%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET860-2 : 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 : n002.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 12:42:11 PM UTC 2026
% Result : Unsatisfiable 3.09s 1.19s
% Output : Refutation 3.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 42 ( 14 unt; 3 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 100 ( 52 ~; 45 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 37 ( 0 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
~ c_lessequals(c_Union(v_C,t_a),v_A,tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
~ c_lessequals(v_B,c_Union(v_C,t_a),tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,negated_conjecture,
! [X0] :
( c_lessequals(X0,v_A,tc_set(t_a))
| c_lessequals(v_B,X0,tc_set(t_a))
| ~ c_in(X0,v_C,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f14,axiom,
! [X2,X0,X1] :
( c_in(c_Main_OUnionE__1(X0,X1,X2),X1,tc_set(X2))
| ~ c_in(X0,c_Union(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
fof(f15,axiom,
! [X2,X0,X1] :
( c_in(X0,c_Main_OUnionE__1(X0,X1,X2),X2)
| ~ c_in(X0,c_Union(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,c_Union(X3,X2),X2)
| ~ c_in(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
fof(f21,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(f22,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/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f23,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/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f40,plain,
c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),c_Union(v_C,t_a),t_a),
inference(resolution,[],[f22,f1]) ).
fof(f41,plain,
c_in(c_Main_OsubsetI__1(v_B,c_Union(v_C,t_a),t_a),v_B,t_a),
inference(resolution,[],[f22,f2]) ).
fof(f42,plain,
~ c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_A,t_a),
inference(resolution,[],[f23,f1]) ).
fof(f43,plain,
~ c_in(c_Main_OsubsetI__1(v_B,c_Union(v_C,t_a),t_a),c_Union(v_C,t_a),t_a),
inference(resolution,[],[f23,f2]) ).
fof(f44,plain,
! [X0,X1] :
( c_lessequals(v_B,X1,tc_set(t_a))
| c_in(X0,v_A,t_a)
| ~ c_in(X0,X1,t_a)
| ~ c_in(X1,v_C,tc_set(t_a)) ),
inference(resolution,[],[f21,f3]) ).
fof(f52,plain,
! [X2,X0,X1] :
( c_in(X2,X1,t_a)
| ~ c_in(X0,X1,t_a)
| ~ c_in(X1,v_C,tc_set(t_a))
| ~ c_in(X2,v_B,t_a)
| c_in(X0,v_A,t_a) ),
inference(resolution,[],[f44,f21]) ).
fof(f73,definition,
( spl1_3
<=> c_in(c_Main_OsubsetI__1(v_B,c_Union(v_C,t_a),t_a),v_B,t_a) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f74,plain,
( ~ c_in(c_Main_OsubsetI__1(v_B,c_Union(v_C,t_a),t_a),v_B,t_a)
| spl1_3 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f90,plain,
( $false
| spl1_3 ),
inference(resolution,[],[f74,f41]) ).
fof(f93,plain,
spl1_3,
inference(avatar_contradiction_clause,[],[f90]) ).
fof(f94,plain,
! [X0] :
( ~ c_in(c_Main_OsubsetI__1(v_B,c_Union(v_C,t_a),t_a),X0,t_a)
| ~ c_in(X0,v_C,tc_set(t_a)) ),
inference(resolution,[],[f16,f43]) ).
fof(f115,definition,
( spl1_9
<=> c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),c_Union(v_C,t_a),t_a) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f116,plain,
( ~ c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),c_Union(v_C,t_a),t_a)
| spl1_9 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f121,plain,
( $false
| spl1_9 ),
inference(resolution,[],[f116,f40]) ).
fof(f125,plain,
spl1_9,
inference(avatar_contradiction_clause,[],[f121]) ).
fof(f128,plain,
! [X0,X1] :
( ~ c_in(X0,v_C,tc_set(t_a))
| ~ c_in(X1,X0,t_a)
| ~ c_in(X0,v_C,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(v_B,c_Union(v_C,t_a),t_a),v_B,t_a)
| c_in(X1,v_A,t_a) ),
inference(resolution,[],[f94,f52]) ).
fof(f140,plain,
! [X0,X1] :
( ~ c_in(X0,v_C,tc_set(t_a))
| ~ c_in(X1,X0,t_a)
| ~ c_in(c_Main_OsubsetI__1(v_B,c_Union(v_C,t_a),t_a),v_B,t_a)
| c_in(X1,v_A,t_a) ),
inference(duplicate_literal_removal,[],[f128]) ).
fof(f142,definition,
( spl1_11
<=> ! [X0,X1] :
( ~ c_in(X0,v_C,tc_set(t_a))
| c_in(X1,v_A,t_a)
| ~ c_in(X1,X0,t_a) ) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f143,plain,
( ! [X0,X1] :
( c_in(X1,v_A,t_a)
| ~ c_in(X0,v_C,tc_set(t_a))
| ~ c_in(X1,X0,t_a) )
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f144,plain,
( ~ spl1_3
| spl1_11 ),
inference(avatar_split_clause,[],[f140,f142,f73]) ).
