%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET840-2 : 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 : 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 12:42:05 PM UTC 2026
% Result : Unsatisfiable 3.02s 1.09s
% Output : Refutation 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 26 ( 6 unt; 0 def)
% Number of atoms : 70 ( 26 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 73 ( 29 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 59 ( 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_b))
| c_lessequals(c_Union(v_S,t_b),X0,tc_set(t_b)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,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(f4,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,c_insert(X3,X1,X2),X2)
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
fof(f5,axiom,
! [X2,X0,X1] : c_in(X0,c_insert(X0,X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,X2,X3)
| ~ c_in(X0,c_insert(X1,X2,X3),X3)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
fof(f7,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(f8,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(f9,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(f10,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| ~ c_lessequals(X1,X0,tc_set(X2))
| X0 = X1 ),
inference(reorient_equations,[],[f9]) ).
fof(f12,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,[],[f8,f1]) ).
fof(f13,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| X0 = X1
| ~ c_in(c_Main_OsubsetI__1(X1,X0,X2),X0,X2) ),
inference(resolution,[],[f10,f8]) ).
fof(f17,plain,
! [X0,X1] :
( c_lessequals(c_Union(v_S,t_b),X0,tc_set(t_b))
| X0 = X1
| ~ c_in(X0,c_insert(X1,v_S,tc_set(t_b)),tc_set(t_b)) ),
inference(resolution,[],[f6,f2]) ).
fof(f20,plain,
! [X0,X1] :
( ~ c_lessequals(X0,c_Union(v_S,t_b),tc_set(t_b))
| ~ c_in(X0,c_insert(X1,v_S,tc_set(t_b)),tc_set(t_b))
| X0 = X1
| c_Union(v_S,t_b) = X0 ),
inference(resolution,[],[f17,f10]) ).
fof(f23,plain,
! [X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_Union(v_S,t_b),t_b),c_Union(v_S,t_b),t_b)
| c_Union(v_S,t_b) = X0
| X0 = X1
| ~ c_in(X0,c_insert(X1,v_S,tc_set(t_b)),tc_set(t_b)) ),
inference(resolution,[],[f13,f17]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ c_in(X2,v_S,tc_set(t_b))
| X0 = X1
| ~ c_in(X0,c_insert(X1,v_S,tc_set(t_b)),tc_set(t_b))
| c_Union(v_S,t_b) = X0
| ~ c_in(c_Main_OsubsetI__1(X0,c_Union(v_S,t_b),t_b),X2,t_b) ),
inference(resolution,[],[f23,f3]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_Union(v_S,t_b),t_b),c_Main_OsubsetI__1(v_S,X2,tc_set(t_b)),t_b)
| ~ c_in(X0,c_insert(X1,v_S,tc_set(t_b)),tc_set(t_b))
| c_Union(v_S,t_b) = X0
| X0 = X1
| c_lessequals(v_S,X2,tc_set(tc_set(t_b))) ),
inference(resolution,[],[f27,f7]) ).
fof(f52,plain,
! [X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(v_S,X0,tc_set(t_b)),c_insert(X1,v_S,tc_set(t_b)),tc_set(t_b))
| c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,X0,tc_set(t_b))
| c_Main_OsubsetI__1(v_S,X0,tc_set(t_b)) = X1
| c_lessequals(v_S,X0,tc_set(tc_set(t_b)))
| c_lessequals(c_Main_OsubsetI__1(v_S,X0,tc_set(t_b)),c_Union(v_S,t_b),tc_set(t_b)) ),
inference(resolution,[],[f43,f7]) ).
fof(f54,plain,
! [X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(v_S,X0,tc_set(t_b)),c_insert(X1,v_S,tc_set(t_b)),tc_set(t_b))
| c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,X0,tc_set(t_b))
| c_Main_OsubsetI__1(v_S,X0,tc_set(t_b)) = X1
| c_lessequals(v_S,X0,tc_set(tc_set(t_b))) ),
inference(forward_subsumption_resolution,[],[f52,f20]) ).
