%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET821-2 : 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 : n014.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 12:42:00 PM UTC 2026
% Result : Unsatisfiable 3.32s 6.38s
% Output : Refutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 46 ( 13 unt; 4 def)
% Number of atoms : 92 ( 7 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 86 ( 40 ~; 42 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ c_less(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ c_in(X0,c_uminus(X1,tc_set(X2)),X2)
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).
fof(f3,axiom,
! [X2,X0,X1] :
( c_in(X0,c_uminus(X1,tc_set(X2)),X2)
| c_in(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplI_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_insert(X1,X2,X3),X3)
| c_in(X0,X2,X3)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
fof(f7,negated_conjecture,
c_less(v_a,v_b,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f8,negated_conjecture,
c_less(v_b,v_c,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f9,negated_conjecture,
! [X0] :
( ~ c_in(v_b,X0,tc_IntDef_Oint)
| c_in(v_c,X0,tc_IntDef_Oint)
| c_in(v_a,X0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f10,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
fof(f11,plain,
! [X0] :
( c_in(v_c,c_insert(v_b,X0,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(v_a,c_insert(v_b,X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(resolution,[],[f5,f9]) ).
fof(f18,plain,
! [X0] :
( c_in(v_c,X0,tc_IntDef_Oint)
| v_b = v_c
| c_in(v_a,c_insert(v_b,X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(resolution,[],[f6,f11]) ).
fof(f20,definition,
( spl0_1
<=> v_b = v_c ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f22,plain,
( v_b = v_c
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f24,definition,
( spl0_2
<=> ! [X0] :
( c_in(v_c,X0,tc_IntDef_Oint)
| c_in(v_a,c_insert(v_b,X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f25,plain,
( ! [X0] :
( c_in(v_a,c_insert(v_b,X0,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(v_c,X0,tc_IntDef_Oint) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f26,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f18,f24,f20]) ).
fof(f27,plain,
( ! [X0] :
( c_in(v_c,X0,tc_IntDef_Oint)
| c_in(v_a,X0,tc_IntDef_Oint)
| v_a = v_b )
| ~ spl0_2 ),
inference(resolution,[],[f25,f6]) ).
fof(f29,definition,
( spl0_3
<=> v_a = v_b ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f31,plain,
( v_a = v_b
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f33,definition,
( spl0_4
<=> ! [X0] :
( c_in(v_c,X0,tc_IntDef_Oint)
| c_in(v_a,X0,tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f34,plain,
( ! [X0] :
( c_in(v_c,X0,tc_IntDef_Oint)
| c_in(v_a,X0,tc_IntDef_Oint) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f35,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f27,f24,f33,f29]) ).
fof(f42,plain,
( c_less(v_a,v_a,tc_IntDef_Oint)
| ~ spl0_3 ),
inference(superposition,[],[f7,f31]) ).
fof(f45,plain,
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| ~ spl0_3 ),
inference(resolution,[],[f42,f1]) ).
fof(f46,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f45,f10]) ).
fof(f47,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f46]) ).
fof(f49,plain,
( ! [X0] :
( c_in(v_a,c_uminus(X0,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint)
| ~ c_in(v_c,X0,tc_IntDef_Oint) )
| ~ spl0_4 ),
inference(resolution,[],[f34,f2]) ).
fof(f58,plain,
( ! [X0] :
( ~ c_in(v_c,X0,tc_IntDef_Oint)
| ~ c_in(v_a,X0,tc_IntDef_Oint) )
| ~ spl0_4 ),
inference(resolution,[],[f49,f2]) ).
fof(f62,plain,
( ! [X0] : ~ c_in(v_a,c_insert(v_c,X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_4 ),
inference(resolution,[],[f58,f5]) ).
fof(f72,plain,
( ! [X0] : ~ c_in(v_a,X0,tc_IntDef_Oint)
| ~ spl0_4 ),
inference(resolution,[],[f62,f4]) ).
fof(f85,plain,
( ! [X0] : c_in(v_a,X0,tc_IntDef_Oint)
| ~ spl0_4 ),
inference(resolution,[],[f72,f3]) ).
fof(f87,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f85,f72]) ).
fof(f88,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f87]) ).
