%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM141-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:11:48 PM UTC 2026
% Result : Unsatisfiable 3.67s 1.47s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 29 ( 12 unt; 2 def)
% Number of atoms : 47 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 22 ~; 16 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair3) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f44,axiom,
! [X0] : union(X0,singleton(X0)) = successor(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor) ).
fof(f176,negated_conjecture,
member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_successor_of_set_is_set2_1) ).
fof(f177,negated_conjecture,
~ member(x,successor(x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_successor_of_set_is_set2_2) ).
fof(f186,plain,
! [X0] : successor(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),
inference(definition_unfolding,[],[f44,f26,f12]) ).
fof(f189,plain,
~ member(x,complement(intersection(complement(x),complement(unordered_pair(x,x))))),
inference(definition_unfolding,[],[f177,f186]) ).
fof(f286,plain,
( ~ member(x,universal_class)
| member(x,intersection(complement(x),complement(unordered_pair(x,x)))) ),
inference(resolution,[],[f25,f189]) ).
fof(f289,definition,
( spl1_1
<=> member(x,intersection(complement(x),complement(unordered_pair(x,x)))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f290,plain,
( member(x,intersection(complement(x),complement(unordered_pair(x,x))))
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f292,definition,
( spl1_2
<=> member(x,universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f293,plain,
( ~ member(x,universal_class)
| spl1_2 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f294,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f286,f292,f289]) ).
fof(f295,plain,
( $false
| spl1_2 ),
inference(resolution,[],[f293,f176]) ).
fof(f297,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f295]) ).
fof(f298,plain,
( member(x,complement(unordered_pair(x,x)))
| ~ spl1_1 ),
inference(resolution,[],[f290,f22]) ).
fof(f301,plain,
( ~ member(x,unordered_pair(x,x))
| ~ spl1_1 ),
inference(resolution,[],[f298,f24]) ).
fof(f303,plain,
( ~ member(x,universal_class)
| ~ spl1_1 ),
inference(resolution,[],[f301,f10]) ).
fof(f304,plain,
( ~ spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f303,f289,f292]) ).
cnf(s1,plain,
( spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f294]) ).
cnf(s2,plain,
spl1_2,
inference(sat_conversion,[],[f297]) ).
cnf(s3,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f304]) ).
cnf(s5,plain,
~ spl1_1,
inference(rat,[],[s3,s2]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s2,s5]) ).
fof(f305,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM141-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n018.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 19:01:39 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.39 Running first-order theorem proving
% 0.09/0.39 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
% 3.67/1.47 % (2671178)Input is clausal, will run a generic CNF schedule.
% 3.67/1.47 % (2671187)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2969999047:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.67/1.47 % (2671186)lrs+10_1_sil=8000:sp=occurrence:random_seed=3474065763:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.67/1.47 % (2671184)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=907825652:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.67/1.47 % (2671185)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3691919600:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.67/1.47 % (2671183)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=3784959481:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.67/1.47 % (2671187)Instruction limit reached!
% 3.67/1.47 % (2671187)------------------------------
% 3.67/1.47 % (2671187)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.47 % (2671187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.47 % (2671187)CaDiCaL version: 2.1.3
% 3.67/1.47 % (2671187)Termination reason: Instruction limit
% 3.67/1.47 % (2671187)Termination phase: Saturation
% 3.67/1.47 % (2671187)Time elapsed: 0.041 s
% 3.67/1.47 % (2671187)Peak memory usage: 89 MB
% 3.67/1.47 % (2671187)Instructions burned: 118 (million)
% 3.67/1.47 % (2671189)dis-21_1_sil=8000:lcm=predicate:random_seed=767497975: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)
% 3.67/1.47 % (2671188)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4043624750:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.67/1.47 % (2671189)First to succeed.
% 3.67/1.47 % (2671189)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2671178"
% 3.67/1.47 % (2671186)Instruction limit reached!
% 3.67/1.47 % (2671186)------------------------------
% 3.67/1.47 % (2671186)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.47 % (2671186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.47 % (2671186)CaDiCaL version: 2.1.3
% 3.67/1.47 % (2671186)Termination reason: Instruction limit
% 3.67/1.47 % (2671186)Termination phase: Saturation
% 3.67/1.47 % (2671186)Time elapsed: 0.074 s
% 3.67/1.47 % (2671186)Peak memory usage: 89 MB
% 3.67/1.47 % (2671186)Instructions burned: 108 (million)
% 3.67/1.47 % (2671197)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=1346176966:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.67/1.47 % (2671197)Refutation not found, incomplete strategy
% 3.67/1.47 % (2671197)------------------------------
% 3.67/1.47 % (2671197)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.47 % (2671197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.47 % (2671197)CaDiCaL version: 2.1.3
% 3.67/1.47 % (2671197)Termination reason: Refutation not found, incomplete strategy
% 3.67/1.47 % (2671197)Time elapsed: 0.001 s
% 3.67/1.47 % (2671197)Peak memory usage: 88 MB
% 3.67/1.47 % (2671197)Instructions burned: 2 (million)
% 3.67/1.47 % (2671188)Instruction limit reached!
% 3.67/1.47 % (2671188)------------------------------
% 3.67/1.47 % (2671188)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.47 % (2671188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.47 % (2671188)CaDiCaL version: 2.1.3
% 3.67/1.47 % (2671188)Termination reason: Instruction limit
% 3.67/1.47 % (2671188)Termination phase: Saturation
% 3.67/1.47 % (2671188)Time elapsed: 0.135 s
% 3.67/1.47 % (2671188)Peak memory usage: 91 MB
% 3.67/1.47 % (2671188)Instructions burned: 180 (million)
% 3.67/1.47 % (2671198)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1200047081:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.67/1.47 % (2671189)Refutation found. Thanks to Tanya!
% 3.67/1.47 % SZS status Unsatisfiable for theBenchmark
% 3.67/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.48 % (2671189)------------------------------
% 3.67/1.48 % (2671189)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.48 % (2671189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.48 % (2671189)CaDiCaL version: 2.1.3
% 3.67/1.48 % (2671189)Termination reason: Refutation
% 3.67/1.48 % (2671189)Time elapsed: 0.006 s
% 3.67/1.48 % (2671189)Peak memory usage: 89 MB
% 3.67/1.48 % (2671189)Instructions burned: 8 (million)
% 3.67/1.48 % (2671189)------------------------------
% 3.67/1.48 % (2671189)------------------------------
% 3.67/1.48 % (2671178)Success in time 0.445 s
% 3.67/1.48 % Vampire exiting
%------------------------------------------------------------------------------