%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM011-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:11:34 PM UTC 2026
% Result : Unsatisfiable 7.15s 2.04s
% Output : Refutation 7.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 37 ( 24 unt; 5 def)
% Number of atoms : 53 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 20 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 27 ( 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| little_set(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
fof(f6,axiom,
! [X2,X0,X1] :
( member(X0,non_ordered_pair(X1,X2))
| ~ little_set(X0)
| X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',non_ordered_pair2) ).
fof(f9,axiom,
! [X0] : singleton_set(X0) = non_ordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f35,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
fof(f37,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f38,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ little_set(X0)
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
fof(f39,axiom,
! [X0,X1] : union(X0,X1) = complement(intersection(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f69,axiom,
! [X0] : successor(X0) = union(X0,singleton_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor) ).
fof(f70,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
fof(f247,axiom,
member(f75,natural_numbers),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_natural_number) ).
fof(f248,negated_conjecture,
empty_set = successor(f75),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_zero_is_first) ).
fof(f249,plain,
! [X0] : successor(X0) = complement(intersection(complement(X0),complement(non_ordered_pair(X0,X0)))),
inference(definition_unfolding,[],[f69,f39,f9]) ).
fof(f317,plain,
empty_set = complement(intersection(complement(f75),complement(non_ordered_pair(f75,f75)))),
inference(definition_unfolding,[],[f248,f249]) ).
fof(f318,plain,
! [X2,X1] :
( member(X1,non_ordered_pair(X1,X2))
| ~ little_set(X1) ),
inference(equality_resolution,[],[f6]) ).
fof(f337,definition,
sF0 = complement(f75),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f338,plain,
complement(f75) = sF0,
inference(reorient_equations,[],[f337]) ).
fof(f339,definition,
sF1 = non_ordered_pair(f75,f75),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f340,plain,
non_ordered_pair(f75,f75) = sF1,
inference(reorient_equations,[],[f339]) ).
fof(f341,definition,
sF2 = complement(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f342,plain,
complement(sF1) = sF2,
inference(reorient_equations,[],[f341]) ).
fof(f343,definition,
sF3 = intersection(sF0,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f344,plain,
intersection(sF0,sF2) = sF3,
inference(reorient_equations,[],[f343]) ).
fof(f345,definition,
sF4 = complement(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f346,plain,
complement(sF3) = sF4,
inference(reorient_equations,[],[f345]) ).
fof(f347,plain,
empty_set = sF4,
inference(definition_folding,[],[f317,f346,f344,f342,f340,f338]) ).
fof(f348,plain,
empty_set = complement(sF3),
inference(forward_demodulation,[],[f346,f347]) ).
fof(f351,plain,
! [X0] :
( member(X0,sF2)
| ~ member(X0,sF3) ),
inference(superposition,[],[f35,f344]) ).
fof(f354,plain,
! [X0] :
( ~ member(X0,sF2)
| ~ member(X0,sF1) ),
inference(superposition,[],[f37,f342]) ).
fof(f358,plain,
little_set(f75),
inference(resolution,[],[f247,f1]) ).
fof(f360,plain,
( member(f75,sF1)
| ~ little_set(f75) ),
inference(superposition,[],[f318,f340]) ).
fof(f361,plain,
member(f75,sF1),
inference(forward_subsumption_resolution,[],[f360,f358]) ).
fof(f364,plain,
! [X0] :
( ~ member(X0,sF3)
| ~ member(X0,sF1) ),
inference(resolution,[],[f354,f351]) ).
fof(f371,plain,
! [X0] :
( member(X0,empty_set)
| ~ little_set(X0)
| member(X0,sF3) ),
inference(superposition,[],[f38,f348]) ).
fof(f374,plain,
! [X0] :
( member(X0,sF3)
| ~ little_set(X0) ),
inference(forward_subsumption_resolution,[],[f371,f70]) ).
fof(f375,plain,
! [X0] :
( ~ little_set(X0)
| ~ member(X0,sF1) ),
inference(resolution,[],[f374,f364]) ).
fof(f379,plain,
! [X0] : ~ member(X0,sF1),
inference(forward_subsumption_resolution,[],[f375,f1]) ).
fof(f428,plain,
$false,
inference(resolution,[],[f361,f379]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM011-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n026.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 : Sun Sep 27 18:41:56 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 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
% 7.15/2.04 % (3133931)Input is clausal, will run a generic CNF schedule.
% 7.15/2.04 % (3133979)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=368849254:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 7.15/2.04 % (3133982)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2959099839:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 7.15/2.04 % (3133978)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2133379576:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 7.15/2.04 % (3133980)lrs+10_1_sil=8000:sp=occurrence:random_seed=2559428482:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 7.15/2.04 % (3133980)Refutation not found, incomplete strategy
% 7.15/2.04 % (3133980)------------------------------
% 7.15/2.04 % (3133980)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.15/2.04 % (3133980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.15/2.04 % (3133980)CaDiCaL version: 2.1.3
% 7.15/2.04 % (3133980)Termination reason: Refutation not found, incomplete strategy
% 7.15/2.04 % (3133980)Time elapsed: 0.002 s
% 7.15/2.04 % (3133980)Peak memory usage: 87 MB
% 7.15/2.04 % (3133980)Instructions burned: 1 (million)
% 7.15/2.04 % (3133981)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=849962630:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 7.15/2.04 % (3133981)Refutation not found, incomplete strategy
% 7.15/2.04 % (3133981)------------------------------
% 7.15/2.04 % (3133981)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.15/2.04 % (3133981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.15/2.04 % (3133981)CaDiCaL version: 2.1.3
% 7.15/2.04 % (3133981)Termination reason: Refutation not found, incomplete strategy
% 7.15/2.04 % (3133981)Time elapsed: 0.003 s
% 7.15/2.04 % (3133981)Peak memory usage: 88 MB
% 7.15/2.04 % (3133981)Instructions burned: 1 (million)
% 7.15/2.04 % (3133983)dis-21_1_sil=8000:lcm=predicate:random_seed=3155751662: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)
% 7.15/2.04 % (3133977)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=968841022:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 7.15/2.04 % (3133982)Instruction limit reached!
