%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV488+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 01:16:01 PM UTC 2026
% Result : Theorem 3.44s 1.29s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 20 unt; 6 def)
% Number of atoms : 215 ( 45 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 270 ( 113 ~; 91 |; 44 &)
% ( 6 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 59 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( int_leq(X0,X1)
<=> ( int_less(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_leq) ).
fof(f11,axiom,
real_zero != real_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',real_constants) ).
fof(f12,axiom,
! [X0,X1] :
( ( int_leq(int_one,X0)
& int_leq(X0,n)
& int_leq(int_one,X1)
& int_leq(X1,n) )
=> ( ! [X2] :
( ( int_less(int_zero,X2)
& X0 = plus(X1,X2) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(plus(X3,X2),X3) = lu(plus(X3,X2),X3) ) )
& ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,X3) = real_one )
& ! [X2] :
( ( int_less(int_zero,X2)
& X1 = plus(X0,X2) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X0) )
=> a(X3,plus(X3,X2)) = real_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qil) ).
fof(f13,conjecture,
! [X0,X1] :
( ( int_leq(int_one,X0)
& int_leq(X0,X1)
& int_leq(X1,n) )
=> ( X0 = X1
=> a(X0,X1) != real_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lti) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( ( int_leq(int_one,X0)
& int_leq(X0,X1)
& int_leq(X1,n) )
=> ( X0 = X1
=> a(X0,X1) != real_zero ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( int_leq(int_one,X0)
& int_leq(X0,n)
& int_leq(int_one,X1)
& int_leq(X1,n) )
=> ( ! [X2] :
( ( int_less(int_zero,X2)
& X0 = plus(X1,X2) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(plus(X3,X2),X3) = lu(plus(X3,X2),X3) ) )
& ! [X4] :
( ( int_leq(int_one,X4)
& int_leq(X4,X1) )
=> real_one = a(X4,X4) )
& ! [X5] :
( ( int_less(int_zero,X5)
& plus(X0,X5) = X1 )
=> ! [X6] :
( ( int_leq(int_one,X6)
& int_leq(X6,X0) )
=> real_zero = a(X6,plus(X6,X5)) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f16,plain,
! [X0,X1] :
( ( ! [X2] :
( ! [X3] :
( a(plus(X3,X2),X3) = lu(plus(X3,X2),X3)
| ~ int_leq(int_one,X3)
| ~ int_leq(X3,X1) )
| ~ int_less(int_zero,X2)
| plus(X1,X2) != X0 )
& ! [X4] :
( real_one = a(X4,X4)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,X1) )
& ! [X5] :
( ! [X6] :
( real_zero = a(X6,plus(X6,X5))
| ~ int_leq(int_one,X6)
| ~ int_leq(X6,X0) )
| ~ int_less(int_zero,X5)
| plus(X0,X5) != X1 ) )
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n) ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( ! [X2] :
( ! [X3] :
( a(plus(X3,X2),X3) = lu(plus(X3,X2),X3)
| ~ int_leq(int_one,X3)
| ~ int_leq(X3,X1) )
| ~ int_less(int_zero,X2)
| plus(X1,X2) != X0 )
& ! [X4] :
( real_one = a(X4,X4)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,X1) )
& ! [X5] :
( ! [X6] :
( real_zero = a(X6,plus(X6,X5))
| ~ int_leq(int_one,X6)
| ~ int_leq(X6,X0) )
| ~ int_less(int_zero,X5)
| plus(X0,X5) != X1 ) )
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
? [X0,X1] :
( real_zero = a(X0,X1)
& X0 = X1
& int_leq(int_one,X0)
& int_leq(X0,X1)
& int_leq(X1,n) ),
inference(ennf_transformation,[],[f14]) ).
fof(f19,plain,
? [X0,X1] :
( real_zero = a(X0,X1)
& X0 = X1
& int_leq(int_one,X0)
& int_leq(X0,X1)
& int_leq(X1,n) ),
inference(flattening,[],[f18]) ).
fof(f25,plain,
( real_zero = a(sK0,sK1)
& sK0 = sK1
& int_leq(int_one,sK0)
& int_leq(sK0,sK1)
& int_leq(sK1,n) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f19]) ).
