%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM921_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:17:26 PM UTC 2026
% Result : Theorem 0.16s 1.40s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 25 ( 11 unt; 0 typ; 8 def)
% Number of atoms : 39 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 3 |; 3 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 55 ( 18 atm; 16 fun; 9 num; 12 var)
% Number of types : 1 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 12 ( 10 !; 2 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
f: $int > $int ).
tff(func_def_6,type,
sK0: $int ).
tff(func_def_7,type,
sF1: $int ).
tff(func_def_8,type,
sF2: $int ).
tff(func_def_9,type,
sF3: $int ).
tff(f1,conjecture,
( ! [X0: $int] : $greater(f(X0),X0)
=> ! [X1: $int] : $less($difference(X1,f(X1)),0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f2,negated_conjecture,
~ ( ! [X0: $int] : $greater(f(X0),X0)
=> ! [X1: $int] : $less($difference(X1,f(X1)),0) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ! [X0: $int] : $less(X0,f(X0))
=> ! [X1: $int] : $less($sum(X1,$uminus(f(X1))),0) ),
inference(theory_normalization,[],[f2]) ).
tff(f16,plain,
( ? [X1: $int] : ~ $less($sum(X1,$uminus(f(X1))),0)
& ! [X0: $int] : $less(X0,f(X0)) ),
inference(ennf_transformation,[],[f3]) ).
tff(f17,plain,
( ? [X0: $int] : ~ $less($sum(X0,$uminus(f(X0))),0)
& ! [X1: $int] : $less(X1,f(X1)) ),
inference(rectify,[],[f16]) ).
tff(f18,plain,
( ~ $less($sum(sK0,$uminus(f(sK0))),0)
& ! [X1: $int] : $less(X1,f(X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f17]) ).
tff(f19,plain,
! [X1: $int] : $less(X1,f(X1)),
inference(cnf_transformation,[],[f18]) ).
tff(f20,plain,
~ $less($sum(sK0,$uminus(f(sK0))),0),
inference(cnf_transformation,[],[f18]) ).
tff(f21,definition,
sF1 = f(sK0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f22,definition,
sF2 = $uminus(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f23,definition,
sF3 = $sum(sK0,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f24,plain,
~ $less(sF3,0),
inference(definition_folding,[],[f20,f23,f22,f21]) ).
tff(f26,definition,
( spl4_1
<=> ( sF2 = $uminus(sF1) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f29,plain,
spl4_1,
inference(avatar_split_clause,[],[f22,f26]) ).
tff(f31,definition,
( spl4_2
<=> $less(sF3,0) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f34,plain,
~ spl4_2,
inference(avatar_split_clause,[],[f24,f31]) ).
tff(f36,definition,
( spl4_3
<=> ( sF1 = f(sK0) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
tff(f38,plain,
( ( sF1 = f(sK0) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f36]) ).
tff(f39,plain,
spl4_3,
inference(avatar_split_clause,[],[f21,f36]) ).
tff(f41,definition,
( spl4_4
<=> ( sF3 = $sum(sK0,sF2) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
tff(f44,plain,
spl4_4,
inference(avatar_split_clause,[],[f23,f41]) ).
tff(f45,plain,
( $less(sK0,sF1)
| ~ spl4_3 ),
inference(superposition,[],[f19,f38]) ).
tff(f47,definition,
( spl4_5
<=> $less(sK0,sF1) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
tff(f50,plain,
( spl4_5
| ~ spl4_3 ),
inference(avatar_split_clause,[],[f45,f36,f47]) ).
tff(f51,plain,
$false,
inference(avatar_smt_refutation,[],[f50,f44,f39,f34,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM921_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 21:37:25 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.16/1.40 % (1802076)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.16/1.40 % (1802188)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2350472009:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 0.16/1.40 % (1802188)First to succeed.
% 0.16/1.40 % (1802188)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1802076"
% 0.16/1.40 % (1802183)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1407751832:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 0.16/1.40 % (1802186)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3238060914:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 0.16/1.40 % (1802187)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2985370607:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 0.16/1.40 % (1802182)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3424573455:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 0.16/1.40 % (1802185)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3674803458:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.16/1.40 % (1802184)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=915925924:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 0.16/1.40 % (1802186)Instruction limit reached!
% 0.16/1.40 % (1802186)------------------------------
% 0.16/1.40 % (1802186)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.40 % (1802186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.40 % (1802186)CaDiCaL version: 2.1.3
% 0.16/1.40 % (1802186)Termination reason: Instruction limit
% 0.16/1.40 % (1802186)Termination phase: Saturation
% 0.16/1.40 % (1802186)Time elapsed: 0.004 s
% 0.16/1.40 % (1802186)Peak memory usage: 89 MB
% 0.16/1.40 % (1802186)Instructions burned: 4 (million)
% 0.16/1.40 % (1802185)Instruction limit reached!
% 0.16/1.40 % (1802185)------------------------------
% 0.16/1.40 % (1802185)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.40 % (1802185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.40 % (1802185)CaDiCaL version: 2.1.3
% 0.16/1.40 % (1802185)Termination reason: Instruction limit
% 0.16/1.40 % (1802185)Termination phase: Saturation
% 0.16/1.40 % (1802185)Time elapsed: 0.006 s
% 0.16/1.40 % (1802185)Peak memory usage: 88 MB
% 0.16/1.40 % (1802185)Instructions burned: 8 (million)
% 0.16/1.40 % (1802187)Refutation not found, incomplete strategy
% 0.16/1.40 % (1802187)------------------------------
% 0.16/1.40 % (1802187)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.40 % (1802187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.40 % (1802187)CaDiCaL version: 2.1.3
% 0.16/1.40 % (1802187)Termination reason: Refutation not found, incomplete strategy
% 0.16/1.40 % (1802187)Time elapsed: 0.028 s
% 0.16/1.40 % (1802187)Peak memory usage: 114 MB
% 0.16/1.40 % (1802187)Instructions burned: 6 (million)
% 0.16/1.40 % (1802182)Instruction limit reached!
% 0.16/1.40 % (1802182)------------------------------
% 0.16/1.40 % (1802182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.40 % (1802182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.40 % (1802182)CaDiCaL version: 2.1.3
% 0.16/1.40 % (1802182)Termination reason: Instruction limit
% 0.16/1.40 % (1802182)Time elapsed: 0.030 s
% 0.16/1.40 % (1802182)Peak memory usage: 116 MB
% 0.16/1.40 % (1802182)Instructions burned: 12 (million)
% 0.16/1.40 % (1802183)Also succeeded, but the first one will report.
% 0.16/1.40 % (1802184)Also succeeded, but the first one will report.
% 0.16/1.40 % (1802188)Refutation found. Thanks to Tanya!
% 0.16/1.40 % SZS status Theorem for theBenchmark
% 0.16/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.40 % (1802188)------------------------------
% 0.16/1.40 % (1802188)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.40 % (1802188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.40 % (1802188)CaDiCaL version: 2.1.3
% 0.16/1.40 % (1802188)Termination reason: Refutation
% 0.16/1.40 % (1802188)Time elapsed: 0.021 s
% 0.16/1.40 % (1802188)Peak memory usage: 116 MB
% 0.16/1.41 % (1802188)Instructions burned: 10 (million)
% 0.16/1.41 % (1802188)------------------------------
% 0.16/1.41 % (1802188)------------------------------
% 0.16/1.41 % (1802076)Success in time 0.34 s
% 0.16/1.41 % Vampire exiting
%------------------------------------------------------------------------------