%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI181_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 : n003.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 09:32:38 AM UTC 2026
% Result : Theorem 3.91s 1.33s
% Output : Refutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 33 ( 13 unt; 0 typ; 10 def)
% Number of atoms : 53 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 32 ( 12 ~; 9 |; 1 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 41 ( 18 atm; 0 fun; 18 num; 5 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 : 12 ( 7 usr; 8 prp; 0-2 aty)
% Number of functors : 6 ( 4 usr; 5 con; 0-1 aty)
% Number of variables : 5 ( 5 !; 0 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
f: $int > $int ).
tff(func_def_7,type,
sF0: $int ).
tff(func_def_8,type,
sF1: $int ).
tff(func_def_9,type,
sF2: $int ).
tff(f1,conjecture,
( ! [X0: $int] : $greater(f(X0),X0)
=> $greatereq(f(f(f(6))),9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f2,negated_conjecture,
~ ( ! [X0: $int] : $greater(f(X0),X0)
=> $greatereq(f(f(f(6))),9) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ! [X0: $int] : $less(X0,f(X0))
=> ~ $less(f(f(f(6))),9) ),
inference(theory_normalization,[],[f2]) ).
tff(f16,plain,
( $less(f(f(f(6))),9)
& ! [X0: $int] : $less(X0,f(X0)) ),
inference(ennf_transformation,[],[f3]) ).
tff(f17,plain,
! [X0: $int] : $less(X0,f(X0)),
inference(cnf_transformation,[],[f16]) ).
tff(f18,plain,
$less(f(f(f(6))),9),
inference(cnf_transformation,[],[f16]) ).
tff(f19,definition,
sF0 = f(6),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f20,plain,
f(6) = sF0,
inference(reorient_equations,[],[f19]) ).
tff(f21,definition,
sF1 = f(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f22,definition,
sF2 = f(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f23,plain,
f(sF1) = sF2,
inference(reorient_equations,[],[f22]) ).
tff(f24,plain,
$less(sF2,9),
inference(definition_folding,[],[f18,f23,f21,f20]) ).
tff(f26,definition,
( spl3_1
<=> ( f(sF1) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f28,plain,
( ( f(sF1) = sF2 )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f26]) ).
tff(f29,plain,
spl3_1,
inference(avatar_split_clause,[],[f23,f26]) ).
tff(f31,definition,
( spl3_2
<=> ( f(6) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f33,plain,
( ( f(6) = sF0 )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f31]) ).
tff(f34,plain,
spl3_2,
inference(avatar_split_clause,[],[f20,f31]) ).
tff(f36,definition,
( spl3_3
<=> $less(sF2,9) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
tff(f39,plain,
spl3_3,
inference(avatar_split_clause,[],[f24,f36]) ).
tff(f41,definition,
( spl3_4
<=> ( sF1 = f(sF0) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
tff(f43,plain,
( ( sF1 = f(sF0) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f41]) ).
tff(f44,plain,
spl3_4,
inference(avatar_split_clause,[],[f21,f41]) ).
tff(f45,plain,
( $less(sF1,sF2)
| ~ spl3_1 ),
inference(superposition,[],[f17,f28]) ).
tff(f47,definition,
( spl3_5
<=> $less(sF1,sF2) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
tff(f50,plain,
( spl3_5
| ~ spl3_1 ),
inference(avatar_split_clause,[],[f45,f26,f47]) ).
tff(f51,plain,
( $less(6,sF0)
| ~ spl3_2 ),
inference(superposition,[],[f17,f33]) ).
tff(f53,definition,
( spl3_6
<=> $less(6,sF0) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
tff(f56,plain,
( spl3_6
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f51,f31,f53]) ).
tff(f57,plain,
( $less(sF0,sF1)
| ~ spl3_4 ),
inference(superposition,[],[f17,f43]) ).
tff(f59,definition,
( spl3_7
<=> $less(sF0,sF1) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
tff(f62,plain,
( spl3_7
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f57,f41,f59]) ).
tff(f63,plain,
$false,
inference(avatar_smt_refutation,[],[f62,f56,f50,f44,f39,f34,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI181_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n003.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 20:45:57 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running first-order theorem proving
% 0.10/0.22 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
% 3.91/1.33 % (1980872)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.91/1.33 % (1981007)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3709834477:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.91/1.33 % (1981007)Instruction limit reached!
% 3.91/1.33 % (1981007)------------------------------
% 3.91/1.33 % (1981007)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.33 % (1981007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.33 % (1981007)CaDiCaL version: 2.1.3
% 3.91/1.33 % (1981007)Termination reason: Instruction limit
% 3.91/1.33 % (1981007)Termination phase: Saturation
% 3.91/1.33 % (1981007)Time elapsed: 0.003 s
% 3.91/1.33 % (1981007)Peak memory usage: 88 MB
% 3.91/1.33 % (1981007)Instructions burned: 7 (million)
% 3.91/1.33 % (1981004)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1451908961:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.91/1.33 % (1981006)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2223178633:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.91/1.33 % (1981008)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3019254190:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.91/1.33 % (1981009)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2612964890:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.91/1.33 % (1981005)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1780598482:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.91/1.33 % (1981010)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1042042981:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.91/1.33 % (1981008)Instruction limit reached!
