%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM841+1 : 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 : n014.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 5.44s 1.72s
% Output : Refutation 5.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 38 ( 26 unt; 0 def)
% Number of atoms : 56 ( 14 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 24 ~; 12 |; 3 &)
% ( 1 <=>; 2 =>; 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 : 56 ( 53 !; 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(f11,axiom,
! [X0,X1,X2] :
( greater(vplus(X0,X2),vplus(X1,X2))
=> greater(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 2)') ).
fof(f14,axiom,
! [X0,X1,X2] :
( greater(X0,X1)
=> greater(vplus(X0,X2),vplus(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).
fof(f15,axiom,
! [X0,X1] : greater(vplus(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
fof(f30,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(f37,axiom,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f40,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(f47,plain,
~ greater(vplus(vd344,vd347),vplus(vd345,vd348)),
inference(flattening,[],[f2]) ).
fof(f48,plain,
! [X0,X1,X2] :
( greater(vplus(X0,X2),vplus(X1,X2))
| ~ greater(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f49,plain,
! [X0,X1,X2] :
( greater(X0,X1)
| ~ greater(vplus(X0,X2),vplus(X1,X2)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f56,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X2] : X1 = vplus(X0,X2)
| ~ greater(X1,X0) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f57,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X3] : vplus(X0,X3) = X1
| ~ greater(X1,X0) ) ),
inference(rectify,[],[f56]) ).
fof(f58,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))],[f57]) ).
fof(f60,plain,
~ greater(vplus(vd344,vd347),vplus(vd345,vd348)),
inference(cnf_transformation,[],[f47]) ).
fof(f61,plain,
greater(vd344,vd345),
inference(cnf_transformation,[],[f8]) ).
fof(f63,plain,
! [X0,X1] :
( ~ greater(X1,X0)
| vplus(X0,sK0(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f58]) ).
fof(f66,plain,
! [X0,X1] : greater(vplus(X0,X1),X0),
inference(cnf_transformation,[],[f15]) ).
fof(f67,plain,
! [X2,X0,X1] :
( greater(vplus(X0,X2),vplus(X1,X2))
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ greater(vplus(X0,X2),vplus(X1,X2))
| greater(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f69,plain,
greater(vd347,vd348),
inference(cnf_transformation,[],[f7]) ).
fof(f72,plain,
! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f40]) ).
fof(f73,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f37]) ).
fof(f91,plain,
~ greater(vplus(vd347,vd344),vplus(vd345,vd348)),
inference(forward_demodulation,[],[f60,f73]) ).
fof(f113,plain,
vd344 = vplus(vd345,sK0(vd345,vd344)),
inference(unit_resulting_resolution,[],[f63,f61]) ).
fof(f114,plain,
vd347 = vplus(vd348,sK0(vd348,vd347)),
inference(unit_resulting_resolution,[],[f63,f69]) ).
fof(f135,plain,
! [X2,X0,X1] :
( greater(vplus(X0,X1),vplus(X2,X0))
| ~ greater(X1,X2) ),
inference(superposition,[],[f67,f73]) ).
fof(f149,plain,
! [X0] : ~ greater(vplus(vplus(vd347,vd344),X0),vplus(vplus(vd345,vd348),X0)),
inference(unit_resulting_resolution,[],[f68,f91]) ).
fof(f160,plain,
! [X0] : ~ greater(vplus(vplus(vd347,vd344),X0),vplus(vd345,vplus(vd348,X0))),
inference(forward_demodulation,[],[f149,f72]) ).
fof(f163,plain,
! [X0] : ~ greater(vplus(vd347,vplus(vd344,X0)),vplus(vd345,vplus(vd348,X0))),
inference(forward_demodulation,[],[f160,f72]) ).
fof(f462,plain,
~ greater(vplus(vd347,vplus(vd344,sK0(vd348,vd347))),vplus(vd345,vd347)),
inference(superposition,[],[f163,f114]) ).
fof(f849,plain,
~ greater(vplus(vd344,sK0(vd348,vd347)),vd345),
inference(unit_resulting_resolution,[],[f135,f462]) ).
fof(f874,plain,
! [X0] : ~ greater(vplus(vplus(vd344,sK0(vd348,vd347)),X0),vplus(vd345,X0)),
inference(unit_resulting_resolution,[],[f68,f849]) ).
fof(f875,plain,
! [X0] : ~ greater(vplus(vd344,vplus(sK0(vd348,vd347),X0)),vplus(vd345,X0)),
inference(forward_demodulation,[],[f874,f72]) ).
fof(f887,plain,
~ greater(vplus(vd344,vplus(sK0(vd348,vd347),sK0(vd345,vd344))),vd344),
inference(superposition,[],[f875,f113]) ).
fof(f892,plain,
$false,
inference(forward_subsumption_resolution,[],[f887,f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM841+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.37 % Computer : n014.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 27 21:29:31 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 5.44/1.72 % (1185123)Detected formulas, will run a generic FOF schedule.
