%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM852+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:17:16 PM UTC 2026
% Result : Theorem 2.75s 1.29s
% Output : Refutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 17 unt; 0 def)
% Number of atoms : 39 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 28 ( 14 ~; 9 |; 3 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 36 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
greater(vmul(vd481,vd469),vmul(vd480,vd469)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)') ).
fof(f2,negated_conjecture,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
greater(vd481,vd480),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq(304)), 483, 0)') ).
fof(f9,axiom,
! [X0,X1] :
( greater(X0,X1)
=> X0 = vplus(X1,vskolem9(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(302, 0), 3)') ).
fof(f11,axiom,
! [X0,X1,X2] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
fof(f12,axiom,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof(f21,axiom,
! [X0,X1] :
( greater(X1,X0)
<=> ? [X2] : X1 = vplus(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof(f22,plain,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(flattening,[],[f2]) ).
fof(f27,plain,
! [X0,X1] :
( X0 = vplus(X1,vskolem9(X0,X1))
| ~ greater(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f33,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X2] : X1 = vplus(X0,X2)
| ~ greater(X1,X0) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f34,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X3] : vplus(X0,X3) = X1
| ~ greater(X1,X0) ) ),
inference(rectify,[],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( vplus(X0,sK1(X0,X1)) = X1
| ~ greater(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f34]) ).
fof(f36,plain,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
greater(vd481,vd480),
inference(cnf_transformation,[],[f3]) ).
fof(f43,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| vplus(X1,vskolem9(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f27]) ).
fof(f45,plain,
! [X2,X0,X1] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
inference(cnf_transformation,[],[f11]) ).
fof(f46,plain,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[],[f12]) ).
fof(f57,plain,
! [X2,X0,X1] :
( greater(X1,X0)
| vplus(X0,X2) != X1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f62,plain,
! [X2,X0] : greater(vplus(X0,X2),X0),
inference(equality_resolution,[],[f57]) ).
fof(f73,plain,
~ greater(vmul(vd481,vd469),vmul(vd469,vd480)),
inference(superposition,[],[f36,f46]) ).
fof(f74,plain,
~ greater(vmul(vd469,vd481),vmul(vd469,vd480)),
inference(forward_demodulation,[],[f73,f46]) ).
fof(f81,plain,
vd481 = vplus(vd480,vskolem9(vd481,vd480)),
inference(resolution,[],[f43,f37]) ).
fof(f112,plain,
! [X2,X0,X1] : greater(vmul(X0,vplus(X1,X2)),vmul(X0,X1)),
inference(superposition,[],[f62,f45]) ).
fof(f212,plain,
! [X0] : greater(vmul(X0,vd481),vmul(X0,vd480)),
inference(superposition,[],[f112,f81]) ).
fof(f787,plain,
$false,
inference(resolution,[],[f212,f74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM852+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n006.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 21:34:42 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 2.75/1.29 % (3335042)Detected formulas, will run a generic FOF schedule.
% 2.75/1.29 % (3335051)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3299975577:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.75/1.29 % (3335053)dis-21_1_sil=8000:lcm=predicate:random_seed=2037664295: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)
% 2.75/1.29 % (3335053)Refutation not found, incomplete strategy
% 2.75/1.29 % (3335053)------------------------------
% 2.75/1.29 % (3335053)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.29 % (3335053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.29 % (3335053)CaDiCaL version: 2.1.3
% 2.75/1.29 % (3335053)Termination reason: Refutation not found, incomplete strategy
% 2.75/1.29 % (3335053)Time elapsed: 0.002 s
% 2.75/1.29 % (3335053)Peak memory usage: 88 MB
% 2.75/1.29 % (3335053)Instructions burned: 1 (million)
% 2.75/1.29 % (3335048)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=943533624:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.75/1.29 % (3335050)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=190847527:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.75/1.29 % (3335047)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=2690596258:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.75/1.29 % (3335049)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=2241303934:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.75/1.29 % (3335050)Refutation not found, incomplete strategy
% 2.75/1.29 % (3335050)------------------------------
% 2.75/1.29 % (3335050)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.29 % (3335050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.29 % (3335050)CaDiCaL version: 2.1.3
% 2.75/1.29 % (3335050)Termination reason: Refutation not found, incomplete strategy
% 2.75/1.29 % (3335050)Time elapsed: 0.001 s
% 2.75/1.29 % (3335050)Peak memory usage: 88 MB
% 2.75/1.29 % (3335051)Instruction limit reached!
% 2.75/1.29 % (3335051)------------------------------
% 2.75/1.29 % (3335051)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.29 % (3335051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.29 % (3335051)CaDiCaL version: 2.1.3
% 2.75/1.29 % (3335051)Termination reason: Instruction limit
% 2.75/1.29 % (3335051)Termination phase: Saturation
% 2.75/1.29 % (3335051)Time elapsed: 0.034 s
% 2.75/1.29 % (3335051)Peak memory usage: 88 MB
% 2.75/1.29 % (3335051)Instructions burned: 119 (million)
% 2.75/1.29 % (3335052)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=993666887:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.75/1.29 % (3335052)First to succeed.
% 2.75/1.29 % (3335052)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3335042"
% 2.75/1.29 % (3335060)lrs+10_1_sil=8000:sp=occurrence:random_seed=3421627951:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.75/1.29 % (3335060)Also succeeded, but the first one will report.
% 2.75/1.29 % (3335052)Refutation found. Thanks to Tanya!
% 2.75/1.29 % SZS status Theorem for theBenchmark
% 2.75/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 2.75/1.29 % (3335052)------------------------------
% 2.75/1.29 % (3335052)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.29 % (3335052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.29 % (3335052)CaDiCaL version: 2.1.3
% 2.75/1.29 % (3335052)Termination reason: Refutation
% 2.75/1.29 % (3335052)Time elapsed: 0.011 s
% 2.75/1.29 % (3335052)Peak memory usage: 89 MB
% 2.75/1.29 % (3335052)Instructions burned: 29 (million)
% 2.75/1.29 % (3335052)------------------------------
% 2.75/1.29 % (3335052)------------------------------
% 2.75/1.29 % (3335042)Success in time 0.327 s
% 2.75/1.29 % Vampire exiting
%------------------------------------------------------------------------------