%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI604_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 09:33:27 AM UTC 2026
% Result : Theorem 3.92s 1.33s
% Output : Refutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 36 ( 16 unt; 0 typ; 11 def)
% Number of atoms : 56 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 35 ( 15 ~; 6 |; 3 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 57 ( 22 atm; 21 fun; 0 num; 14 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 : 11 ( 7 usr; 8 prp; 0-2 aty)
% Number of functors : 7 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 14 ( 12 !; 2 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
f: $int > $int ).
tff(func_def_5,type,
sK0: $int ).
tff(func_def_6,type,
sF1: $int ).
tff(func_def_7,type,
sF2: $int ).
tff(func_def_8,type,
sF3: $int ).
tff(func_def_9,type,
sF4: $int ).
tff(f1,conjecture,
( ! [X0: $int] : $greater(f(X0),X0)
=> ! [X0: $int] : $less($uminus(f($uminus(X0))),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fX_gt_X_implies_negfnegX_lt_fX) ).
tff(f2,negated_conjecture,
~ ( ! [X0: $int] : $greater(f(X0),X0)
=> ! [X0: $int] : $less($uminus(f($uminus(X0))),f(X0)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ! [X0: $int] : $less(X0,f(X0))
=> ! [X0: $int] : $less($uminus(f($uminus(X0))),f(X0)) ),
inference(theory_normalization,[],[f2]) ).
tff(f16,plain,
~ ( ! [X0: $int] : $less(X0,f(X0))
=> ! [X1: $int] : $less($uminus(f($uminus(X1))),f(X1)) ),
inference(rectify,[],[f3]) ).
tff(f17,plain,
( ? [X1: $int] : ~ $less($uminus(f($uminus(X1))),f(X1))
& ! [X0: $int] : $less(X0,f(X0)) ),
inference(ennf_transformation,[],[f16]) ).
tff(f18,plain,
( ? [X0: $int] : ~ $less($uminus(f($uminus(X0))),f(X0))
& ! [X1: $int] : $less(X1,f(X1)) ),
inference(rectify,[],[f17]) ).
tff(f19,plain,
( ~ $less($uminus(f($uminus(sK0))),f(sK0))
& ! [X1: $int] : $less(X1,f(X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f18]) ).
tff(f20,plain,
! [X1: $int] : $less(X1,f(X1)),
inference(cnf_transformation,[],[f19]) ).
tff(f21,plain,
~ $less($uminus(f($uminus(sK0))),f(sK0)),
inference(cnf_transformation,[],[f19]) ).
tff(f22,definition,
sF1 = $uminus(sK0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f23,definition,
sF2 = f(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f24,plain,
f(sF1) = sF2,
inference(reorient_equations,[],[f23]) ).
tff(f25,definition,
sF3 = $uminus(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f26,plain,
$uminus(sF2) = sF3,
inference(reorient_equations,[],[f25]) ).
tff(f27,definition,
sF4 = f(sK0),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f28,plain,
f(sK0) = sF4,
inference(reorient_equations,[],[f27]) ).
tff(f29,plain,
~ $less(sF3,sF4),
inference(definition_folding,[],[f21,f28,f26,f24,f22]) ).
tff(f31,definition,
( spl5_1
<=> ( $uminus(sF2) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
tff(f34,plain,
spl5_1,
inference(avatar_split_clause,[],[f26,f31]) ).
tff(f36,definition,
( spl5_2
<=> ( f(sF1) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
tff(f38,plain,
( ( f(sF1) = sF2 )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f36]) ).
tff(f39,plain,
spl5_2,
inference(avatar_split_clause,[],[f24,f36]) ).
tff(f41,definition,
( spl5_3
<=> $less(sF3,sF4) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
tff(f44,plain,
~ spl5_3,
inference(avatar_split_clause,[],[f29,f41]) ).
tff(f46,definition,
( spl5_4
<=> ( sF1 = $uminus(sK0) ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
tff(f49,plain,
spl5_4,
inference(avatar_split_clause,[],[f22,f46]) ).
