%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM022-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 12:11:36 PM UTC 2026
% Result : Unsatisfiable 3.64s 1.50s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 29 ( 9 unt; 2 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 25 ~; 24 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ less(X2,X0)
| ~ less(X0,X1)
| less(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ equalish(add(successor(X0),X1),X2)
| less(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',smaller_number) ).
fof(f3,axiom,
! [X0,X1] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(X1,X0)),X0),X1)
| ~ less(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_lemma) ).
fof(f4,axiom,
! [X0,X1] :
( ~ divides(X0,X1)
| less(X0,X1)
| equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_only_less_or_equal) ).
fof(f7,axiom,
! [X2,X0,X1] :
( ~ equalish(X2,X0)
| ~ equalish(X0,X1)
| equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
fof(f8,axiom,
less(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_less_than_b) ).
fof(f9,axiom,
divides(b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_divides_d) ).
fof(f10,negated_conjecture,
~ less(a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_less_than_d) ).
fof(f12,plain,
! [X0] :
( ~ less(b,X0)
| less(a,X0) ),
inference(resolution,[],[f1,f8]) ).
fof(f13,plain,
( less(b,d)
| equalish(b,d) ),
inference(resolution,[],[f4,f9]) ).
fof(f16,definition,
( spl0_1
<=> equalish(b,d) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f18,plain,
( equalish(b,d)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f20,definition,
( spl0_2
<=> less(b,d) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f22,plain,
( less(b,d)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f23,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f13,f20,f16]) ).
fof(f24,plain,
( less(a,d)
| ~ spl0_2 ),
inference(resolution,[],[f22,f12]) ).
fof(f27,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f24,f10]) ).
fof(f28,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f27]) ).
fof(f32,plain,
! [X2,X0,X1] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(X1,X0)),X0),X2)
| ~ equalish(X1,X2)
| ~ less(X0,X1) ),
inference(resolution,[],[f3,f7]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ equalish(X0,X1)
| ~ less(X2,X0)
| less(X2,X1) ),
inference(resolution,[],[f32,f2]) ).
fof(f38,plain,
( ! [X0] :
( ~ less(X0,b)
| less(X0,d) )
| ~ spl0_1 ),
inference(resolution,[],[f35,f18]) ).
fof(f42,plain,
( less(a,d)
| ~ spl0_1 ),
inference(resolution,[],[f38,f8]) ).
fof(f43,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f42,f10]) ).
fof(f44,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f43]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f23]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f28]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f44]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f45,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM022-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n019.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 18:40:18 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.43 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
% 3.64/1.50 % (3331256)Input is clausal, will run a generic CNF schedule.
% 3.64/1.50 % (3331266)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=839779939:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.64/1.50 % (3331266)Instruction limit reached!
% 3.64/1.50 % (3331266)------------------------------
% 3.64/1.50 % (3331266)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.50 % (3331266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.50 % (3331266)CaDiCaL version: 2.1.3
% 3.64/1.50 % (3331266)Termination reason: Instruction limit
% 3.64/1.50 % (3331266)Termination phase: Saturation
% 3.64/1.50 % (3331266)Time elapsed: 0.036 s
% 3.64/1.50 % (3331266)Peak memory usage: 87 MB
% 3.64/1.50 % (3331266)Instructions burned: 186 (million)
% 3.64/1.50 % (3331267)dis-21_1_sil=8000:lcm=predicate:random_seed=3562286603: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)
% 3.64/1.50 % (3331265)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1364148807:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.64/1.50 % (3331263)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2560660190:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.64/1.50 % (3331262)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=68751555:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.64/1.50 % (3331261)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=3314111114:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.64/1.50 % (3331264)lrs+10_1_sil=8000:sp=occurrence:random_seed=3412303038:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.64/1.50 % (3331264)First to succeed.
% 3.64/1.50 % (3331267)Also succeeded, but the first one will report.
% 3.64/1.50 % (3331264)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3331256"
% 3.64/1.50 % (3331265)Instruction limit reached!
% 3.64/1.50 % (3331265)------------------------------
% 3.64/1.50 % (3331265)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.50 % (3331265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.50 % (3331265)CaDiCaL version: 2.1.3
% 3.64/1.50 % (3331265)Termination reason: Instruction limit
% 3.64/1.50 % (3331265)Termination phase: Saturation
% 3.64/1.50 % (3331265)Time elapsed: 0.045 s
% 3.64/1.50 % (3331265)Peak memory usage: 87 MB
% 3.64/1.50 % (3331265)Instructions burned: 115 (million)
% 3.64/1.50 % (3331269)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=2312440703:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.64/1.50 % (3331269)Refutation not found, incomplete strategy
% 3.64/1.50 % (3331269)------------------------------
% 3.64/1.50 % (3331269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.50 % (3331269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.50 % (3331269)CaDiCaL version: 2.1.3
% 3.64/1.50 % (3331269)Termination reason: Refutation not found, incomplete strategy
% 3.64/1.50 % (3331269)Time elapsed: 0.001 s
% 3.64/1.50 % (3331269)Peak memory usage: 88 MB
% 3.64/1.50 % (3331276)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2935301787: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)
% 3.64/1.50 % (3331276)Also succeeded, but the first one will report.
% 3.64/1.50 % (3331264)Refutation found. Thanks to Tanya!
% 3.64/1.50 % SZS status Unsatisfiable for theBenchmark
% 3.64/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.50 % (3331264)------------------------------
% 0.18/1.50 % (3331264)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.50 % (3331264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.50 % (3331264)CaDiCaL version: 2.1.3
% 0.18/1.50 % (3331264)Termination reason: Refutation
% 0.18/1.50 % (3331264)Time elapsed: 0.003 s
% 0.18/1.50 % (3331264)Peak memory usage: 89 MB
% 0.18/1.50 % (3331264)Instructions burned: 1 (million)
% 0.18/1.50 % (3331264)------------------------------
% 0.18/1.50 % (3331264)------------------------------
% 0.18/1.50 % (3331256)Success in time 0.434 s
% 0.18/1.50 % Vampire exiting
%------------------------------------------------------------------------------