (4168955)Instructions burned: 127 (million)
% 6.87/1.96 % (4168958)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=1556604560:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 6.87/1.96 % (4168938)Refutation not found, incomplete strategy
% 6.87/1.96 % (4168938)------------------------------
% 6.87/1.96 % (4168938)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.87/1.96 % (4168938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.96 % (4168938)CaDiCaL version: 2.1.3
% 6.87/1.96 % (4168938)Termination reason: Refutation not found, incomplete strategy
% 6.87/1.96 % (4168938)Time elapsed: 0.585 s
% 6.87/1.96 % (4168938)Peak memory usage: 125 MB
% 6.87/1.96 % (4168938)Instructions burned: 861 (million)
% 6.87/1.96 % (4168962)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=1287964309:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 6.87/1.96 % (4168939)First to succeed.
% 6.87/1.96 % (4168939)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4168932"
% 6.87/1.96 % (4168958)Instruction limit reached!
% 6.87/1.96 % (4168958)------------------------------
% 6.87/1.96 % (4168958)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.87/1.96 % (4168958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.96 % (4168958)CaDiCaL version: 2.1.3
% 6.87/1.96 % (4168958)Termination reason: Instruction limit
% 6.87/1.96 % (4168958)Termination phase: Saturation
% 6.87/1.96 % (4168958)Time elapsed: 0.102 s
% 6.87/1.96 % (4168958)Peak memory usage: 90 MB
% 6.87/1.96 % (4168958)Instructions burned: 158 (million)
% 6.87/1.96 % (4168954)------------------------------
% 6.87/1.96 % (4168954)------------------------------
% 6.87/1.96 % (4168963)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=1475896239:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 6.87/1.96 % (4168963)Instruction limit reached!
% 6.87/1.96 % (4168963)------------------------------
% 6.87/1.96 % (4168963)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.87/1.96 % (4168963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.96 % (4168963)CaDiCaL version: 2.1.3
% 6.87/1.96 % (4168963)Termination reason: Instruction limit
% 6.87/1.96 % (4168963)Termination phase: Saturation
% 6.87/1.96 % (4168963)Time elapsed: 0.056 s
% 6.87/1.96 % (4168963)Peak memory usage: 89 MB
% 6.87/1.96 % (4168963)Instructions burned: 107 (million)
% 6.87/1.96 % (4168967)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=503846863:i=107_2991 on theBenchmark for (2991ds/107Mi)
% 6.87/1.96 % (4168938)------------------------------
% 6.87/1.96 % (4168938)------------------------------
% 6.87/1.96 % (4168968)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=953134336:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2991 on theBenchmark for (2991ds/242Mi)
% 6.87/1.96 % (4168937)Also succeeded, but the first one will report.
% 6.87/1.96 % (4168967)Instruction limit reached!
% 6.87/1.96 % (4168967)------------------------------
% 6.87/1.96 % (4168967)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.87/1.96 % (4168967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.96 % (4168967)CaDiCaL version: 2.1.3
% 6.87/1.96 % (4168967)Termination reason: Instruction limit
% 6.87/1.96 % (4168967)Termination phase: Saturation
% 6.87/1.96 % (4168967)Time elapsed: 0.063 s
% 6.87/1.96 % (4168967)Peak memory usage: 88 MB
% 6.87/1.96 % (4168967)Instructions burned: 108 (million)
% 6.87/1.96 % (4168969)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=2120547283:cond=fast:i=5208:av=off_2991 on theBenchmark for (2991ds/5208Mi)
% 6.87/1.96 % (4168939)Refutation found. Thanks to Tanya!
% 6.87/1.96 % SZS status Unsatisfiable for theBenchmark
% 6.87/1.96 % SZS output start Proof for theBenchmark
% See solution above
% 8.41/2.15 % (4168939)------------------------------
% 8.41/2.15 % (4168939)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.41/2.15 % (4168939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.41/2.15 % (4168939)CaDiCaL version: 2.1.3
% 8.41/2.15 % (4168939)Termination reason: Refutation
% 8.41/2.15 % (4168939)Time elapsed: 0.654 s
% 8.41/2.15 % (4168939)Peak memory usage: 127 MB
% 8.41/2.15 % (4168939)Instructions burned: 953 (million)
% 8.41/2.15 % (4168939)------------------------------
% 8.41/2.15 % (4168939)------------------------------
% 8.41/2.15 % (4168932)Success in time 1.103 s
% 8.41/2.15 % Vampire exiting
%------------------------------------------------------------------------------