% 5.44/1.72 % (1185129)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=1754988513:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.44/1.72 % (1185132)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2210906052:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.44/1.72 % (1185130)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=1085829157:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.44/1.72 % (1185131)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=900113980:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.44/1.72 % (1185128)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=2961029397:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.44/1.72 % (1185134)dis-21_1_sil=8000:lcm=predicate:random_seed=68954867: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)
% 5.44/1.72 % (1185133)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=88488767:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.44/1.72 % (1185131)Refutation not found, incomplete strategy
% 5.44/1.72 % (1185131)------------------------------
% 5.44/1.72 % (1185131)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.44/1.72 % (1185131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.44/1.72 % (1185131)CaDiCaL version: 2.1.3
% 5.44/1.72 % (1185131)Termination reason: Refutation not found, incomplete strategy
% 5.44/1.72 % (1185131)Time elapsed: 0.002 s
% 5.44/1.72 % (1185131)Peak memory usage: 88 MB
% 5.44/1.72 % (1185131)Instructions burned: 1 (million)
% 5.44/1.72 % (1185132)Instruction limit reached!
% 5.44/1.72 % (1185132)------------------------------
% 5.44/1.72 % (1185132)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.44/1.72 % (1185132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.44/1.72 % (1185132)CaDiCaL version: 2.1.3
% 5.44/1.72 % (1185132)Termination reason: Instruction limit
% 5.44/1.72 % (1185132)Termination phase: Saturation
% 5.44/1.72 % (1185132)Time elapsed: 0.070 s
% 5.44/1.72 % (1185132)Peak memory usage: 88 MB
% 5.44/1.72 % (1185132)Instructions burned: 120 (million)
% 5.44/1.72 % (1185134)Instruction limit reached!
% 5.44/1.72 % (1185134)------------------------------
% 5.44/1.72 % (1185134)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.44/1.72 % (1185134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.44/1.72 % (1185134)CaDiCaL version: 2.1.3
% 5.44/1.72 % (1185134)Termination reason: Instruction limit
% 5.44/1.72 % (1185134)Termination phase: Saturation
% 5.44/1.72 % (1185134)Time elapsed: 0.082 s
% 5.44/1.72 % (1185134)Peak memory usage: 88 MB
% 5.44/1.72 % (1185134)Instructions burned: 129 (million)
% 5.44/1.72 % (1185133)Instruction limit reached!
% 5.44/1.72 % (1185133)------------------------------
% 5.44/1.72 % (1185133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.44/1.72 % (1185133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.44/1.72 % (1185133)CaDiCaL version: 2.1.3
% 5.44/1.72 % (1185133)Termination reason: Instruction limit
% 5.44/1.72 % (1185133)Termination phase: Saturation
% 5.44/1.72 % (1185133)Time elapsed: 0.083 s
% 5.44/1.72 % (1185133)Peak memory usage: 90 MB
% 5.44/1.72 % (1185133)Instructions burned: 141 (million)
% 5.44/1.72 % (1185142)lrs+10_1_sil=8000:sp=occurrence:random_seed=1851993902:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.44/1.72 % (1185143)lrs+10_1_sil=32000:urr=on:br=off:random_seed=575399044:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.44/1.72 % (1185144)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4003950100:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.44/1.72 % (1185131)------------------------------
% 5.44/1.72 % (1185131)------------------------------
% 5.44/1.72 % (1185143)First to succeed.
% 5.44/1.72 % (1185143)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1185123"
% 5.44/1.72 % (1185129)Also succeeded, but the first one will report.
% 5.44/1.72 % (1185142)Instruction limit reached!
% 5.44/1.72 % (1185142)------------------------------
% 5.44/1.72 % (1185142)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.44/1.72 % (1185142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.44/1.72 % (1185142)CaDiCaL version: 2.1.3
% 5.44/1.72 % (1185142)Termination reason: Instruction limit
% 5.44/1.72 % (1185142)Termination phase: Saturation
% 5.44/1.72 % (1185142)Time elapsed: 0.167 s
% 5.44/1.72 % (1185142)Peak memory usage: 90 MB
% 5.44/1.72 % (1185142)Instructions burned: 286 (million)
% 5.44/1.72 % (1185148)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=997841180:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 5.44/1.72 % (1185144)Instruction limit reached!
% 5.44/1.72 % (1185144)------------------------------
% 5.44/1.72 % (1185144)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.44/1.72 % (1185144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.44/1.72 % (1185144)CaDiCaL version: 2.1.3
% 5.44/1.72 % (1185144)Termination reason: Instruction limit
% 5.44/1.72 % (1185144)Termination phase: Saturation
% 5.44/1.72 % (1185144)Time elapsed: 0.197 s
% 5.44/1.72 % (1185144)Peak memory usage: 91 MB
% 5.44/1.72 % (1185144)Instructions burned: 326 (million)
% 5.44/1.72 % (1185143)Refutation found. Thanks to Tanya!
% 5.44/1.72 % SZS status Theorem for theBenchmark
% 5.44/1.72 % SZS output start Proof for theBenchmark
% See solution above
% 5.44/1.72 % (1185143)------------------------------
% 5.44/1.72 % (1185143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.44/1.72 % (1185143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.44/1.72 % (1185143)CaDiCaL version: 2.1.3
% 5.44/1.72 % (1185143)Termination reason: Refutation
% 5.44/1.72 % (1185143)Time elapsed: 0.026 s
% 5.44/1.72 % (1185143)Peak memory usage: 89 MB
% 5.44/1.72 % (1185143)Instructions burned: 37 (million)
% 5.44/1.72 % (1185143)------------------------------
% 5.44/1.72 % (1185143)------------------------------
% 5.44/1.72 % (1185123)Success in time 0.699 s
% 5.44/1.72 % Vampire exiting
%------------------------------------------------------------------------------