%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI592_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 09:33:26 AM UTC 2026
% Result : Theorem 4.06s 1.43s
% Output : Refutation 4.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 5 unt; 0 typ; 3 def)
% Number of atoms : 75 ( 21 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 74 ( 27 ~; 33 |; 8 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 112 ( 37 atm; 8 fun; 42 num; 25 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 : 6 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 2 usr; 5 con; 0-2 aty)
% Number of variables : 25 ( 20 !; 5 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_5,type,
sK0: $int ).
tff(func_def_6,type,
sK1: $int ).
tff(f1,conjecture,
! [X1: $int,X0: $int] :
( $less(2,X1)
=> ? [X2: $int] :
( ( X0 != X2 )
& $less(0,X2)
& $less(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exists_X_0_Z_noteq_Y) ).
tff(f2,negated_conjecture,
~ ! [X1: $int,X0: $int] :
( $less(2,X1)
=> ? [X2: $int] :
( ( X0 != X2 )
& $less(0,X2)
& $less(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
! [X0: $int,X1: $int] : ( $sum(X1,X0) = $sum(X0,X1) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f5,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(definition,[],[tha_right_identity]) ).
tff(f10,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) ),
introduced(definition,[],[tha_order_totality]) ).
tff(f12,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(definition,[],[tha_order_plus_one_dichotomy]) ).
tff(f15,plain,
~ ! [X1: $int,X0: $int] :
( $less(2,X0)
=> ? [X2: $int] :
( ( X1 != X2 )
& $less(X2,X0)
& $less(0,X2) ) ),
inference(rectify,[],[f2]) ).
tff(f16,plain,
? [X0: $int,X1: $int] :
( ! [X2: $int] :
( ( X1 = X2 )
| ~ $less(0,X2)
| ~ $less(X2,X0) )
& $less(2,X0) ),
inference(ennf_transformation,[],[f15]) ).
tff(f17,plain,
( ! [X2: $int] :
( ( sK1 = X2 )
| ~ $less(0,X2)
| ~ $less(X2,sK0) )
& $less(2,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16]) ).
tff(f18,plain,
$less(2,sK0),
inference(cnf_transformation,[],[f17]) ).
tff(f19,plain,
! [X2: $int] :
( ~ $less(0,X2)
| ( sK1 = X2 )
| ~ $less(X2,sK0) ),
inference(cnf_transformation,[],[f17]) ).
tff(f21,definition,
( spl2_1
<=> $less(2,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f23,plain,
( $less(2,sK0)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f21]) ).
tff(f24,plain,
spl2_1,
inference(avatar_split_clause,[],[f18,f21]) ).
tff(f31,plain,
! [X0: $int] :
( ~ $less($sum(X0,1),sK0)
| $less(X0,0)
| ( $sum(X0,1) = sK1 ) ),
inference(resolution,[],[f12,f19]) ).
tff(f36,plain,
! [X0: $int] :
( ~ $less($sum(1,X0),sK0)
| $less(X0,0)
| ( sK1 = $sum(1,X0) ) ),
inference(superposition,[],[f31,f3]) ).
tff(f40,plain,
( ~ $less(1,sK0)
| ( sK1 = 1 )
| $less(0,0) ),
inference(superposition,[],[f36,f5]) ).
tff(f44,plain,
( ( sK1 = 1 )
| ~ $less(1,sK0) ),
inference(evaluation,[],[f40]) ).
tff(f46,definition,
( spl2_2
<=> $less(1,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f50,definition,
( spl2_3
<=> ( sK1 = 1 ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f52,plain,
( ( sK1 = 1 )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f50]) ).
tff(f53,plain,
( ~ spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f44,f50,f46]) ).
tff(f56,plain,
! [X0: $int] :
( $less(X0,0)
| ( sK1 = X0 )
| ~ $less(X0,sK0)
| ( 0 = X0 ) ),
inference(resolution,[],[f10,f19]) ).
tff(f67,plain,
( ! [X0: $int] :
( ~ $less(X0,sK0)
| ( 0 = X0 )
| ( 1 = X0 )
| $less(X0,0) )
| ~ spl2_3 ),
inference(forward_demodulation,[],[f56,f52]) ).
tff(f109,plain,
( $less(2,0)
| ( 2 = 0 )
| ( 2 = 1 )
| ~ spl2_1
| ~ spl2_3 ),
inference(resolution,[],[f67,f23]) ).
tff(f113,plain,
( $false
| ~ spl2_1
| ~ spl2_3 ),
inference(evaluation,[],[f109]) ).
tff(f114,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f113]) ).
tff(f115,plain,
$false,
inference(avatar_smt_refutation,[],[f114,f53,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI592_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n002.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 20:55:37 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running first-order theorem proving
% 0.10/0.23 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
% 4.06/1.43 % (748132)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.06/1.43 % (748282)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1355203714:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.06/1.43 % (748279)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2940114512:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.06/1.43 % (748279)Instruction limit reached!