fof(f29,plain,
! [X0,X1] :
( ( int_leq(X0,X1)
| ( ~ int_less(X0,X1)
& X0 != X1 ) )
& ( int_less(X0,X1)
| X0 = X1
| ~ int_leq(X0,X1) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f30,plain,
! [X0,X1] :
( ( int_leq(X0,X1)
| ( ~ int_less(X0,X1)
& X0 != X1 ) )
& ( int_less(X0,X1)
| X0 = X1
| ~ int_leq(X0,X1) ) ),
inference(flattening,[],[f29]) ).
fof(f33,plain,
! [X0,X1,X4] :
( real_one = a(X4,X4)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,X1)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n) ),
inference(cnf_transformation,[],[f17]) ).
fof(f35,plain,
int_leq(sK1,n),
inference(cnf_transformation,[],[f25]) ).
fof(f37,plain,
int_leq(int_one,sK0),
inference(cnf_transformation,[],[f25]) ).
fof(f38,plain,
sK0 = sK1,
inference(cnf_transformation,[],[f25]) ).
fof(f39,plain,
real_zero = a(sK0,sK1),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
! [X0,X1] :
( int_leq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f30]) ).
fof(f55,plain,
real_zero != real_one,
inference(cnf_transformation,[],[f11]) ).
fof(f56,plain,
real_zero = a(sK1,sK1),
inference(definition_unfolding,[],[f39,f38]) ).
fof(f57,plain,
int_leq(int_one,sK1),
inference(definition_unfolding,[],[f37,f38]) ).
fof(f59,definition,
~ sP3(real_zero),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f60,plain,
sP3(real_one),
inference(inequality_splitting,[],[f55,f59]) ).
fof(f65,plain,
! [X1] : int_leq(X1,X1),
inference(equality_resolution,[],[f47]) ).
fof(f66,plain,
! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| sP4 ),
inference(cnf_transformation,[],[f66_D]) ).
fof(f66_D,definition,
( ! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) )
<=> ~ sP4 ),
introduced(definition,[new_symbols(definition,[sP4])],[general_splitting_component_introduction]) ).
fof(f67,plain,
! [X1,X4] :
( real_one = a(X4,X4)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,X1)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ sP4 ),
inference(general_splitting,[],[f33,f66_D]) ).
fof(f70,definition,
( spl5_1
<=> sP4 ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f74,definition,
( spl5_2
<=> ! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f75,plain,
( ! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f66,f74,f70]) ).
fof(f78,definition,
( spl5_3
<=> ! [X4,X1] :
( real_one = a(X4,X4)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X4,X1)
| ~ int_leq(int_one,X4) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f79,plain,
( ! [X1,X4] :
( real_one = a(X4,X4)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X4,X1)
| ~ int_leq(int_one,X4) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f80,plain,
( ~ spl5_1
| spl5_3 ),
inference(avatar_split_clause,[],[f67,f78,f70]) ).
fof(f104,plain,
~ sP3(a(sK1,sK1)),
inference(superposition,[],[f59,f56]) ).
fof(f117,plain,
( ~ int_leq(sK1,n)
| ~ spl5_2 ),
inference(resolution,[],[f75,f57]) ).
fof(f119,plain,
( $false
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f117,f35]) ).
fof(f120,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f119]) ).
fof(f126,plain,
( ! [X0] :
( ~ sP3(real_one)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(sK1,X0)
| ~ int_leq(int_one,sK1) )
| ~ spl5_3 ),
inference(superposition,[],[f104,f79]) ).
fof(f129,plain,
( ! [X0] :
( ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(sK1,X0)
| ~ int_leq(int_one,sK1) )
| ~ spl5_3 ),
inference(forward_subsumption_resolution,[],[f126,f60]) ).