tff(f51,definition,
( spl5_5
<=> ( f(sK0) = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
tff(f53,plain,
( ( f(sK0) = sF4 )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f51]) ).
tff(f54,plain,
spl5_5,
inference(avatar_split_clause,[],[f28,f51]) ).
tff(f55,plain,
( $less(sF1,sF2)
| ~ spl5_2 ),
inference(superposition,[],[f20,f38]) ).
tff(f57,definition,
( spl5_6
<=> $less(sF1,sF2) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
tff(f60,plain,
( spl5_6
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f55,f36,f57]) ).
tff(f61,plain,
( $less(sK0,sF4)
| ~ spl5_5 ),
inference(superposition,[],[f20,f53]) ).
tff(f63,definition,
( spl5_7
<=> $less(sK0,sF4) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
tff(f66,plain,
( spl5_7
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f61,f51,f63]) ).
tff(f67,plain,
$false,
inference(avatar_smt_refutation,[],[f66,f60,f54,f49,f44,f39,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI604_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n016.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 20:58:18 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running first-order theorem proving
% 0.07/0.23 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
% 3.92/1.33 % (3996613)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.92/1.33 % (3996618)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2007810790:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.92/1.33 % (3996618)Refutation not found, incomplete strategy
% 3.92/1.33 % (3996618)------------------------------
% 3.92/1.33 % (3996618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.33 % (3996618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.33 % (3996618)CaDiCaL version: 2.1.3
% 3.92/1.33 % (3996618)Termination reason: Refutation not found, incomplete strategy
% 3.92/1.33 % (3996618)Time elapsed: 0.021 s
% 3.92/1.33 % (3996618)Peak memory usage: 116 MB
% 3.92/1.33 % (3996618)Instructions burned: 12 (million)
% 3.92/1.33 % (3996623)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2289684920:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.92/1.33 % (3996624)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1635030865:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.92/1.33 % (3996619)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1402902645:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.92/1.33 % (3996620)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=863581057:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.92/1.33 % (3996621)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2020939202:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.92/1.33 % (3996622)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=4201238863:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.92/1.33 % (3996622)Instruction limit reached!
% 3.92/1.33 % (3996622)------------------------------
% 3.92/1.33 % (3996622)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.33 % (3996622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.33 % (3996622)CaDiCaL version: 2.1.3
% 3.92/1.33 % (3996622)Termination reason: Instruction limit
% 3.92/1.33 % (3996622)Termination phase: Saturation
% 3.92/1.33 % (3996622)Time elapsed: 0.004 s
% 3.92/1.33 % (3996622)Peak memory usage: 88 MB
% 3.92/1.33 % (3996622)Instructions burned: 5 (million)
% 3.92/1.33 % (3996621)Instruction limit reached!
% 3.92/1.33 % (3996621)------------------------------
% 3.92/1.33 % (3996621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.33 % (3996621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.33 % (3996621)CaDiCaL version: 2.1.3
% 3.92/1.33 % (3996621)Termination reason: Instruction limit
% 3.92/1.33 % (3996621)Termination phase: Saturation
% 3.92/1.33 % (3996621)Time elapsed: 0.006 s
% 3.92/1.33 % (3996621)Peak memory usage: 88 MB
% 3.92/1.33 % (3996621)Instructions burned: 7 (million)
% 3.92/1.33 % (3996623)Refutation not found, incomplete strategy
% 3.92/1.33 % (3996623)------------------------------
% 3.92/1.33 % (3996623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.33 % (3996623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.33 % (3996623)CaDiCaL version: 2.1.3
% 3.92/1.33 % (3996623)Termination reason: Refutation not found, incomplete strategy
% 3.92/1.33 % (3996623)Time elapsed: 0.029 s
% 3.92/1.33 % (3996623)Peak memory usage: 115 MB
% 3.92/1.33 % (3996623)Instructions burned: 6 (million)
% 3.92/1.33 % (3996619)Refutation not found, incomplete strategy
% 3.92/1.33 % (3996619)------------------------------
% 3.92/1.33 % (3996619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.33 % (3996619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.33 % (3996619)CaDiCaL version: 2.1.3
% 3.92/1.33 % (3996619)Termination reason: Refutation not found, incomplete strategy
% 3.92/1.33 % (3996619)Time elapsed: 0.031 s
% 3.92/1.33 % (3996619)Peak memory usage: 115 MB
% 3.92/1.33 % (3996619)Instructions burned: 9 (million)
% 3.92/1.33 % (3996624)First to succeed.
