%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET860-1 : 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 : n019.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 3.90s 1.47s
% Output : Refutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 14 unt; 2 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 60 ( 33 ~; 25 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 24 ( 0 sgn 24 !; 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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
fof(f369,axiom,
! [X2,X0,X1] :
( ~ c_in(X0,c_Union(X1,X2),X2)
| c_in(c_Main_OUnionE__1(X0,X1,X2),X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
fof(f370,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(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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f1434,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(f1435,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(f1436,negated_conjecture,
! [X0] :
( ~ c_in(X0,v_C,tc_set(t_a))
| c_lessequals(X0,v_A,tc_set(t_a))
| c_lessequals(v_B,X0,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1447,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,[],[f379,f1434]) ).
fof(f1448,plain,
c_in(c_Main_OsubsetI__1(v_B,c_Union(v_C,t_a),t_a),v_B,t_a),
inference(resolution,[],[f379,f1435]) ).
fof(f1449,plain,
~ c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_A,t_a),
inference(resolution,[],[f380,f1434]) ).
fof(f1450,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,[],[f380,f1435]) ).
fof(f1464,plain,
c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),v_C,tc_set(t_a)),
inference(resolution,[],[f369,f1447]) ).
fof(f1465,plain,
( c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),tc_set(t_a)) ),
inference(resolution,[],[f1464,f1436]) ).
fof(f1467,definition,
( spl0_1
<=> c_lessequals(v_B,c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f1469,plain,
( c_lessequals(v_B,c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),tc_set(t_a))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f1467]) ).
fof(f1471,definition,
( spl0_2
<=> c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),v_A,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f1473,plain,
( c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),v_A,tc_set(t_a))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f1471]) ).
fof(f1474,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f1465,f1471,f1467]) ).
fof(f1478,plain,
( ! [X0] :
( c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),t_a) )
| ~ spl0_2 ),
inference(resolution,[],[f1473,f378]) ).
fof(f1496,plain,
( ~ c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),t_a)
| ~ spl0_2 ),
inference(resolution,[],[f1478,f1449]) ).
fof(f1499,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)
| ~ spl0_2 ),
inference(resolution,[],[f1496,f370]) ).
fof(f1500,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1499,f1447]) ).
fof(f1501,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f1500]) ).
fof(f1505,plain,
( ! [X0] :
( c_in(X0,c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),t_a)
| ~ c_in(X0,v_B,t_a) )
| ~ spl0_1 ),
inference(resolution,[],[f1469,f378]) ).
fof(f1524,plain,
! [X0] :
( ~ 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),X0,t_a) ),
inference(resolution,[],[f224,f1450]) ).
fof(f1525,plain,
~ c_in(c_Main_OsubsetI__1(v_B,c_Union(v_C,t_a),t_a),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C,t_a),v_A,t_a),v_C,t_a),t_a),
inference(resolution,[],[f1524,f1464]) ).
fof(f1538,plain,
( ~ c_in(c_Main_OsubsetI__1(v_B,c_Union(v_C,t_a),t_a),v_B,t_a)
| ~ spl0_1 ),
inference(resolution,[],[f1525,f1505]) ).
fof(f1539,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f1538,f1448]) ).
fof(f1540,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f1539]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f1474]) ).
cnf(s3,plain,
~ spl0_2,
inference(sat_conversion,[],[f1501]) ).
cnf(s5,plain,
~ spl0_1,
inference(sat_conversion,[],[f1540]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
fof(f1541,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET860-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n019.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:02:57 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 3.90/1.47 % (3622604)Input is clausal, will run a generic CNF schedule.
% 3.90/1.47 % (3622613)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1281786990:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.90/1.47 % (3622615)dis-21_1_sil=8000:lcm=predicate:random_seed=2959628563: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)
% 3.90/1.47 % (3622612)lrs+10_1_sil=8000:sp=occurrence:random_seed=1002995041:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.90/1.47 % (3622610)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=933139275:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.90/1.47 % (3622611)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1979522844:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.90/1.47 % (3622609)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=3656746796:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.90/1.47 % (3622613)Instruction limit reached!
% 3.90/1.47 % (3622613)------------------------------
% 3.90/1.47 % (3622613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.47 % (3622613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.47 % (3622613)CaDiCaL version: 2.1.3
% 3.90/1.47 % (3622613)Termination reason: Instruction limit
% 3.90/1.47 % (3622613)Termination phase: Saturation
% 3.90/1.47 % (3622613)Time elapsed: 0.037 s
% 3.90/1.47 % (3622613)Peak memory usage: 89 MB
% 3.90/1.47 % (3622613)Instructions burned: 117 (million)
% 3.90/1.47 % (3622614)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=58950790:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.90/1.47 % (3622614)First to succeed.
