%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET822-2 : 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 : n009.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 12:42:01 PM UTC 2026
% Result : Unsatisfiable 3.48s 1.89s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 7 unt; 0 def)
% Number of atoms : 19 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : ~ c_in(X0,c_emptyset,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
fof(f2,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(f3,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(f4,negated_conjecture,
v_P(v_f(v_b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f5,negated_conjecture,
! [X0,X1] :
( c_in(v_x(X0,X1),X1,tc_IntDef_Oint)
| ~ c_in(v_f(X0),X1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f6,negated_conjecture,
! [X0,X1] :
( ~ c_in(v_f(X0),X1,tc_IntDef_Oint)
| ~ v_P(v_x(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f8,plain,
! [X0,X1] : ~ v_P(v_x(X0,c_insert(v_f(X0),X1,tc_IntDef_Oint))),
inference(resolution,[],[f2,f6]) ).
fof(f9,plain,
! [X2,X0,X1] :
( c_in(v_x(X0,c_insert(X1,X2,tc_IntDef_Oint)),X2,tc_IntDef_Oint)
| v_x(X0,c_insert(X1,X2,tc_IntDef_Oint)) = X1
| ~ c_in(v_f(X0),c_insert(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(resolution,[],[f3,f5]) ).
fof(f11,plain,
! [X0,X1] :
( ~ c_in(v_f(X0),c_insert(X1,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint)
| v_x(X0,c_insert(X1,c_emptyset,tc_IntDef_Oint)) = X1 ),
inference(resolution,[],[f9,f1]) ).
fof(f13,plain,
! [X0] : v_f(X0) = v_x(X0,c_insert(v_f(X0),c_emptyset,tc_IntDef_Oint)),
inference(resolution,[],[f11,f2]) ).
fof(f16,plain,
! [X0] : ~ v_P(v_f(X0)),
inference(superposition,[],[f8,f13]) ).
fof(f19,plain,
$false,
inference(resolution,[],[f16,f4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET822-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.81 % Computer : n009.cluster.edu
% 0.12/0.81 % Model : x86_64 x86_64
% 0.12/0.81 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.81 % Memory : 8046.5625MB
% 0.12/0.81 % OS : Linux 6.8.0-71-generic
% 0.12/0.81 % CPULimit : 300
% 0.12/0.81 % WCLimit : 300
% 0.12/0.81 % DateTime : Mon Sep 28 02:55:01 UTC 2026
% 0.12/0.82 % CPUTime :
% 0.12/0.82 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.85 Running first-order theorem proving
% 0.12/0.85 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
% 3.48/1.89 % (2618771)Input is clausal, will run a generic CNF schedule.
% 3.48/1.89 % (2618841)dis-21_1_sil=8000:lcm=predicate:random_seed=3644045387: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)
% 3.48/1.89 % (2618841)Refutation not found, incomplete strategy
% 3.48/1.89 % (2618841)------------------------------
% 3.48/1.89 % (2618841)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.89 % (2618841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.89 % (2618841)CaDiCaL version: 2.1.3
% 3.48/1.89 % (2618841)Termination reason: Refutation not found, incomplete strategy
% 3.48/1.89 % (2618841)Time elapsed: 0.001 s
% 3.48/1.89 % (2618841)Peak memory usage: 88 MB
% 3.48/1.89 % (2618840)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2279874521:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.48/1.89 % (2618836)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1639057306:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.48/1.89 % (2618835)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=313143340:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.48/1.89 % (2618837)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2110962531:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.48/1.89 % (2618838)lrs+10_1_sil=8000:sp=occurrence:random_seed=3645729760:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.48/1.89 % (2618839)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3502559042:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.48/1.89 % (2618839)Refutation not found, incomplete strategy
% 3.48/1.89 % (2618839)------------------------------
% 3.48/1.89 % (2618839)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.89 % (2618839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.89 % (2618839)CaDiCaL version: 2.1.3
% 3.48/1.89 % (2618839)Termination reason: Refutation not found, incomplete strategy
% 3.48/1.89 % (2618839)Time elapsed: 0.001 s
% 3.48/1.89 % (2618839)Peak memory usage: 87 MB
% 3.48/1.89 % (2618840)Also succeeded, but the first one will report.
% 3.48/1.89 % (2618838)First to succeed.
% 3.48/1.89 % (2618838)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2618771"
% 3.48/1.89 % (2618841)------------------------------
% 3.48/1.89 % (2618841)------------------------------
% 3.48/1.89 % (2618849)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=1969973751:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.48/1.89 % (2618849)Also succeeded, but the first one will report.
% 3.48/1.89 % (2618839)------------------------------
% 3.48/1.89 % (2618839)------------------------------
% 3.48/1.89 % (2618838)Refutation found. Thanks to Tanya!
% 3.48/1.89 % SZS status Unsatisfiable for theBenchmark
% 3.48/1.89 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.89 % (2618838)------------------------------
% 3.48/1.89 % (2618838)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.89 % (2618838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.89 % (2618838)CaDiCaL version: 2.1.3
% 3.48/1.89 % (2618838)Termination reason: Refutation
% 3.48/1.89 % (2618838)Time elapsed: 0.002 s
% 3.48/1.89 % (2618838)Peak memory usage: 88 MB
% 3.48/1.89 % (2618838)Instructions burned: 1 (million)
% 3.48/1.89 % (2618838)------------------------------
% 3.48/1.89 % (2618838)------------------------------
% 3.48/1.89 % (2618771)Success in time 0.411 s
% 3.48/1.89 % Vampire exiting
%------------------------------------------------------------------------------