% 3.92/1.33 % (3996624)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3996613"
% 3.92/1.33 % (3996618)------------------------------
% 3.92/1.33 % (3996618)------------------------------
% 3.92/1.33 % (3996620)Instruction limit reached!
% 3.92/1.33 % (3996620)------------------------------
% 3.92/1.33 % (3996620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.33 % (3996620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.33 % (3996620)CaDiCaL version: 2.1.3
% 3.92/1.33 % (3996620)Termination reason: Instruction limit
% 3.92/1.33 % (3996620)Termination phase: Saturation
% 3.92/1.33 % (3996620)Time elapsed: 0.171 s
% 3.92/1.33 % (3996620)Peak memory usage: 117 MB
% 3.92/1.33 % (3996620)Instructions burned: 201 (million)
% 3.92/1.33 % (3996632)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=4107861155:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.92/1.33 % (3996633)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=2339198261:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.92/1.33 % (3996632)Refutation not found, incomplete strategy
% 3.92/1.33 % (3996632)------------------------------
% 3.92/1.33 % (3996632)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.33 % (3996632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.33 % (3996632)CaDiCaL version: 2.1.3
% 3.92/1.33 % (3996632)Termination reason: Refutation not found, incomplete strategy
% 3.92/1.33 % (3996632)Time elapsed: 0.001 s
% 3.92/1.33 % (3996632)Peak memory usage: 88 MB
% 3.92/1.33 % (3996633)Instruction limit reached!
% 3.92/1.33 % (3996633)------------------------------
% 3.92/1.33 % (3996633)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.33 % (3996633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.33 % (3996633)CaDiCaL version: 2.1.3
% 3.92/1.33 % (3996633)Termination reason: Instruction limit
% 3.92/1.33 % (3996633)Termination phase: Saturation
% 3.92/1.33 % (3996633)Time elapsed: 0.023 s
% 3.92/1.33 % (3996633)Peak memory usage: 88 MB
% 3.92/1.33 % (3996633)Instructions burned: 29 (million)
% 3.92/1.33 % (3996634)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=198483662:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/16Mi)
% 3.92/1.33 % (3996634)Also succeeded, but the first one will report.
% 3.92/1.33 % (3996619)------------------------------
% 3.92/1.33 % (3996619)------------------------------
% 3.92/1.33 % (3996623)------------------------------
% 3.92/1.33 % (3996623)------------------------------
% 3.92/1.33 % (3996624)Refutation found. Thanks to Tanya!
% 3.92/1.33 % SZS status Theorem for theBenchmark
% 3.92/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.92/1.33 % (3996624)------------------------------
% 3.92/1.33 % (3996624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.33 % (3996624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.33 % (3996624)CaDiCaL version: 2.1.3
% 3.92/1.33 % (3996624)Termination reason: Refutation
% 3.92/1.33 % (3996624)Time elapsed: 0.035 s
% 3.92/1.33 % (3996624)Peak memory usage: 116 MB
% 3.92/1.33 % (3996624)Instructions burned: 12 (million)
% 3.92/1.33 % (3996624)------------------------------
% 3.92/1.33 % (3996624)------------------------------
% 3.92/1.33 % (3996613)Success in time 0.464 s
% 3.92/1.33 % Vampire exiting
%------------------------------------------------------------------------------