% 3.90/1.47 % (3622614)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3622604"
% 3.90/1.47 % (3622612)Instruction limit reached!
% 3.90/1.47 % (3622612)------------------------------
% 3.90/1.47 % (3622612)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.47 % (3622612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.47 % (3622612)CaDiCaL version: 2.1.3
% 3.90/1.47 % (3622612)Termination reason: Instruction limit
% 3.90/1.47 % (3622612)Termination phase: Saturation
% 3.90/1.47 % (3622612)Time elapsed: 0.067 s
% 3.90/1.47 % (3622612)Peak memory usage: 89 MB
% 3.90/1.47 % (3622612)Instructions burned: 107 (million)
% 3.90/1.47 % (3622615)Instruction limit reached!
% 3.90/1.47 % (3622615)------------------------------
% 3.90/1.47 % (3622615)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.47 % (3622615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.47 % (3622615)CaDiCaL version: 2.1.3
% 3.90/1.47 % (3622615)Termination reason: Instruction limit
% 3.90/1.47 % (3622615)Termination phase: Saturation
% 3.90/1.47 % (3622615)Time elapsed: 0.070 s
% 3.90/1.47 % (3622615)Peak memory usage: 89 MB
% 3.90/1.47 % (3622615)Instructions burned: 118 (million)
% 3.90/1.47 % (3622622)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=577214244:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.90/1.47 % (3622622)Refutation not found, incomplete strategy
% 3.90/1.47 % (3622622)------------------------------
% 3.90/1.47 % (3622622)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.47 % (3622622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.47 % (3622622)CaDiCaL version: 2.1.3
% 3.90/1.47 % (3622622)Termination reason: Refutation not found, incomplete strategy
% 3.90/1.47 % (3622622)Time elapsed: 0.002 s
% 3.90/1.47 % (3622622)Peak memory usage: 89 MB
% 3.90/1.47 % (3622622)Instructions burned: 4 (million)
% 3.90/1.47 % (3622624)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2272617824: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)
% 3.90/1.47 % (3622625)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=4248097798:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.90/1.47 % (3622624)Refutation not found, incomplete strategy
% 3.90/1.47 % (3622624)------------------------------
% 3.90/1.47 % (3622624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.47 % (3622624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.47 % (3622624)CaDiCaL version: 2.1.3
% 3.90/1.47 % (3622624)Termination reason: Refutation not found, incomplete strategy
% 3.90/1.47 % (3622624)Time elapsed: 0.010 s
% 3.90/1.47 % (3622624)Peak memory usage: 89 MB
% 3.90/1.47 % (3622624)Instructions burned: 16 (million)
% 3.90/1.47 % (3622625)Refutation not found, incomplete strategy
% 3.90/1.47 % (3622625)------------------------------
% 3.90/1.47 % (3622625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.47 % (3622625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.47 % (3622625)CaDiCaL version: 2.1.3
% 3.90/1.47 % (3622625)Termination reason: Refutation not found, incomplete strategy
% 3.90/1.47 % (3622625)Time elapsed: 0.011 s
% 3.90/1.47 % (3622625)Peak memory usage: 89 MB
% 3.90/1.47 % (3622625)Instructions burned: 15 (million)
% 3.90/1.47 % (3622622)------------------------------
% 3.90/1.47 % (3622622)------------------------------
% 3.90/1.47 % (3622614)Refutation found. Thanks to Tanya!
% 3.90/1.47 % SZS status Unsatisfiable for theBenchmark
% 3.90/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.90/1.47 % (3622614)------------------------------
% 3.90/1.47 % (3622614)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.47 % (3622614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.47 % (3622614)CaDiCaL version: 2.1.3
% 3.90/1.47 % (3622614)Termination reason: Refutation
% 3.90/1.47 % (3622614)Time elapsed: 0.016 s
% 3.90/1.47 % (3622614)Peak memory usage: 90 MB
% 3.90/1.47 % (3622614)Instructions burned: 24 (million)
% 3.90/1.47 % (3622614)------------------------------
% 3.90/1.47 % (3622614)------------------------------
% 3.90/1.47 % (3622604)Success in time 0.506 s
% 3.90/1.47 % Vampire exiting
%------------------------------------------------------------------------------