fof(f59,plain,
! [X0,X1] :
( c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,X0,tc_set(t_b))
| c_Main_OsubsetI__1(v_S,X0,tc_set(t_b)) = X1
| c_lessequals(v_S,X0,tc_set(tc_set(t_b)))
| ~ c_in(c_Main_OsubsetI__1(v_S,X0,tc_set(t_b)),v_S,tc_set(t_b)) ),
inference(resolution,[],[f54,f4]) ).
fof(f61,plain,
! [X0,X1] :
( c_lessequals(v_S,X0,tc_set(tc_set(t_b)))
| c_Main_OsubsetI__1(v_S,X0,tc_set(t_b)) = X1
| c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,X0,tc_set(t_b)) ),
inference(forward_subsumption_resolution,[],[f59,f7]) ).
fof(f65,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_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)) = X1 ),
inference(resolution,[],[f61,f1]) ).
fof(f83,plain,
! [X0,X1] :
( c_Union(v_S,t_b) != X1
| c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)) = X1 ),
inference(equality_factoring,[],[f65]) ).
fof(f135,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)),
inference(equality_resolution,[],[f83]) ).
fof(f139,plain,
! [X0] : ~ c_in(c_Union(v_S,t_b),c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)),
inference(superposition,[],[f12,f135]) ).
fof(f153,plain,
$false,
inference(resolution,[],[f139,f5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET840-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % 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 02:58:17 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 3.02/1.09 % (1518419)Input is clausal, will run a generic CNF schedule.
% 3.02/1.09 % (1518429)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2164566310:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.02/1.09 % (1518427)lrs+10_1_sil=8000:sp=occurrence:random_seed=3954485118:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.02/1.09 % (1518428)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1847818813:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.02/1.09 % (1518425)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2327307991:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.02/1.09 % (1518424)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=922742625:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.02/1.09 % (1518430)dis-21_1_sil=8000:lcm=predicate:random_seed=2958437472: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)
% 3.02/1.09 % (1518426)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1017347236:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.02/1.09 % (1518428)Refutation not found, incomplete strategy
% 3.02/1.09 % (1518428)------------------------------
% 3.02/1.09 % (1518428)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.09 % (1518428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.09 % (1518428)CaDiCaL version: 2.1.3
% 3.02/1.09 % (1518428)Termination reason: Refutation not found, incomplete strategy
% 3.02/1.09 % (1518428)Time elapsed: 0.001 s
% 3.02/1.09 % (1518428)Peak memory usage: 87 MB
% 3.02/1.09 % (1518430)Refutation not found, incomplete strategy
% 3.02/1.09 % (1518430)------------------------------
% 3.02/1.09 % (1518430)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.09 % (1518430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.09 % (1518430)CaDiCaL version: 2.1.3
% 3.02/1.09 % (1518430)Termination reason: Refutation not found, incomplete strategy
% 3.02/1.09 % (1518430)Time elapsed: 0.001 s
% 3.02/1.09 % (1518430)Peak memory usage: 88 MB
% 3.02/1.09 % (1518429)First to succeed.
% 3.02/1.09 % (1518429)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1518419"
% 3.02/1.09 % (1518427)Also succeeded, but the first one will report.
% 3.02/1.09 % (1518428)------------------------------
% 3.02/1.09 % (1518428)------------------------------
% 3.02/1.09 % (1518430)------------------------------
% 3.02/1.09 % (1518430)------------------------------
% 3.02/1.09 % (1518429)Refutation found. Thanks to Tanya!
% 3.02/1.09 % SZS status Unsatisfiable for theBenchmark
% 3.02/1.09 % SZS output start Proof for theBenchmark
% See solution above
% 3.02/1.09 % (1518429)------------------------------
% 3.02/1.09 % (1518429)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.09 % (1518429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.09 % (1518429)CaDiCaL version: 2.1.3
% 3.02/1.09 % (1518429)Termination reason: Refutation
% 3.02/1.09 % (1518429)Time elapsed: 0.009 s
% 3.02/1.09 % (1518429)Peak memory usage: 88 MB
% 3.02/1.09 % (1518429)Instructions burned: 11 (million)
% 3.02/1.09 % (1518429)------------------------------
% 3.02/1.09 % (1518429)------------------------------
% 3.02/1.09 % (1518419)Success in time 0.389 s
% 3.02/1.09 % Vampire exiting
%------------------------------------------------------------------------------