%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM855+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:17:17 PM UTC 2026
% Result : Theorem 3.26s 1.26s
% Output : Refutation 3.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 18 unt; 0 def)
% Number of atoms : 43 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 18 ~; 12 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
greater(vmul(vd508,vd511),vmul(vd509,vd512)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq_conjunct2(315), 516, 0)') ).
fof(f2,negated_conjecture,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f4,axiom,
greater(vmul(vd511,vd509),vmul(vd512,vd509)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct2(315), 515, 1)') ).
fof(f5,axiom,
vmul(vd509,vd511) = vmul(vd511,vd509),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct2(315), 515, 0)') ).
fof(f6,axiom,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(315), 514, 0)') ).
fof(f17,axiom,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof(f26,axiom,
! [X0,X1,X2,X3] :
( ( greater(X2,X3)
& greater(X0,X1) )
=> greater(vplus(X0,X2),vplus(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(209, 0), 0)') ).
fof(f29,axiom,
! [X0,X1,X2] :
( greater(vplus(X0,X2),vplus(X1,X2))
=> greater(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 2)') ).
fof(f55,axiom,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f65,plain,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(flattening,[],[f2]) ).
fof(f67,plain,
! [X0,X1,X2] :
( greater(X0,X1)
| ~ greater(vplus(X0,X2),vplus(X1,X2)) ),
inference(ennf_transformation,[],[f29]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( greater(vplus(X0,X2),vplus(X1,X3))
| ~ greater(X2,X3)
| ~ greater(X0,X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( greater(vplus(X0,X2),vplus(X1,X3))
| ~ greater(X2,X3)
| ~ greater(X0,X1) ),
inference(flattening,[],[f68]) ).
fof(f84,plain,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(cnf_transformation,[],[f65]) ).
fof(f86,plain,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(cnf_transformation,[],[f6]) ).
fof(f92,plain,
! [X2,X0,X1] :
( ~ greater(vplus(X0,X2),vplus(X1,X2))
| greater(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f93,plain,
! [X2,X3,X0,X1] :
( greater(vplus(X0,X2),vplus(X1,X3))
| ~ greater(X2,X3)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f94,plain,
vmul(vd511,vd509) = vmul(vd509,vd511),
inference(cnf_transformation,[],[f5]) ).
fof(f95,plain,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[],[f17]) ).
fof(f103,plain,
greater(vmul(vd511,vd509),vmul(vd512,vd509)),
inference(cnf_transformation,[],[f4]) ).
fof(f106,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f55]) ).
fof(f122,plain,
greater(vmul(vd508,vd511),vmul(vd511,vd509)),
inference(superposition,[],[f86,f94]) ).
fof(f123,plain,
~ greater(vmul(vd508,vd511),vmul(vd512,vd509)),
inference(superposition,[],[f84,f95]) ).
fof(f155,plain,
! [X2,X0,X1] :
( ~ greater(vplus(X0,X1),vplus(X2,X0))
| greater(X1,X2) ),
inference(superposition,[],[f92,f106]) ).
fof(f530,plain,
! [X2,X0,X1] :
( greater(X0,X1)
| ~ greater(X0,X2)
| ~ greater(X2,X1) ),
inference(resolution,[],[f155,f93]) ).
fof(f1189,plain,
! [X0] :
( ~ greater(vmul(vd508,vd511),X0)
| ~ greater(X0,vmul(vd512,vd509)) ),
inference(resolution,[],[f530,f123]) ).
fof(f1201,plain,
~ greater(vmul(vd511,vd509),vmul(vd512,vd509)),
inference(resolution,[],[f1189,f122]) ).
fof(f1209,plain,
$false,
inference(forward_subsumption_resolution,[],[f1201,f103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM855+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 % Computer : n016.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Sun Sep 27 21:36:48 UTC 2026
% 0.12/0.42 % CPUTime :
% 0.12/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.45 Running first-order theorem proving
% 0.12/0.45 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
% 3.26/1.26 % (3012751)Detected formulas, will run a generic FOF schedule.
% 3.26/1.26 % (3012756)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=843748269:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.26/1.26 % (3012761)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4017677136:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.26/1.26 % (3012760)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1571973112:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.26/1.26 % (3012759)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3378481326:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.26/1.26 % (3012758)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=1934071117:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.26/1.26 % (3012762)dis-21_1_sil=8000:lcm=predicate:random_seed=1669090947: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)
% 3.26/1.26 % (3012757)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=3704292839:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.26/1.26 % (3012759)Refutation not found, incomplete strategy
% 3.26/1.26 % (3012759)------------------------------
% 3.26/1.26 % (3012759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.26 % (3012759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.26 % (3012759)CaDiCaL version: 2.1.3
% 3.26/1.26 % (3012759)Termination reason: Refutation not found, incomplete strategy
% 3.26/1.26 % (3012759)Time elapsed: 0.002 s
% 3.26/1.26 % (3012759)Peak memory usage: 88 MB
% 3.26/1.26 % (3012759)Instructions burned: 1 (million)
% 3.26/1.26 % (3012760)First to succeed.
% 3.26/1.26 % (3012760)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3012751"
% 3.26/1.26 % (3012762)Instruction limit reached!
% 3.26/1.26 % (3012762)------------------------------
% 3.26/1.26 % (3012762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.26 % (3012762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.26 % (3012762)CaDiCaL version: 2.1.3
% 3.26/1.26 % (3012762)Termination reason: Instruction limit
% 3.26/1.26 % (3012762)Termination phase: Saturation
% 3.26/1.26 % (3012762)Time elapsed: 0.081 s
% 3.26/1.26 % (3012762)Peak memory usage: 89 MB
% 3.26/1.26 % (3012762)Instructions burned: 130 (million)
% 3.26/1.26 % (3012761)Instruction limit reached!
% 3.26/1.26 % (3012761)------------------------------
% 3.26/1.26 % (3012761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.26 % (3012761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.26 % (3012761)CaDiCaL version: 2.1.3
% 3.26/1.26 % (3012761)Termination reason: Instruction limit
% 3.26/1.26 % (3012761)Termination phase: Saturation
% 3.26/1.26 % (3012761)Time elapsed: 0.088 s
% 3.26/1.26 % (3012761)Peak memory usage: 90 MB
% 3.26/1.26 % (3012761)Instructions burned: 140 (million)
% 3.26/1.26 % (3012770)lrs+10_1_sil=8000:sp=occurrence:random_seed=3704937619:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.26/1.26 % (3012770)Also succeeded, but the first one will report.
% 3.26/1.26 % (3012771)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2994465589:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.26/1.26 % (3012759)------------------------------
% 3.26/1.26 % (3012759)------------------------------
% 3.26/1.26 % (3012760)Refutation found. Thanks to Tanya!
% 3.26/1.26 % SZS status Theorem for theBenchmark
% 3.26/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.26/1.26 % (3012760)------------------------------
% 3.26/1.26 % (3012760)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.26 % (3012760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.26 % (3012760)CaDiCaL version: 2.1.3
% 3.26/1.26 % (3012760)Termination reason: Refutation
% 3.26/1.26 % (3012760)Time elapsed: 0.024 s
% 3.26/1.26 % (3012760)Peak memory usage: 88 MB
% 3.26/1.26 % (3012760)Instructions burned: 37 (million)
% 3.26/1.26 % (3012760)------------------------------
% 3.26/1.26 % (3012760)------------------------------
% 3.26/1.26 % (3012751)Success in time 0.408 s
% 3.26/1.26 % Vampire exiting
%------------------------------------------------------------------------------