fof(f102,plain,
( c_less(v_b,v_b,tc_IntDef_Oint)
| ~ spl0_1 ),
inference(superposition,[],[f8,f22]) ).
fof(f108,plain,
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| ~ spl0_1 ),
inference(resolution,[],[f102,f1]) ).
fof(f109,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f108,f10]) ).
fof(f110,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f109]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f26]) ).
cnf(s2,plain,
( ~ spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f35]) ).
cnf(s3,plain,
~ spl0_3,
inference(sat_conversion,[],[f47]) ).
cnf(s5,plain,
~ spl0_4,
inference(sat_conversion,[],[f88]) ).
cnf(s9,plain,
~ spl0_1,
inference(sat_conversion,[],[f110]) ).
cnf(s10,plain,
~ spl0_2,
inference(rat,[],[s2,s5,s3]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s10,s9]) ).
fof(f111,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET821-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.41 % Computer : n014.cluster.edu
% 0.13/5.41 % Model : x86_64 x86_64
% 0.13/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.41 % Memory : 8046.5625MB
% 0.13/5.41 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.41 % WCLimit : 300
% 0.13/5.41 % DateTime : Mon Sep 28 02:54:52 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.44 Running first-order theorem proving
% 0.13/5.44 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
% 3.32/6.38 % (1394402)Input is clausal, will run a generic CNF schedule.
% 3.32/6.38 % (1394408)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3036221997:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.32/6.38 % (1394413)dis-21_1_sil=8000:lcm=predicate:random_seed=2871023454: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)
% 3.32/6.38 % (1394410)lrs+10_1_sil=8000:sp=occurrence:random_seed=2211184104:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.32/6.38 % (1394409)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1176963446:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.32/6.38 % (1394407)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=114431221:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.32/6.38 % (1394411)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=510941936:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.32/6.38 % (1394412)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2926076987:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.32/6.38 % (1394411)Refutation not found, incomplete strategy
% 3.32/6.38 % (1394411)------------------------------
% 3.32/6.38 % (1394411)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/6.38 % (1394411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/6.38 % (1394411)CaDiCaL version: 2.1.3
% 3.32/6.38 % (1394411)Termination reason: Refutation not found, incomplete strategy
% 3.32/6.38 % (1394411)Time elapsed: 0.001 s
% 3.32/6.38 % (1394411)Peak memory usage: 87 MB
% 3.32/6.38 % (1394413)Refutation not found, incomplete strategy
% 3.32/6.38 % (1394413)------------------------------
% 3.32/6.38 % (1394413)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/6.38 % (1394413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/6.38 % (1394413)CaDiCaL version: 2.1.3
% 3.32/6.38 % (1394413)Termination reason: Refutation not found, incomplete strategy
% 3.32/6.38 % (1394413)Time elapsed: 0.002 s
% 3.32/6.38 % (1394413)Peak memory usage: 88 MB
% 3.32/6.38 % (1394413)Instructions burned: 1 (million)
% 3.32/6.38 % (1394410)First to succeed.
% 3.32/6.38 % (1394410)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1394402"
% 3.32/6.38 % (1394412)Also succeeded, but the first one will report.
% 3.32/6.38 % (1394413)------------------------------
% 3.32/6.38 % (1394413)------------------------------
% 3.32/6.38 % (1394411)------------------------------
% 3.32/6.38 % (1394411)------------------------------
% 3.32/6.38 % (1394410)Refutation found. Thanks to Tanya!
% 3.32/6.38 % SZS status Unsatisfiable for theBenchmark
% 3.32/6.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.32/6.38 % (1394410)------------------------------
% 3.32/6.38 % (1394410)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/6.38 % (1394410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/6.38 % (1394410)CaDiCaL version: 2.1.3
% 3.32/6.38 % (1394410)Termination reason: Refutation
% 3.32/6.38 % (1394410)Time elapsed: 0.004 s
% 3.32/6.38 % (1394410)Peak memory usage: 89 MB
% 3.32/6.38 % (1394410)Instructions burned: 4 (million)
% 3.32/6.38 % (1394410)------------------------------
% 3.32/6.38 % (1394410)------------------------------
% 3.32/6.38 % (1394402)Success in time 0.399 s
% 3.32/6.38 % Vampire exiting
%------------------------------------------------------------------------------