% 4.06/1.43 % (748279)------------------------------
% 4.06/1.43 % (748279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.06/1.43 % (748279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.06/1.43 % (748279)CaDiCaL version: 2.1.3
% 4.06/1.43 % (748279)Termination reason: Instruction limit
% 4.06/1.43 % (748279)Termination phase: Saturation
% 4.06/1.43 % (748279)Time elapsed: 0.006 s
% 4.06/1.43 % (748279)Peak memory usage: 89 MB
% 4.06/1.43 % (748279)Instructions burned: 7 (million)
% 4.06/1.43 % (748282)First to succeed.
% 4.06/1.43 % (748282)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-748132"
% 4.06/1.43 % (748277)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=4243798190:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.06/1.43 % (748274)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2988343771:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.06/1.43 % (748275)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3080389039:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.06/1.43 % (748280)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3496912805:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.06/1.43 % (748280)Instruction limit reached!
% 4.06/1.43 % (748280)------------------------------
% 4.06/1.43 % (748280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.06/1.43 % (748280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.06/1.43 % (748280)CaDiCaL version: 2.1.3
% 4.06/1.43 % (748280)Termination reason: Instruction limit
% 4.06/1.43 % (748280)Termination phase: Saturation
% 4.06/1.43 % (748280)Time elapsed: 0.006 s
% 4.06/1.43 % (748280)Peak memory usage: 88 MB
% 4.06/1.43 % (748280)Instructions burned: 4 (million)
% 4.06/1.43 % (748281)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=121760032:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.06/1.43 % (748275)Refutation not found, incomplete strategy
% 4.06/1.43 % (748275)------------------------------
% 4.06/1.43 % (748275)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.06/1.43 % (748275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.06/1.43 % (748275)CaDiCaL version: 2.1.3
% 4.06/1.43 % (748275)Termination reason: Refutation not found, incomplete strategy
% 4.06/1.43 % (748275)Time elapsed: 0.042 s
% 4.06/1.43 % (748275)Peak memory usage: 115 MB
% 4.06/1.43 % (748275)Instructions burned: 6 (million)
% 4.06/1.43 % (748274)Instruction limit reached!
% 4.06/1.43 % (748274)------------------------------
% 4.06/1.43 % (748274)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.06/1.43 % (748274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.06/1.43 % (748274)CaDiCaL version: 2.1.3
% 4.06/1.43 % (748274)Termination reason: Instruction limit
% 4.06/1.43 % (748274)Termination phase: Saturation
% 4.06/1.43 % (748274)Time elapsed: 0.045 s
% 4.06/1.43 % (748274)Peak memory usage: 115 MB
% 4.06/1.43 % (748274)Instructions burned: 13 (million)
% 4.06/1.43 % (748277)Also succeeded, but the first one will report.
% 4.06/1.43 % (748281)Refutation not found, incomplete strategy
% 4.06/1.43 % (748281)------------------------------
% 4.06/1.43 % (748281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.06/1.43 % (748281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.06/1.43 % (748281)CaDiCaL version: 2.1.3
% 4.06/1.43 % (748281)Termination reason: Refutation not found, incomplete strategy
% 4.06/1.43 % (748281)Time elapsed: 0.041 s
% 4.06/1.43 % (748281)Peak memory usage: 115 MB
% 4.06/1.43 % (748281)Instructions burned: 6 (million)
% 4.06/1.43 % (748289)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=69081542:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 4.06/1.43 % (748289)Refutation not found, incomplete strategy
% 4.06/1.43 % (748289)------------------------------
% 4.06/1.43 % (748289)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.06/1.43 % (748289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.06/1.43 % (748289)CaDiCaL version: 2.1.3
% 4.06/1.43 % (748289)Termination reason: Refutation not found, incomplete strategy
% 4.06/1.43 % (748289)Time elapsed: 0.006 s
% 4.06/1.43 % (748289)Peak memory usage: 88 MB
% 4.06/1.43 % (748282)Refutation found. Thanks to Tanya!
% 4.06/1.43 % SZS status Theorem for theBenchmark
% 4.06/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 4.06/1.43 % (748282)------------------------------
% 4.06/1.43 % (748282)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.06/1.43 % (748282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.06/1.43 % (748282)CaDiCaL version: 2.1.3
% 4.06/1.43 % (748282)Termination reason: Refutation
% 4.06/1.43 % (748282)Time elapsed: 0.030 s
% 4.06/1.43 % (748282)Peak memory usage: 116 MB
% 4.06/1.43 % (748282)Instructions burned: 13 (million)
% 4.06/1.43 % (748282)------------------------------
% 4.06/1.43 % (748282)------------------------------
% 4.06/1.43 % (748132)Success in time 0.477 s
% 4.06/1.43 % Vampire exiting
%------------------------------------------------------------------------------