%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET840-1 : 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 : n007.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 3.86s 1.55s
% Output : Refutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 10 unt; 2 def)
% Number of atoms : 73 ( 11 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 76 ( 39 ~; 35 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 50 ( 0 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f224,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
fof(f227,axiom,
! [X2,X0,X1] : c_in(X0,c_insert(X0,X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f378,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f379,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(f380,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(f381,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| ~ c_lessequals(X1,X0,tc_set(X2))
| X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f382,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| ~ c_lessequals(X1,X0,tc_set(X2))
| X0 = X1 ),
inference(reorient_equations,[],[f381]) ).
fof(f1434,negated_conjecture,
! [X0] : ~ c_lessequals(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1435,negated_conjecture,
! [X0] :
( c_lessequals(c_Union(v_S,t_b),X0,tc_set(t_b))
| ~ c_in(X0,v_S,tc_set(t_b)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1449,plain,
! [X0] : c_in(c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)),v_S,tc_set(t_b)),
inference(resolution,[],[f379,f1434]) ).
fof(f1450,plain,
! [X0] : ~ c_in(c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)),c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)),
inference(resolution,[],[f380,f1434]) ).
fof(f1460,plain,
! [X0,X1] :
( ~ c_in(X0,c_Union(v_S,t_b),t_b)
| c_in(X0,X1,t_b)
| ~ c_in(X1,v_S,tc_set(t_b)) ),
inference(resolution,[],[f378,f1435]) ).
fof(f1466,plain,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_b))
| c_Union(v_S,t_b) = X0
| ~ c_lessequals(X0,c_Union(v_S,t_b),tc_set(t_b)) ),
inference(resolution,[],[f382,f1435]) ).
fof(f1468,plain,
! [X0] :
( ~ c_lessequals(c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)),c_Union(v_S,t_b),tc_set(t_b))
| c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)) ),
inference(resolution,[],[f1466,f1449]) ).
fof(f1473,plain,
! [X0] :
( ~ c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)),c_Union(v_S,t_b),t_b),c_Union(v_S,t_b),t_b)
| c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)) ),
inference(resolution,[],[f1468,f380]) ).
fof(f1474,plain,
! [X0] :
( c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)),c_Union(v_S,t_b),t_b),c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)),t_b)
| c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)) ),
inference(resolution,[],[f1468,f379]) ).
fof(f1491,plain,
! [X2,X0,X1] :
( ~ c_in(X0,v_S,tc_set(t_b))
| ~ c_in(X1,X0,t_b)
| c_in(X1,X2,t_b)
| ~ c_in(X2,v_S,tc_set(t_b)) ),
inference(resolution,[],[f224,f1460]) ).
fof(f1493,plain,
! [X2,X0,X1] :
( ~ c_in(X0,c_Main_OsubsetI__1(v_S,c_insert(X1,c_emptyset,tc_set(t_b)),tc_set(t_b)),t_b)
| c_in(X0,X2,t_b)
| ~ c_in(X2,v_S,tc_set(t_b)) ),
inference(resolution,[],[f1491,f1449]) ).
fof(f1499,plain,
! [X0,X1] :
( ~ c_in(X1,v_S,tc_set(t_b))
| c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b))
| ~ c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)),c_Union(v_S,t_b),t_b),X1,t_b) ),
inference(resolution,[],[f1473,f224]) ).
fof(f1505,plain,
! [X0,X1] :
( c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b))
| c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)),c_Union(v_S,t_b),t_b),X1,t_b)
| ~ c_in(X1,v_S,tc_set(t_b)) ),
inference(resolution,[],[f1474,f1493]) ).
fof(f1506,plain,
! [X0,X1] :
( c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b))
| ~ c_in(X1,v_S,tc_set(t_b)) ),
inference(forward_subsumption_resolution,[],[f1505,f1499]) ).
fof(f1508,definition,
( spl0_1
<=> ! [X1] : ~ c_in(X1,v_S,tc_set(t_b)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f1509,plain,
( ! [X1] : ~ c_in(X1,v_S,tc_set(t_b))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f1508]) ).
fof(f1511,definition,
( spl0_2
<=> ! [X0] : c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f1512,plain,
( ! [X0] : c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f1511]) ).
fof(f1513,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f1506,f1511,f1508]) ).
fof(f1522,plain,
( ! [X0] : ~ c_in(c_Union(v_S,t_b),c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b))
| ~ spl0_2 ),
inference(superposition,[],[f1450,f1512]) ).
fof(f1527,plain,
( $false
| ~ spl0_2 ),
inference(resolution,[],[f1522,f227]) ).
fof(f1529,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f1527]) ).
fof(f1530,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f1509,f1449]) ).
fof(f1531,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f1530]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f1513]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f1529]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f1531]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f1532,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET840-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n007.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 02:55:25 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.86/1.55 % (1984152)Input is clausal, will run a generic CNF schedule.
