%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET820-2 : 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 : n004.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 3.62s 1.47s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 8 unt; 0 def)
% Number of atoms : 17 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 21 ( 21 !; 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_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f5,negated_conjecture,
! [X0,X1] :
( ~ c_in(X0,X1,tc_IntDef_Oint)
| c_in(v_x(X1),X1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f6,negated_conjecture,
! [X0,X1] :
( ~ c_in(X0,X1,tc_IntDef_Oint)
| ~ v_P(v_x(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f7,plain,
! [X0,X1] : c_in(v_x(c_insert(X0,X1,tc_IntDef_Oint)),c_insert(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint),
inference(resolution,[],[f2,f5]) ).
fof(f8,plain,
! [X0,X1] : ~ v_P(v_x(c_insert(X0,X1,tc_IntDef_Oint))),
inference(resolution,[],[f2,f6]) ).
fof(f10,plain,
! [X0,X1] :
( c_in(v_x(c_insert(X0,X1,tc_IntDef_Oint)),X1,tc_IntDef_Oint)
| v_x(c_insert(X0,X1,tc_IntDef_Oint)) = X0 ),
inference(resolution,[],[f7,f3]) ).
fof(f15,plain,
! [X0] : v_x(c_insert(X0,c_emptyset,tc_IntDef_Oint)) = X0,
inference(resolution,[],[f10,f1]) ).
fof(f18,plain,
! [X0] : ~ v_P(X0),
inference(superposition,[],[f8,f15]) ).
fof(f19,plain,
$false,
inference(resolution,[],[f18,f4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET820-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n004.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 02:53:52 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 3.62/1.47 % (4105015)Input is clausal, will run a generic CNF schedule.
% 3.62/1.47 % (4105024)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=581782587:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.62/1.47 % (4105024)Refutation not found, incomplete strategy
% 3.62/1.47 % (4105024)------------------------------
% 3.62/1.47 % (4105024)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.47 % (4105024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.47 % (4105024)CaDiCaL version: 2.1.3
% 3.62/1.47 % (4105024)Termination reason: Refutation not found, incomplete strategy
% 3.62/1.47 % (4105024)Time elapsed: 0.001 s
% 3.62/1.47 % (4105024)Peak memory usage: 87 MB
% 3.62/1.47 % (4105022)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=634040250:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.62/1.47 % (4105020)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=3850453407:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.62/1.47 % (4105021)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3063332682:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.62/1.47 % (4105026)dis-21_1_sil=8000:lcm=predicate:random_seed=3082389433: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)
% 3.62/1.47 % (4105023)lrs+10_1_sil=8000:sp=occurrence:random_seed=384383507:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.62/1.47 % (4105025)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1925148940:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.62/1.47 % (4105026)Refutation not found, incomplete strategy
% 3.62/1.47 % (4105026)------------------------------
% 3.62/1.47 % (4105026)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.47 % (4105026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.47 % (4105026)CaDiCaL version: 2.1.3
% 3.62/1.47 % (4105026)Termination reason: Refutation not found, incomplete strategy
% 3.62/1.47 % (4105026)Time elapsed: 0.001 s
% 3.62/1.47 % (4105026)Peak memory usage: 88 MB
% 3.62/1.47 % (4105023)First to succeed.
% 3.62/1.47 % (4105023)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4105015"
% 3.62/1.47 % (4105025)Also succeeded, but the first one will report.
% 3.62/1.47 % (4105024)------------------------------
% 3.62/1.47 % (4105024)------------------------------
% 3.62/1.47 % (4105034)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=1554159737:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.62/1.47 % (4105034)Also succeeded, but the first one will report.
% 3.62/1.47 % (4105026)------------------------------
% 3.62/1.47 % (4105026)------------------------------
% 3.62/1.47 % (4105023)Refutation found. Thanks to Tanya!
% 3.62/1.47 % SZS status Unsatisfiable for theBenchmark
% 3.62/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.62/1.47 % (4105023)------------------------------
% 3.62/1.47 % (4105023)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.47 % (4105023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.47 % (4105023)CaDiCaL version: 2.1.3
% 3.62/1.47 % (4105023)Termination reason: Refutation
% 3.62/1.47 % (4105023)Time elapsed: 0.002 s
% 3.62/1.47 % (4105023)Peak memory usage: 88 MB
% 3.62/1.47 % (4105023)Instructions burned: 1 (million)
% 3.62/1.47 % (4105023)------------------------------
% 3.62/1.47 % (4105023)------------------------------
% 3.62/1.47 % (4105015)Success in time 0.43 s
% 3.62/1.47 % Vampire exiting
%------------------------------------------------------------------------------