fof(f132,definition,
( spl5_8
<=> ! [X3] :
( ~ int_leq(X3,n)
| ~ int_leq(sK1,X3)
| ~ int_leq(int_one,X3) ) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
fof(f133,plain,
( ! [X3] :
( ~ int_leq(sK1,X3)
| ~ int_leq(X3,n)
| ~ int_leq(int_one,X3) )
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f138,plain,
( ! [X0] :
( ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(sK1,X0) )
| ~ spl5_3 ),
inference(forward_subsumption_resolution,[],[f129,f57]) ).
fof(f140,plain,
( spl5_8
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f138,f78,f132]) ).
fof(f152,plain,
( ~ int_leq(sK1,n)
| ~ int_leq(int_one,sK1)
| ~ spl5_8 ),
inference(resolution,[],[f133,f65]) ).
fof(f153,plain,
( ~ int_leq(int_one,sK1)
| ~ spl5_8 ),
inference(forward_subsumption_resolution,[],[f152,f35]) ).
fof(f155,plain,
( $false
| ~ spl5_8 ),
inference(forward_subsumption_resolution,[],[f153,f57]) ).
fof(f156,plain,
~ spl5_8,
inference(avatar_contradiction_clause,[],[f155]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f76]) ).
cnf(s2,plain,
( ~ spl5_1
| spl5_3 ),
inference(sat_conversion,[],[f80]) ).
cnf(s5,plain,
~ spl5_2,
inference(sat_conversion,[],[f120]) ).
cnf(s8,plain,
( ~ spl5_3
| spl5_8 ),
inference(sat_conversion,[],[f140]) ).
cnf(s9,plain,
~ spl5_8,
inference(sat_conversion,[],[f156]) ).
cnf(s11,plain,
~ spl5_3,
inference(rat,[],[s8,s9]) ).
cnf(s12,plain,
~ spl5_1,
inference(rat,[],[s2,s11]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s1,s5,s12]) ).
fof(f159,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV488+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 % Computer : n010.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Mon Sep 28 11:14:47 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 Running first-order theorem proving
% 0.11/0.23 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
% 3.44/1.29 % (1858261)Detected formulas, will run a generic FOF schedule.
% 3.44/1.29 % (1858372)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3252121817:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.44/1.29 % (1858372)First to succeed.
% 3.44/1.29 % (1858372)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1858261"
% 3.44/1.29 % (1858371)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=607041632:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.44/1.29 % (1858370)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3762322863:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.44/1.29 % (1858375)dis-21_1_sil=8000:lcm=predicate:random_seed=683968504:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.44/1.29 % (1858374)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3726045182:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.44/1.29 % (1858373)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1219466119:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.44/1.29 % (1858374)Also succeeded, but the first one will report.
% 3.44/1.29 % (1858373)Also succeeded, but the first one will report.
% 3.44/1.29 % (1858369)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3023738439:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.44/1.29 % (1858375)Instruction limit reached!
% 3.44/1.29 % (1858375)------------------------------
% 3.44/1.29 % (1858375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.29 % (1858375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.29 % (1858375)CaDiCaL version: 2.1.3
% 3.44/1.29 % (1858375)Termination reason: Instruction limit
% 3.44/1.29 % (1858375)Termination phase: Saturation
% 3.44/1.29 % (1858375)Time elapsed: 0.125 s
% 3.44/1.29 % (1858375)Peak memory usage: 88 MB
% 3.44/1.29 % (1858375)Instructions burned: 130 (million)
% 3.44/1.29 % (1858372)Refutation found. Thanks to Tanya!
% 3.44/1.29 % SZS status Theorem for theBenchmark
% 3.44/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.29 % (1858372)------------------------------
% 3.44/1.29 % (1858372)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.29 % (1858372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.29 % (1858372)CaDiCaL version: 2.1.3
% 3.44/1.29 % (1858372)Termination reason: Refutation
% 3.44/1.29 % (1858372)Time elapsed: 0.023 s
% 3.44/1.29 % (1858372)Peak memory usage: 90 MB
% 3.44/1.29 % (1858372)Instructions burned: 6 (million)
% 3.44/1.29 % (1858372)------------------------------
% 3.44/1.29 % (1858372)------------------------------
% 3.44/1.29 % (1858261)Success in time 0.416 s
% 3.44/1.29 % Vampire exiting
%------------------------------------------------------------------------------