% 3.91/1.33 % (1981008)------------------------------
% 3.91/1.33 % (1981008)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.33 % (1981008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.33 % (1981008)CaDiCaL version: 2.1.3
% 3.91/1.33 % (1981008)Termination reason: Instruction limit
% 3.91/1.33 % (1981008)Termination phase: Saturation
% 3.91/1.33 % (1981008)Time elapsed: 0.004 s
% 3.91/1.33 % (1981008)Peak memory usage: 88 MB
% 3.91/1.33 % (1981008)Instructions burned: 5 (million)
% 3.91/1.33 % (1981009)Refutation not found, incomplete strategy
% 3.91/1.33 % (1981009)------------------------------
% 3.91/1.33 % (1981009)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.33 % (1981009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.33 % (1981009)CaDiCaL version: 2.1.3
% 3.91/1.33 % (1981009)Termination reason: Refutation not found, incomplete strategy
% 3.91/1.33 % (1981009)Time elapsed: 0.029 s
% 3.91/1.33 % (1981009)Peak memory usage: 114 MB
% 3.91/1.33 % (1981009)Instructions burned: 6 (million)
% 3.91/1.33 % (1981004)Refutation not found, incomplete strategy
% 3.91/1.33 % (1981004)------------------------------
% 3.91/1.33 % (1981004)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.33 % (1981004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.33 % (1981004)CaDiCaL version: 2.1.3
% 3.91/1.33 % (1981004)Termination reason: Refutation not found, incomplete strategy
% 3.91/1.33 % (1981004)Time elapsed: 0.032 s
% 3.91/1.33 % (1981004)Peak memory usage: 115 MB
% 3.91/1.33 % (1981004)Instructions burned: 9 (million)
% 3.91/1.33 % (1981005)Refutation not found, incomplete strategy
% 3.91/1.33 % (1981005)------------------------------
% 3.91/1.33 % (1981005)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.33 % (1981005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.33 % (1981005)CaDiCaL version: 2.1.3
% 3.91/1.33 % (1981005)Termination reason: Refutation not found, incomplete strategy
% 3.91/1.33 % (1981005)Time elapsed: 0.033 s
% 3.91/1.33 % (1981005)Peak memory usage: 115 MB
% 3.91/1.33 % (1981005)Instructions burned: 10 (million)
% 3.91/1.33 % (1981010)First to succeed.
% 3.91/1.33 % (1981010)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1980872"
% 3.91/1.33 % (1981012)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=742761091:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.91/1.33 % (1981012)Refutation not found, incomplete strategy
% 3.91/1.33 % (1981012)------------------------------
% 3.91/1.33 % (1981012)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.33 % (1981012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.33 % (1981012)CaDiCaL version: 2.1.3
% 3.91/1.33 % (1981012)Termination reason: Refutation not found, incomplete strategy
% 3.91/1.33 % (1981012)Time elapsed: 0.001 s
% 3.91/1.33 % (1981012)Peak memory usage: 88 MB
% 3.91/1.33 % (1981006)Instruction limit reached!
% 3.91/1.33 % (1981006)------------------------------
% 3.91/1.33 % (1981006)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.33 % (1981006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.33 % (1981006)CaDiCaL version: 2.1.3
% 3.91/1.33 % (1981006)Termination reason: Instruction limit
% 3.91/1.33 % (1981006)Termination phase: Saturation
% 3.91/1.33 % (1981006)Time elapsed: 0.149 s
% 3.91/1.33 % (1981006)Peak memory usage: 118 MB
% 3.91/1.33 % (1981006)Instructions burned: 202 (million)
% 3.91/1.33 % (1981019)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=235097786:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.91/1.33 % (1981019)Instruction limit reached!
% 3.91/1.33 % (1981019)------------------------------
% 3.91/1.33 % (1981019)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.33 % (1981019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.33 % (1981019)CaDiCaL version: 2.1.3
% 3.91/1.33 % (1981019)Termination reason: Instruction limit
% 3.91/1.33 % (1981019)Termination phase: Saturation
% 3.91/1.33 % (1981019)Time elapsed: 0.023 s
% 3.91/1.33 % (1981019)Peak memory usage: 88 MB
% 3.91/1.33 % (1981019)Instructions burned: 30 (million)
% 3.91/1.33 % (1981012)------------------------------
% 3.91/1.33 % (1981012)------------------------------
% 3.91/1.33 % (1981009)------------------------------
% 3.91/1.33 % (1981009)------------------------------
% 3.91/1.33 % (1981004)------------------------------
% 3.91/1.33 % (1981004)------------------------------
% 3.91/1.33 % (1981005)------------------------------
% 3.91/1.33 % (1981005)------------------------------
% 3.91/1.33 % (1981010)Refutation found. Thanks to Tanya!
% 3.91/1.33 % SZS status Theorem for theBenchmark
% 3.91/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.91/1.33 % (1981010)------------------------------
% 3.91/1.33 % (1981010)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.33 % (1981010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.33 % (1981010)CaDiCaL version: 2.1.3
% 3.91/1.33 % (1981010)Termination reason: Refutation
% 3.91/1.33 % (1981010)Time elapsed: 0.035 s
% 3.91/1.33 % (1981010)Peak memory usage: 116 MB
% 3.91/1.33 % (1981010)Instructions burned: 12 (million)
% 3.91/1.33 % (1981010)------------------------------
% 3.91/1.33 % (1981010)------------------------------
% 3.91/1.33 % (1980872)Success in time 0.457 s
% 3.91/1.33 % Vampire exiting
%------------------------------------------------------------------------------