%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET822-1 : 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 : n020.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 0.19s 1.40s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 10 ( 6 unt; 0 def)
% Number of atoms : 14 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 16 ( 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f227,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(f375,axiom,
! [X2,X0,X1] :
( ~ c_in(X0,c_insert(X1,c_emptyset,X2),X2)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
fof(f1434,negated_conjecture,
v_P(v_f(v_b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1435,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(f1436,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(f1700,plain,
! [X0,X1] : ~ v_P(v_x(X0,c_insert(v_f(X0),X1,tc_IntDef_Oint))),
inference(resolution,[],[f227,f1436]) ).
fof(f1705,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,[],[f375,f1435]) ).
fof(f1710,plain,
! [X0] : v_f(X0) = v_x(X0,c_insert(v_f(X0),c_emptyset,tc_IntDef_Oint)),
inference(resolution,[],[f1705,f227]) ).
fof(f1712,plain,
! [X0] : ~ v_P(v_f(X0)),
inference(superposition,[],[f1700,f1710]) ).
fof(f1715,plain,
$false,
inference(resolution,[],[f1712,f1434]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET822-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n020.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 02:56:04 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 0.19/1.40 % (3986499)Input is clausal, will run a generic CNF schedule.
% 0.19/1.40 % (3986508)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=828353551:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.19/1.40 % (3986508)First to succeed.
% 0.19/1.40 % (3986508)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3986499"
% 0.19/1.40 % (3986507)lrs+10_1_sil=8000:sp=occurrence:random_seed=2197727929:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.19/1.40 % (3986506)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2135972639:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.19/1.40 % (3986504)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=4113781437:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.19/1.40 % (3986510)dis-21_1_sil=8000:lcm=predicate:random_seed=3282412280: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)
% 0.19/1.40 % (3986505)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2076056154:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.19/1.40 % (3986509)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1685978077:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.19/1.40 % (3986507)Refutation not found, incomplete strategy
% 0.19/1.40 % (3986507)------------------------------
% 0.19/1.40 % (3986507)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.40 % (3986507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.40 % (3986507)CaDiCaL version: 2.1.3
% 0.19/1.40 % (3986507)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.40 % (3986507)Time elapsed: 0.003 s
% 0.19/1.40 % (3986507)Peak memory usage: 88 MB
% 0.19/1.40 % (3986507)Instructions burned: 2 (million)
% 0.19/1.40 % (3986509)Also succeeded, but the first one will report.
% 0.19/1.40 % (3986510)Instruction limit reached!
% 0.19/1.40 % (3986510)------------------------------
% 0.19/1.40 % (3986510)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.40 % (3986510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.40 % (3986510)CaDiCaL version: 2.1.3
% 0.19/1.40 % (3986510)Termination reason: Instruction limit
% 0.19/1.40 % (3986510)Termination phase: Saturation
% 0.19/1.40 % (3986510)Time elapsed: 0.071 s
% 0.19/1.40 % (3986510)Peak memory usage: 89 MB
% 0.19/1.40 % (3986510)Instructions burned: 119 (million)
% 0.19/1.40 % (3986508)Refutation found. Thanks to Tanya!
% 0.19/1.40 % SZS status Unsatisfiable for theBenchmark
% 0.19/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.40 % (3986508)------------------------------
% 0.19/1.40 % (3986508)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.40 % (3986508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.40 % (3986508)CaDiCaL version: 2.1.3
% 0.19/1.40 % (3986508)Termination reason: Refutation
% 0.19/1.40 % (3986508)Time elapsed: 0.006 s
% 0.19/1.40 % (3986508)Peak memory usage: 89 MB
% 0.19/1.40 % (3986508)Instructions burned: 15 (million)
% 0.19/1.40 % (3986508)------------------------------
% 0.19/1.40 % (3986508)------------------------------
% 0.19/1.40 % (3986499)Success in time 0.325 s
% 0.19/1.40 % Vampire exiting
%------------------------------------------------------------------------------