%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET834-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:42:04 PM UTC 2026
% Result : Unsatisfiable 3.66s 1.48s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 35 ( 10 unt; 2 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 29 ~; 27 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 25 ( 0 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,c_union(X3,X1,X2),X2)
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,c_union(X1,X3,X2),X2)
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,X2,X3)
| ~ c_in(X0,c_union(X1,X2,X3),X3)
| c_in(X0,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f5,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f6,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f7,negated_conjecture,
c_in(v_x,v_X,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f8,negated_conjecture,
~ c_in(v_x,v_Z,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f9,negated_conjecture,
~ c_in(v_x,v_Y,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f10,negated_conjecture,
! [X0] :
( 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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f13,plain,
! [X0] :
( c_in(v_x,X0,t_a)
| ~ c_in(v_x,c_union(X0,v_Z,t_a),t_a) ),
inference(resolution,[],[f3,f8]) ).
fof(f44,plain,
~ c_in(v_x,c_union(v_Y,v_Z,t_a),t_a),
inference(resolution,[],[f13,f9]) ).
fof(f60,plain,
! [X0] :
( ~ c_lessequals(X0,c_union(v_Y,v_Z,t_a),tc_set(t_a))
| ~ c_in(v_x,X0,t_a) ),
inference(resolution,[],[f44,f4]) ).
fof(f153,plain,
( ~ c_in(v_x,v_X,t_a)
| ~ c_lessequals(v_Z,c_union(v_Y,v_Z,t_a),tc_set(t_a))
| ~ c_lessequals(v_Y,c_union(v_Y,v_Z,t_a),tc_set(t_a)) ),
inference(resolution,[],[f60,f10]) ).
fof(f156,plain,
( ~ c_lessequals(v_Z,c_union(v_Y,v_Z,t_a),tc_set(t_a))
| ~ c_lessequals(v_Y,c_union(v_Y,v_Z,t_a),tc_set(t_a)) ),
inference(forward_subsumption_resolution,[],[f153,f7]) ).
fof(f158,definition,
( spl0_7
<=> c_lessequals(v_Y,c_union(v_Y,v_Z,t_a),tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f160,plain,
( ~ c_lessequals(v_Y,c_union(v_Y,v_Z,t_a),tc_set(t_a))
| spl0_7 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f162,definition,
( spl0_8
<=> c_lessequals(v_Z,c_union(v_Y,v_Z,t_a),tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f164,plain,
( ~ c_lessequals(v_Z,c_union(v_Y,v_Z,t_a),tc_set(t_a))
| spl0_8 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f165,plain,
( ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f156,f162,f158]) ).
fof(f181,plain,
( ~ c_in(c_Main_OsubsetI__1(v_Y,c_union(v_Y,v_Z,t_a),t_a),c_union(v_Y,v_Z,t_a),t_a)
| spl0_7 ),
inference(resolution,[],[f160,f6]) ).
fof(f182,plain,
( c_in(c_Main_OsubsetI__1(v_Y,c_union(v_Y,v_Z,t_a),t_a),v_Y,t_a)
| spl0_7 ),
inference(resolution,[],[f160,f5]) ).
fof(f346,plain,
( ~ c_in(c_Main_OsubsetI__1(v_Y,c_union(v_Y,v_Z,t_a),t_a),v_Y,t_a)
| spl0_7 ),
inference(resolution,[],[f181,f2]) ).
fof(f350,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f346,f182]) ).
fof(f351,plain,
spl0_7,
inference(avatar_contradiction_clause,[],[f350]) ).
fof(f353,plain,
( ~ c_in(c_Main_OsubsetI__1(v_Z,c_union(v_Y,v_Z,t_a),t_a),c_union(v_Y,v_Z,t_a),t_a)
| spl0_8 ),
inference(resolution,[],[f164,f6]) ).
fof(f354,plain,
( c_in(c_Main_OsubsetI__1(v_Z,c_union(v_Y,v_Z,t_a),t_a),v_Z,t_a)
| spl0_8 ),
inference(resolution,[],[f164,f5]) ).
fof(f548,plain,
( ~ c_in(c_Main_OsubsetI__1(v_Z,c_union(v_Y,v_Z,t_a),t_a),v_Z,t_a)
| spl0_8 ),
inference(resolution,[],[f353,f1]) ).
fof(f551,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f548,f354]) ).
fof(f552,plain,
spl0_8,
inference(avatar_contradiction_clause,[],[f551]) ).
cnf(s5,plain,
( ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f165]) ).
cnf(s8,plain,
spl0_7,
inference(sat_conversion,[],[f351]) ).
cnf(s20,plain,
spl0_8,
inference(sat_conversion,[],[f552]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s5,s20,s8]) ).
fof(f553,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET834-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 02:57:02 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.66/1.48 % (1517178)Input is clausal, will run a generic CNF schedule.
