%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM841+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 : n018.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 12:17:13 PM UTC 2026
% Result : Theorem 5.17s 1.82s
% Output : Refutation 5.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 27 unt; 0 def)
% Number of atoms : 43 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 21 ( 10 ~; 7 |; 3 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 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 : 44 ( 41 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
greater(vplus(vd344,vd347),vplus(vd345,vd348)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(214, 352, 0)') ).
fof(f2,negated_conjecture,
~ greater(vplus(vd344,vd347),vplus(vd345,vd348)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f7,axiom,
greater(vd347,vd348),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(211), 349, 0)') ).
fof(f8,axiom,
greater(vd344,vd345),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(211), 346, 0)') ).
fof(f15,axiom,
! [X0,X1] : greater(vplus(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
fof(f20,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,axiom,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f25,axiom,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof(f28,plain,
~ greater(vplus(vd344,vd347),vplus(vd345,vd348)),
inference(flattening,[],[f2]) ).
fof(f34,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X2] : X1 = vplus(X0,X2)
| ~ greater(X1,X0) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f35,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X3] : vplus(X0,X3) = X1
| ~ greater(X1,X0) ) ),
inference(rectify,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( vplus(X0,sK0(X0,X1)) = X1
| ~ greater(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f35]) ).
fof(f37,plain,
~ greater(vplus(vd344,vd347),vplus(vd345,vd348)),
inference(cnf_transformation,[],[f28]) ).
fof(f38,plain,
greater(vd344,vd345),
inference(cnf_transformation,[],[f8]) ).
fof(f40,plain,
! [X0,X1] :
( ~ greater(X1,X0)
| vplus(X0,sK0(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f36]) ).
fof(f42,plain,
! [X0,X1] : greater(vplus(X0,X1),X0),
inference(cnf_transformation,[],[f15]) ).
fof(f45,plain,
greater(vd347,vd348),
inference(cnf_transformation,[],[f7]) ).
fof(f49,plain,
! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f25]) ).
fof(f50,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f22]) ).
fof(f67,plain,
vd344 = vplus(vd345,sK0(vd345,vd344)),
inference(resolution,[],[f40,f38]) ).
fof(f68,plain,
vd347 = vplus(vd348,sK0(vd348,vd347)),
inference(resolution,[],[f40,f45]) ).
fof(f103,plain,
! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X1,vplus(X0,X2)),
inference(superposition,[],[f49,f50]) ).
fof(f104,plain,
! [X0] : vplus(vd345,vplus(sK0(vd345,vd344),X0)) = vplus(vd344,X0),
inference(superposition,[],[f49,f67]) ).
fof(f108,plain,
! [X2,X0,X1] : greater(vplus(X0,vplus(X1,X2)),vplus(X0,X1)),
inference(superposition,[],[f42,f49]) ).
fof(f114,plain,
! [X2,X0,X1] : vplus(X0,vplus(X1,X2)) = vplus(X2,vplus(X0,X1)),
inference(superposition,[],[f50,f49]) ).
fof(f339,plain,
! [X0] : vplus(vd347,X0) = vplus(sK0(vd348,vd347),vplus(vd348,X0)),
inference(superposition,[],[f103,f68]) ).
fof(f394,plain,
! [X0] : vplus(vd347,X0) = vplus(vd348,vplus(X0,sK0(vd348,vd347))),
inference(forward_demodulation,[],[f339,f114]) ).
fof(f2509,plain,
! [X0,X1] : greater(vplus(X1,vplus(vd344,X0)),vplus(X1,vd345)),
inference(superposition,[],[f108,f104]) ).
fof(f5903,plain,
greater(vplus(vd347,vd344),vplus(vd348,vd345)),
inference(superposition,[],[f2509,f394]) ).
fof(f5912,plain,
greater(vplus(vd347,vd344),vplus(vd345,vd348)),
inference(forward_demodulation,[],[f5903,f50]) ).
fof(f5921,plain,
greater(vplus(vd344,vd347),vplus(vd345,vd348)),
inference(forward_demodulation,[],[f5912,f50]) ).
fof(f5924,plain,
$false,
inference(forward_subsumption_resolution,[],[f5921,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM841+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n018.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 21:31:40 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.42 Running first-order theorem proving
% 0.17/0.42 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
% 5.17/1.82 % (2745180)Detected formulas, will run a generic FOF schedule.