% 3.86/1.55 % (1984163)dis-21_1_sil=8000:lcm=predicate:random_seed=4042413560: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)
% 3.86/1.55 % (1984163)Instruction limit reached!
% 3.86/1.55 % (1984163)------------------------------
% 3.86/1.55 % (1984163)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.55 % (1984163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.55 % (1984163)CaDiCaL version: 2.1.3
% 3.86/1.55 % (1984163)Termination reason: Instruction limit
% 3.86/1.55 % (1984163)Termination phase: Saturation
% 3.86/1.55 % (1984163)Time elapsed: 0.039 s
% 3.86/1.55 % (1984163)Peak memory usage: 89 MB
% 3.86/1.55 % (1984163)Instructions burned: 120 (million)
% 3.86/1.55 % (1984162)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3961312782:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.86/1.55 % (1984158)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2011159408:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.86/1.55 % (1984157)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=1166683407:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.86/1.55 % (1984159)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1152870717:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.86/1.55 % (1984161)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3027311027:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.86/1.55 % (1984160)lrs+10_1_sil=8000:sp=occurrence:random_seed=1679514930:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.86/1.55 % (1984162)First to succeed.
% 3.86/1.55 % (1984162)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1984152"
% 3.86/1.55 % (1984161)Instruction limit reached!
% 3.86/1.55 % (1984161)------------------------------
% 3.86/1.55 % (1984161)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.55 % (1984161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.55 % (1984161)CaDiCaL version: 2.1.3
% 3.86/1.55 % (1984161)Termination reason: Instruction limit
% 3.86/1.55 % (1984161)Termination phase: Saturation
% 3.86/1.55 % (1984161)Time elapsed: 0.067 s
% 3.86/1.55 % (1984161)Peak memory usage: 89 MB
% 3.86/1.55 % (1984161)Instructions burned: 115 (million)
% 3.86/1.55 % (1984160)Instruction limit reached!
% 3.86/1.55 % (1984160)------------------------------
% 3.86/1.55 % (1984160)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.55 % (1984160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.55 % (1984160)CaDiCaL version: 2.1.3
% 3.86/1.55 % (1984160)Termination reason: Instruction limit
% 3.86/1.55 % (1984160)Termination phase: Saturation
% 3.86/1.55 % (1984160)Time elapsed: 0.069 s
% 3.86/1.55 % (1984160)Peak memory usage: 89 MB
% 3.86/1.55 % (1984160)Instructions burned: 108 (million)
% 3.86/1.55 % (1984165)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=326820069:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.86/1.55 % (1984165)Refutation not found, incomplete strategy
% 3.86/1.55 % (1984165)------------------------------
% 3.86/1.55 % (1984165)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.55 % (1984165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.55 % (1984165)CaDiCaL version: 2.1.3
% 3.86/1.55 % (1984165)Termination reason: Refutation not found, incomplete strategy
% 3.86/1.55 % (1984165)Time elapsed: 0.003 s
% 3.86/1.55 % (1984165)Peak memory usage: 89 MB
% 3.86/1.55 % (1984165)Instructions burned: 5 (million)
% 3.86/1.55 % (1984173)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=9831139:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.86/1.55 % (1984172)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2694067318: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)
% 3.86/1.55 % (1984165)------------------------------
% 3.86/1.55 % (1984165)------------------------------
% 3.86/1.55 % (1984162)Refutation found. Thanks to Tanya!
% 3.86/1.55 % SZS status Unsatisfiable for theBenchmark
% 3.86/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 3.86/1.55 % (1984162)------------------------------
% 3.86/1.55 % (1984162)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.55 % (1984162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.55 % (1984162)CaDiCaL version: 2.1.3
% 3.86/1.55 % (1984162)Termination reason: Refutation
% 3.86/1.55 % (1984162)Time elapsed: 0.019 s
% 3.86/1.55 % (1984162)Peak memory usage: 90 MB
% 3.86/1.55 % (1984162)Instructions burned: 28 (million)
% 3.86/1.55 % (1984162)------------------------------
% 3.86/1.55 % (1984162)------------------------------
% 3.86/1.55 % (1984152)Success in time 0.478 s
% 3.86/1.55 % Vampire exiting
%------------------------------------------------------------------------------