% 3.66/1.48 % (1517189)dis-21_1_sil=8000:lcm=predicate:random_seed=3114482637: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)
% 3.66/1.48 % (1517187)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=358730807:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.66/1.48 % (1517186)lrs+10_1_sil=8000:sp=occurrence:random_seed=3260575317:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.66/1.48 % (1517184)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=819647998:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.66/1.48 % (1517183)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=2763151727:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.66/1.48 % (1517185)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2335272932:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.66/1.48 % (1517187)Refutation not found, incomplete strategy
% 3.66/1.48 % (1517187)------------------------------
% 3.66/1.48 % (1517187)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.48 % (1517187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.48 % (1517187)CaDiCaL version: 2.1.3
% 3.66/1.48 % (1517187)Termination reason: Refutation not found, incomplete strategy
% 3.66/1.48 % (1517187)Time elapsed: 0.001 s
% 3.66/1.48 % (1517187)Peak memory usage: 87 MB
% 3.66/1.48 % (1517186)Refutation not found, incomplete strategy
% 3.66/1.48 % (1517186)------------------------------
% 3.66/1.48 % (1517186)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.48 % (1517186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.48 % (1517186)CaDiCaL version: 2.1.3
% 3.66/1.48 % (1517186)Termination reason: Refutation not found, incomplete strategy
% 3.66/1.48 % (1517186)Time elapsed: 0.001 s
% 3.66/1.48 % (1517186)Peak memory usage: 88 MB
% 3.66/1.48 % (1517189)Instruction limit reached!
% 3.66/1.48 % (1517189)------------------------------
% 3.66/1.48 % (1517189)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.48 % (1517189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.48 % (1517189)CaDiCaL version: 2.1.3
% 3.66/1.48 % (1517189)Termination reason: Instruction limit
% 3.66/1.48 % (1517189)Termination phase: Saturation
% 3.66/1.48 % (1517189)Time elapsed: 0.038 s
% 3.66/1.48 % (1517189)Peak memory usage: 88 MB
% 3.66/1.48 % (1517189)Instructions burned: 117 (million)
% 3.66/1.48 % (1517188)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3400354303:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.66/1.48 % (1517188)First to succeed.
% 3.66/1.48 % (1517188)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1517178"
% 3.66/1.48 % (1517196)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=3796770400:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.66/1.48 % (1517196)Refutation not found, incomplete strategy
% 3.66/1.48 % (1517196)------------------------------
% 3.66/1.48 % (1517196)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.48 % (1517196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.48 % (1517196)CaDiCaL version: 2.1.3
% 3.66/1.48 % (1517196)Termination reason: Refutation not found, incomplete strategy
% 3.66/1.48 % (1517196)Time elapsed: 0.0000 s
% 3.66/1.48 % (1517196)Peak memory usage: 87 MB
% 3.66/1.48 % (1517186)------------------------------
% 3.66/1.48 % (1517186)------------------------------
% 3.66/1.48 % (1517187)------------------------------
% 3.66/1.48 % (1517187)------------------------------
% 3.66/1.48 % (1517196)------------------------------
% 3.66/1.48 % (1517196)------------------------------
% 3.66/1.48 % (1517188)Refutation found. Thanks to Tanya!
% 3.66/1.48 % SZS status Unsatisfiable for theBenchmark
% 3.66/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.66/1.48 % (1517188)------------------------------
% 3.66/1.48 % (1517188)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.48 % (1517188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.48 % (1517188)CaDiCaL version: 2.1.3
% 3.66/1.48 % (1517188)Termination reason: Refutation
% 3.66/1.48 % (1517188)Time elapsed: 0.012 s
% 3.66/1.48 % (1517188)Peak memory usage: 89 MB
% 3.66/1.48 % (1517188)Instructions burned: 13 (million)
% 3.66/1.48 % (1517188)------------------------------
% 3.66/1.48 % (1517188)------------------------------
% 3.66/1.48 % (1517178)Success in time 0.433 s
% 3.66/1.48 % Vampire exiting
%------------------------------------------------------------------------------