fof(f149,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),X0,t_a)
| ~ c_in(X0,v_C,tc_set(t_a)) )
| ~ spl1_11 ),
inference(resolution,[],[f143,f42]) ).
fof(f163,plain,
( ! [X0] :
( ~ c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),X0,t_a),v_C,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),c_Union(X0,t_a),t_a) )
| ~ spl1_11 ),
inference(resolution,[],[f149,f15]) ).
fof(f235,plain,
( ~ c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),c_Union(v_C,t_a),t_a)
| ~ c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),c_Union(v_C,t_a),t_a)
| ~ spl1_11 ),
inference(resolution,[],[f163,f14]) ).
fof(f236,plain,
( ~ c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),c_Union(v_C,t_a),t_a)
| ~ spl1_11 ),
inference(duplicate_literal_removal,[],[f235]) ).
fof(f237,plain,
( ~ spl1_9
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f236,f142,f115]) ).
cnf(s5,plain,
spl1_3,
inference(sat_conversion,[],[f93]) ).
cnf(s8,plain,
spl1_9,
inference(sat_conversion,[],[f125]) ).
cnf(s9,plain,
( ~ spl1_3
| spl1_11 ),
inference(sat_conversion,[],[f144]) ).
cnf(s11,plain,
( ~ spl1_9
| ~ spl1_11 ),
inference(sat_conversion,[],[f237]) ).
cnf(s12,plain,
~ spl1_11,
inference(rat,[],[s11,s8]) ).
cnf(s13,plain,
~ spl1_3,
inference(rat,[],[s9,s12]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s5,s13]) ).
fof(f238,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET860-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n002.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:05:31 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.09/1.19 % (4113829)Input is clausal, will run a generic CNF schedule.
% 3.09/1.19 % (4113838)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=709131846:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.09/1.19 % (4113837)lrs+10_1_sil=8000:sp=occurrence:random_seed=2553559520:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.09/1.19 % (4113836)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=38415655:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.09/1.19 % (4113840)dis-21_1_sil=8000:lcm=predicate:random_seed=2052345807: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)
% 3.09/1.19 % (4113835)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2927955180:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.09/1.19 % (4113839)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1931897845:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.09/1.19 % (4113834)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=2562115774:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.09/1.19 % (4113838)Refutation not found, incomplete strategy
% 3.09/1.19 % (4113838)------------------------------
% 3.09/1.19 % (4113838)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/1.19 % (4113838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/1.19 % (4113838)CaDiCaL version: 2.1.3
% 3.09/1.19 % (4113838)Termination reason: Refutation not found, incomplete strategy
% 3.09/1.19 % (4113838)Time elapsed: 0.001 s
% 3.09/1.19 % (4113838)Peak memory usage: 87 MB
% 3.09/1.19 % (4113840)First to succeed.
% 3.09/1.19 % (4113839)Also succeeded, but the first one will report.
% 3.09/1.19 % (4113840)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4113829"
% 3.09/1.19 % (4113837)Instruction limit reached!
% 3.09/1.19 % (4113837)------------------------------
% 3.09/1.19 % (4113837)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/1.19 % (4113837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/1.19 % (4113837)CaDiCaL version: 2.1.3
% 3.09/1.19 % (4113837)Termination reason: Instruction limit
% 3.09/1.19 % (4113837)Termination phase: Saturation
% 3.09/1.19 % (4113837)Time elapsed: 0.062 s
% 3.09/1.19 % (4113837)Peak memory usage: 89 MB
% 3.09/1.19 % (4113837)Instructions burned: 107 (million)
% 3.09/1.19 % (4113848)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=4223714691:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.09/1.19 % (4113848)Refutation not found, incomplete strategy
% 3.09/1.19 % (4113848)------------------------------
% 3.09/1.19 % (4113848)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/1.19 % (4113848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/1.19 % (4113848)CaDiCaL version: 2.1.3
% 3.09/1.19 % (4113848)Termination reason: Refutation not found, incomplete strategy
% 3.09/1.19 % (4113848)Time elapsed: 0.003 s
% 3.09/1.19 % (4113848)Peak memory usage: 87 MB
% 3.09/1.19 % (4113848)Instructions burned: 4 (million)
% 3.09/1.19 % (4113838)------------------------------
% 3.09/1.19 % (4113838)------------------------------
% 3.09/1.19 % (4113840)Refutation found. Thanks to Tanya!
% 3.09/1.19 % SZS status Unsatisfiable for theBenchmark
% 3.09/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 3.09/1.19 % (4113840)------------------------------
% 3.09/1.19 % (4113840)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/1.19 % (4113840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/1.19 % (4113840)CaDiCaL version: 2.1.3
% 3.09/1.19 % (4113840)Termination reason: Refutation
% 3.09/1.19 % (4113840)Time elapsed: 0.006 s
% 3.09/1.19 % (4113840)Peak memory usage: 89 MB
% 3.09/1.19 % (4113840)Instructions burned: 8 (million)
% 3.09/1.19 % (4113840)------------------------------
% 3.09/1.19 % (4113840)------------------------------
% 3.09/1.19 % (4113829)Success in time 0.384 s
% 3.09/1.19 % Vampire exiting
%------------------------------------------------------------------------------