% 7.15/2.04 % (3133982)------------------------------
% 7.15/2.04 % (3133982)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.15/2.04 % (3133982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.15/2.04 % (3133982)CaDiCaL version: 2.1.3
% 7.15/2.04 % (3133982)Termination reason: Instruction limit
% 7.15/2.04 % (3133982)Termination phase: Saturation
% 7.15/2.04 % (3133982)Time elapsed: 0.154 s
% 7.15/2.04 % (3133982)Peak memory usage: 90 MB
% 7.15/2.04 % (3133982)Instructions burned: 180 (million)
% 7.15/2.04 % (3133983)Instruction limit reached!
% 7.15/2.04 % (3133983)------------------------------
% 7.15/2.04 % (3133983)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.15/2.04 % (3133983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.15/2.04 % (3133983)CaDiCaL version: 2.1.3
% 7.15/2.04 % (3133983)Termination reason: Instruction limit
% 7.15/2.04 % (3133983)Termination phase: Saturation
% 7.15/2.04 % (3133983)Time elapsed: 0.116 s
% 7.15/2.04 % (3133983)Peak memory usage: 90 MB
% 7.15/2.04 % (3133983)Instructions burned: 117 (million)
% 7.15/2.04 % (3133994)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3358060154:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 7.15/2.04 % (3133991)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=4171913844:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 7.15/2.04 % (3133991)Refutation not found, incomplete strategy
% 7.15/2.04 % (3133991)------------------------------
% 7.15/2.04 % (3133991)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.15/2.04 % (3133991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.15/2.04 % (3133991)CaDiCaL version: 2.1.3
% 7.15/2.04 % (3133991)Termination reason: Refutation not found, incomplete strategy
% 7.15/2.04 % (3133991)Time elapsed: 0.002 s
% 7.15/2.04 % (3133991)Peak memory usage: 88 MB
% 7.15/2.04 % (3133991)Instructions burned: 1 (million)
% 7.15/2.04 % (3133980)------------------------------
% 7.15/2.04 % (3133980)------------------------------
% 7.15/2.04 % (3133981)------------------------------
% 7.15/2.04 % (3133981)------------------------------
% 7.15/2.04 % (3133994)Instruction limit reached!
% 7.15/2.04 % (3133994)------------------------------
% 7.15/2.04 % (3133994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.15/2.04 % (3133994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.15/2.04 % (3133994)CaDiCaL version: 2.1.3
% 7.15/2.04 % (3133994)Termination reason: Instruction limit
% 7.15/2.04 % (3133994)Termination phase: Saturation
% 7.15/2.04 % (3133994)Time elapsed: 0.131 s
% 7.15/2.04 % (3133994)Peak memory usage: 91 MB
% 7.15/2.04 % (3133994)Instructions burned: 189 (million)
% 7.15/2.04 % (3133979)First to succeed.
% 7.15/2.04 % (3133979)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3133931"
% 7.15/2.04 % (3134005)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3558243995:avsq=on:i=194:fgj=on:bd=preordered_2993 on theBenchmark for (2993ds/194Mi)
% 7.15/2.04 % (3134005)Also succeeded, but the first one will report.
% 7.15/2.04 % (3134003)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1290582021:st=4:i=219:sd=3:ss=axioms_2993 on theBenchmark for (2993ds/219Mi)
% 7.15/2.04 % (3134004)lrs+10_64_to=lpo:sil=8000:random_seed=2243741944:i=126:bd=preordered_2993 on theBenchmark for (2993ds/126Mi)
% 7.15/2.04 % (3133991)------------------------------
% 7.15/2.04 % (3133991)------------------------------
% 7.15/2.04 % (3133979)Refutation found. Thanks to Tanya!
% 7.15/2.04 % SZS status Unsatisfiable for theBenchmark
% 7.15/2.04 % SZS output start Proof for theBenchmark
% See solution above
% 7.15/2.04 % (3133979)------------------------------
% 7.15/2.04 % (3133979)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.15/2.04 % (3133979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.15/2.04 % (3133979)CaDiCaL version: 2.1.3
% 7.15/2.04 % (3133979)Termination reason: Refutation
% 7.15/2.04 % (3133979)Time elapsed: 0.574 s
% 7.15/2.04 % (3133979)Peak memory usage: 131 MB
% 7.15/2.04 % (3133979)Instructions burned: 1025 (million)
% 7.15/2.04 % (3133979)------------------------------
% 7.15/2.04 % (3133979)------------------------------
% 7.15/2.04 % (3133931)Success in time 0.928 s
% 7.15/2.04 % Vampire exiting
%------------------------------------------------------------------------------