%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV488+3 : TPTP v9.3.1. Released v4.0.0.
% 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 01:16:01 PM UTC 2026
% Result : Theorem 0.18s 1.13s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 12 unt; 0 def)
% Number of atoms : 139 ( 37 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 177 ( 66 ~; 55 |; 40 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 48 ( 44 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
real_zero != real_one,
file('/export/starexec/sandbox2/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) = real_zero ) )
& ! [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/sandbox2/benchmark/theBenchmark.p',qii) ).
fof(f13,conjecture,
! [X0,X1] :
( ( int_leq(int_one,X1)
& int_leq(X1,X0)
& int_leq(X0,n) )
=> ( X0 = X1
=> a(X0,X1) != real_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uti) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( ( int_leq(int_one,X1)
& int_leq(X1,X0)
& int_leq(X0,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) = real_zero ) )
& ! [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) = real_zero
| ~ 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) = real_zero
| ~ 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,X1)
& int_leq(X1,X0)
& int_leq(X0,n) ),
inference(ennf_transformation,[],[f14]) ).
fof(f19,plain,
? [X0,X1] :
( real_zero = a(X0,X1)
& X0 = X1
& int_leq(int_one,X1)
& int_leq(X1,X0)
& int_leq(X0,n) ),
inference(flattening,[],[f18]) ).
fof(f25,plain,
( real_zero = a(sK0,sK1)
& sK0 = sK1
& int_leq(int_one,sK1)
& int_leq(sK1,sK0)
& int_leq(sK0,n) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f19]) ).
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(sK0,n),
inference(cnf_transformation,[],[f25]) ).
fof(f36,plain,
int_leq(sK1,sK0),
inference(cnf_transformation,[],[f25]) ).
fof(f37,plain,
int_leq(int_one,sK1),
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(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(sK1,sK1),
inference(definition_unfolding,[],[f36,f38]) ).
fof(f58,plain,
int_leq(sK1,n),
inference(definition_unfolding,[],[f35,f38]) ).
fof(f116,plain,
! [X0,X1] :
( real_zero = real_one
| ~ int_leq(int_one,sK1)
| ~ int_leq(sK1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) ),
inference(superposition,[],[f56,f33]) ).
fof(f117,plain,
! [X0,X1] :
( ~ int_leq(int_one,sK1)
| ~ int_leq(sK1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) ),
inference(forward_subsumption_resolution,[],[f116,f55]) ).
fof(f119,plain,
! [X0,X1] :
( ~ int_leq(sK1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) ),
inference(forward_subsumption_resolution,[],[f117,f37]) ).
fof(f124,plain,
! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,sK1)
| ~ int_leq(sK1,n) ),
inference(resolution,[],[f119,f57]) ).
fof(f127,plain,
! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(sK1,n) ),
inference(forward_subsumption_resolution,[],[f124,f37]) ).
fof(f131,plain,
! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) ),
inference(forward_subsumption_resolution,[],[f127,f58]) ).
fof(f165,plain,
~ int_leq(sK1,n),
inference(resolution,[],[f131,f37]) ).
fof(f166,plain,
$false,
inference(forward_subsumption_resolution,[],[f165,f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV488+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n002.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 11:17:07 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running first-order theorem proving
% 0.07/0.20 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
% 0.18/1.13 % (291525)Detected formulas, will run a generic FOF schedule.
% 0.18/1.13 % (291534)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2127442200:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.18/1.13 % (291534)First to succeed.
% 0.18/1.13 % (291534)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-291525"
% 0.18/1.13 % (291531)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=2944071613:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.18/1.13 % (291533)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=926060677:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.18/1.13 % (291530)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=480238658:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.18/1.13 % (291532)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=1916900671:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.18/1.13 % (291533)Also succeeded, but the first one will report.
% 0.18/1.13 % (291535)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2237209907:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.18/1.13 % (291536)dis-21_1_sil=8000:lcm=predicate:random_seed=1608016480: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)
% 0.18/1.13 % (291535)Also succeeded, but the first one will report.
% 0.18/1.13 % (291536)Instruction limit reached!
% 0.18/1.13 % (291536)------------------------------
% 0.18/1.13 % (291536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.13 % (291536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.13 % (291536)CaDiCaL version: 2.1.3
% 0.18/1.13 % (291536)Termination reason: Instruction limit
% 0.18/1.13 % (291536)Termination phase: Saturation
% 0.18/1.13 % (291536)Time elapsed: 0.080 s
% 0.18/1.13 % (291536)Peak memory usage: 88 MB
% 0.18/1.13 % (291536)Instructions burned: 130 (million)
% 0.18/1.13 % (291534)Refutation found. Thanks to Tanya!
% 0.18/1.13 % SZS status Theorem for theBenchmark
% 0.18/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.13 % (291534)------------------------------
% 0.18/1.13 % (291534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.13 % (291534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.13 % (291534)CaDiCaL version: 2.1.3
% 0.18/1.13 % (291534)Termination reason: Refutation
% 0.18/1.13 % (291534)Time elapsed: 0.003 s
% 0.18/1.13 % (291534)Peak memory usage: 88 MB
% 0.18/1.13 % (291534)Instructions burned: 6 (million)
% 0.18/1.13 % (291534)------------------------------
% 0.18/1.13 % (291534)------------------------------
% 0.18/1.13 % (291525)Success in time 0.295 s
% 0.18/1.13 % Vampire exiting
%------------------------------------------------------------------------------