%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM906_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 : n026.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 12:17:24 PM UTC 2026
% Result : Theorem 3.41s 1.15s
% Output : Refutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 1 unt; 0 typ; 3 def)
% Number of atoms : 51 ( 13 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 53 ( 19 ~; 21 |; 6 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number arithmetic : 39 ( 27 atm; 0 fun; 0 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 : 7 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 12 ( 6 !; 6 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
sK0: $rat ).
tff(func_def_1,type,
sK1: $rat ).
tff(f1,conjecture,
! [X0: $rat,X1: $rat] :
( $lesseq(X0,X1)
<=> ( ( X0 = X1 )
| $less(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rat_combined_problem_1) ).
tff(f2,negated_conjecture,
~ ! [X0: $rat,X1: $rat] :
( $lesseq(X0,X1)
<=> ( ( X0 = X1 )
| $less(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X0: $rat,X1: $rat] :
( ( ( X0 = X1 )
| $less(X0,X1) )
<=> ~ $less(X1,X0) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
? [X0: $rat,X1: $rat] :
( ( ( X0 = X1 )
| $less(X0,X1) )
<~> ~ $less(X1,X0) ),
inference(ennf_transformation,[],[f3]) ).
tff(f5,plain,
? [X0: $rat,X1: $rat] :
( ( $less(X1,X0)
| ( ( X0 != X1 )
& ~ $less(X0,X1) ) )
& ( ~ $less(X1,X0)
| ( X0 = X1 )
| $less(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
tff(f6,plain,
? [X0: $rat,X1: $rat] :
( ( $less(X1,X0)
| ( ( X0 != X1 )
& ~ $less(X0,X1) ) )
& ( ~ $less(X1,X0)
| ( X0 = X1 )
| $less(X0,X1) ) ),
inference(flattening,[],[f5]) ).
tff(f7,plain,
( ( $less(sK1,sK0)
| ( ( sK1 != sK0 )
& ~ $less(sK0,sK1) ) )
& ( ~ $less(sK1,sK0)
| ( sK1 = sK0 )
| $less(sK0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f6]) ).
tff(f8,plain,
( ~ $less(sK1,sK0)
| ( sK1 = sK0 )
| $less(sK0,sK1) ),
inference(cnf_transformation,[],[f7]) ).
tff(f9,plain,
( $less(sK1,sK0)
| ~ $less(sK0,sK1) ),
inference(cnf_transformation,[],[f7]) ).
tff(f10,plain,
( ( sK1 != sK0 )
| $less(sK1,sK0) ),
inference(cnf_transformation,[],[f7]) ).
tff(f12,definition,
( spl2_1
<=> $less(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f16,definition,
( spl2_2
<=> $less(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f19,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f9,f16,f12]) ).
tff(f21,definition,
( spl2_3
<=> ( sK1 = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f24,plain,
( ~ spl2_2
| spl2_1
| spl2_3 ),
inference(avatar_split_clause,[],[f8,f21,f12,f16]) ).
tff(f25,plain,
( spl2_2
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f10,f21,f16]) ).
tff(f26,plain,
$false,
inference(avatar_smt_refutation,[],[f25,f24,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM906_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 21:41:42 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.41/1.15 % (3229961)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.41/1.15 % (3230006)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3762262490:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.41/1.15 % (3230007)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=441926790:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.41/1.15 % (3230012)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2384943043:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.41/1.15 % (3230009)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1997697185:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.41/1.15 % (3230011)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2955353449:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.41/1.15 % (3230004)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2925380268:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.41/1.15 % (3230008)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3528257012:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.41/1.15 % (3230009)Instruction limit reached!
% 3.41/1.15 % (3230009)------------------------------
% 3.41/1.15 % (3230009)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.15 % (3230009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.15 % (3230009)CaDiCaL version: 2.1.3
% 3.41/1.15 % (3230009)Termination reason: Instruction limit
% 3.41/1.15 % (3230009)Termination phase: Saturation
% 3.41/1.15 % (3230009)Time elapsed: 0.004 s
% 3.41/1.15 % (3230009)Peak memory usage: 88 MB
% 3.41/1.15 % (3230009)Instructions burned: 6 (million)
% 3.41/1.15 % (3230008)Instruction limit reached!
% 3.41/1.15 % (3230008)------------------------------
% 3.41/1.15 % (3230008)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.15 % (3230008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.15 % (3230008)CaDiCaL version: 2.1.3
% 3.41/1.15 % (3230008)Termination reason: Instruction limit
% 3.41/1.15 % (3230008)Termination phase: Saturation
% 3.41/1.15 % (3230008)Time elapsed: 0.006 s
% 3.41/1.15 % (3230008)Peak memory usage: 88 MB
% 3.41/1.15 % (3230008)Instructions burned: 8 (million)
% 3.41/1.15 % (3230006)First to succeed.
% 3.41/1.15 % (3230011)Also succeeded, but the first one will report.
% 3.41/1.15 % (3230012)Also succeeded, but the first one will report.
% 3.41/1.15 % (3230004)Also succeeded, but the first one will report.
% 3.41/1.15 % (3230007)Also succeeded, but the first one will report.
% 3.41/1.15 % (3230006)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3229961"
% 3.41/1.15 % (3230022)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2241884207:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.41/1.15 % (3230023)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=3915563474:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.41/1.15 % (3230022)Refutation not found, incomplete strategy
% 3.41/1.15 % (3230022)------------------------------
% 3.41/1.15 % (3230022)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.15 % (3230022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.15 % (3230022)CaDiCaL version: 2.1.3
% 3.41/1.15 % (3230022)Termination reason: Refutation not found, incomplete strategy
% 3.41/1.15 % (3230022)Time elapsed: 0.001 s
% 3.41/1.15 % (3230022)Peak memory usage: 89 MB
% 3.41/1.15 % (3230023)Also succeeded, but the first one will report.
% 3.41/1.15 % (3230006)Refutation found. Thanks to Tanya!
% 3.41/1.15 % SZS status Theorem for theBenchmark
% 3.41/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 3.41/1.15 % (3230006)------------------------------
% 3.41/1.15 % (3230006)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.15 % (3230006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.15 % (3230006)CaDiCaL version: 2.1.3
% 3.41/1.15 % (3230006)Termination reason: Refutation
% 3.41/1.15 % (3230006)Time elapsed: 0.034 s
% 3.41/1.15 % (3230006)Peak memory usage: 115 MB
% 3.41/1.15 % (3230006)Instructions burned: 8 (million)
% 3.41/1.15 % (3230006)------------------------------
% 3.41/1.15 % (3230006)------------------------------
% 3.41/1.15 % (3229961)Success in time 0.448 s
% 3.41/1.15 % Vampire exiting
%------------------------------------------------------------------------------