% 5.17/1.82 % (2745284)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=688464364:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.17/1.82 % (2745284)Instruction limit reached!
% 5.17/1.82 % (2745284)------------------------------
% 5.17/1.82 % (2745284)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.17/1.82 % (2745284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.17/1.82 % (2745284)CaDiCaL version: 2.1.3
% 5.17/1.82 % (2745284)Termination reason: Instruction limit
% 5.17/1.82 % (2745284)Termination phase: Saturation
% 5.17/1.82 % (2745284)Time elapsed: 0.038 s
% 5.17/1.82 % (2745284)Peak memory usage: 88 MB
% 5.17/1.82 % (2745284)Instructions burned: 120 (million)
% 5.17/1.82 % (2745282)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=3027232191:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.17/1.82 % (2745281)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=2203314116:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.17/1.82 % (2745280)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=355189729:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.17/1.82 % (2745283)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3245252558:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.17/1.82 % (2745285)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=658321490:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.17/1.82 % (2745286)dis-21_1_sil=8000:lcm=predicate:random_seed=2232589168: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)
% 5.17/1.82 % (2745283)Refutation not found, incomplete strategy
% 5.17/1.82 % (2745283)------------------------------
% 5.17/1.82 % (2745283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.17/1.82 % (2745283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.17/1.82 % (2745283)CaDiCaL version: 2.1.3
% 5.17/1.82 % (2745283)Termination reason: Refutation not found, incomplete strategy
% 5.17/1.82 % (2745283)Time elapsed: 0.002 s
% 5.17/1.82 % (2745283)Peak memory usage: 88 MB
% 5.17/1.82 % (2745286)Instruction limit reached!
% 5.17/1.82 % (2745286)------------------------------
% 5.17/1.82 % (2745286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.17/1.82 % (2745286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.17/1.82 % (2745286)CaDiCaL version: 2.1.3
% 5.17/1.82 % (2745286)Termination reason: Instruction limit
% 5.17/1.82 % (2745286)Termination phase: Saturation
% 5.17/1.82 % (2745286)Time elapsed: 0.070 s
% 5.17/1.82 % (2745286)Peak memory usage: 88 MB
% 5.17/1.82 % (2745286)Instructions burned: 129 (million)
% 5.17/1.82 % (2745285)Instruction limit reached!
% 5.17/1.82 % (2745285)------------------------------
% 5.17/1.82 % (2745285)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.17/1.82 % (2745285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.17/1.82 % (2745285)CaDiCaL version: 2.1.3
% 5.17/1.82 % (2745285)Termination reason: Instruction limit
% 5.17/1.82 % (2745285)Termination phase: Saturation
% 5.17/1.82 % (2745285)Time elapsed: 0.080 s
% 5.17/1.82 % (2745285)Peak memory usage: 90 MB
% 5.17/1.82 % (2745285)Instructions burned: 139 (million)
% 5.17/1.82 % (2745297)lrs+10_1_sil=8000:sp=occurrence:random_seed=2885456272:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 5.17/1.82 % (2745297)First to succeed.
% 5.17/1.82 % (2745297)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2745180"
% 5.17/1.82 % (2745283)------------------------------
% 5.17/1.82 % (2745283)------------------------------
% 5.17/1.82 % (2745301)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4197708620:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.17/1.82 % (2745302)lrs+1011_1_sil=32000:sp=occurrence:random_seed=995350947:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.17/1.82 % (2745302)Also succeeded, but the first one will report.
% 5.17/1.82 % (2745297)Refutation found. Thanks to Tanya!
% 5.17/1.82 % SZS status Theorem for theBenchmark
% 5.17/1.82 % SZS output start Proof for theBenchmark
% See solution above
% 5.17/1.82 % (2745297)------------------------------
% 5.17/1.82 % (2745297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.17/1.82 % (2745297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.17/1.82 % (2745297)CaDiCaL version: 2.1.3
% 5.17/1.82 % (2745297)Termination reason: Refutation
% 5.17/1.82 % (2745297)Time elapsed: 0.087 s
% 5.17/1.82 % (2745297)Peak memory usage: 90 MB
% 5.17/1.82 % (2745297)Instructions burned: 205 (million)
% 5.17/1.82 % (2745297)------------------------------
% 5.17/1.82 % (2745297)------------------------------
% 5.17/1.82 % (2745180)Success in time 0.62 s
% 5.17/1.82 % Vampire exiting
%------------------------------------------------------------------------------