%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE150+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 11:40:29 AM UTC 2026
% Result : Theorem 5.18s 1.78s
% Output : Refutation 5.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 50 ( 30 unt; 5 def)
% Number of atoms : 72 ( 28 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 43 ( 21 ~; 16 |; 3 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 29 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f10,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
fof(f15,axiom,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_unfold1) ).
fof(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f19,conjecture,
! [X0] :
( leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero)))
& leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero)))
& leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero))) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f24,plain,
? [X0] :
( ~ leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero)))
| ~ leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero))) ),
inference(ennf_transformation,[],[f20]) ).
fof(f25,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f26,plain,
( ~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero)))
| ~ leq(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f24]) ).
fof(f27,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f30,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f31,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f36,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f41,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[],[f15]) ).
fof(f45,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
( ~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero)))
| ~ leq(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero))) ),
inference(cnf_transformation,[],[f26]) ).
fof(f47,definition,
sF1 = multiplication(sK0,zero),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f48,plain,
multiplication(sK0,zero) = sF1,
inference(reorient_equations,[],[f47]) ).
fof(f49,definition,
sF2 = strong_iteration(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f50,plain,
strong_iteration(sF1) = sF2,
inference(reorient_equations,[],[f49]) ).
fof(f51,definition,
sF3 = addition(one,sF1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f52,plain,
addition(one,sF1) = sF3,
inference(reorient_equations,[],[f51]) ).
fof(f53,plain,
( ~ leq(sF2,sF3)
| ~ leq(sF3,sF2) ),
inference(definition_folding,[],[f46,f50,f48,f52,f48,f52,f48,f50,f48]) ).
fof(f55,definition,
( spl4_1
<=> leq(sF3,sF2) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f57,plain,
( ~ leq(sF3,sF2)
| spl4_1 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f59,definition,
( spl4_2
<=> leq(sF2,sF3) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f61,plain,
( ~ leq(sF2,sF3)
| spl4_2 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f62,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f53,f59,f55]) ).
fof(f66,plain,
sF3 = addition(sF1,one),
inference(superposition,[],[f52,f27]) ).
fof(f163,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f45,f30]) ).
fof(f167,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f163]) ).
fof(f282,plain,
! [X0] : multiplication(sK0,multiplication(zero,X0)) = multiplication(sF1,X0),
inference(superposition,[],[f31,f48]) ).
fof(f296,plain,
! [X0] : multiplication(sK0,zero) = multiplication(sF1,X0),
inference(forward_demodulation,[],[f282,f36]) ).
fof(f301,plain,
! [X0] : sF1 = multiplication(sF1,X0),
inference(forward_demodulation,[],[f296,f48]) ).
fof(f305,plain,
strong_iteration(sF1) = addition(sF1,one),
inference(superposition,[],[f41,f301]) ).
fof(f320,plain,
strong_iteration(sF1) = sF3,
inference(forward_demodulation,[],[f305,f66]) ).
fof(f323,plain,
sF2 = sF3,
inference(forward_demodulation,[],[f320,f50]) ).
fof(f325,plain,
( ~ leq(sF2,sF2)
| spl4_1 ),
inference(superposition,[],[f57,f323]) ).
fof(f326,plain,
( $false
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f325,f167]) ).
fof(f327,plain,
spl4_1,
inference(avatar_contradiction_clause,[],[f326]) ).
fof(f329,plain,
( ~ leq(sF2,sF2)
| spl4_2 ),
inference(forward_demodulation,[],[f61,f323]) ).
fof(f330,plain,
( $false
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f329,f167]) ).
fof(f331,plain,
spl4_2,
inference(avatar_contradiction_clause,[],[f330]) ).
cnf(s1,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f62]) ).
cnf(s4,plain,
spl4_1,
inference(sat_conversion,[],[f327]) ).
cnf(s5,plain,
spl4_2,
inference(sat_conversion,[],[f331]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5,s4]) ).
fof(f332,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE150+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n017.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 13:08:20 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 5.18/1.78 % (2543536)Detected formulas, will run a generic FOF schedule.
% 5.18/1.78 % (2543637)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=2466579307:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.18/1.78 % (2543643)dis-21_1_sil=8000:lcm=predicate:random_seed=2450070228: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)
% 5.18/1.78 % (2543638)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=3786370020:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.18/1.78 % (2543639)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=298467227:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.18/1.78 % (2543640)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3278871375:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.18/1.78 % (2543643)Refutation not found, incomplete strategy
% 5.18/1.78 % (2543643)------------------------------
% 5.18/1.78 % (2543643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.78 % (2543640)Refutation not found, incomplete strategy
% 5.18/1.78 % (2543640)------------------------------
% 5.18/1.78 % (2543640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.78 % (2543643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.78 % (2543640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.78 % (2543640)CaDiCaL version: 2.1.3
% 5.18/1.78 % (2543643)CaDiCaL version: 2.1.3
% 5.18/1.78 % (2543640)Termination reason: Refutation not found, incomplete strategy
% 5.18/1.78 % (2543640)Time elapsed: 0.002 s
% 5.18/1.78 % (2543643)Termination reason: Refutation not found, incomplete strategy
% 5.18/1.78 % (2543643)Time elapsed: 0.002 s
% 5.18/1.78 % (2543640)Peak memory usage: 88 MB
% 5.18/1.78 % (2543643)Peak memory usage: 88 MB
% 5.18/1.78 % (2543640)Instructions burned: 1 (million)
% 5.18/1.78 % (2543643)Instructions burned: 1 (million)
% 5.18/1.78 % (2543641)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1218695145:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.18/1.78 % (2543642)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2709789715:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.18/1.78 % (2543642)Instruction limit reached!
% 5.18/1.78 % (2543642)------------------------------
% 5.18/1.78 % (2543642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.78 % (2543642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.78 % (2543642)CaDiCaL version: 2.1.3
% 5.18/1.78 % (2543642)Termination reason: Instruction limit
% 5.18/1.78 % (2543642)Termination phase: Saturation
% 5.18/1.78 % (2543642)Time elapsed: 0.081 s
% 5.18/1.78 % (2543642)Peak memory usage: 90 MB
% 5.18/1.78 % (2543642)Instructions burned: 141 (million)
% 5.18/1.78 % (2543641)Instruction limit reached!
% 5.18/1.78 % (2543641)------------------------------
% 5.18/1.78 % (2543641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.78 % (2543641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.78 % (2543641)CaDiCaL version: 2.1.3
% 5.18/1.78 % (2543641)Termination reason: Instruction limit
% 5.18/1.78 % (2543641)Termination phase: Saturation
% 5.18/1.78 % (2543641)Time elapsed: 0.118 s
% 5.18/1.78 % (2543641)Peak memory usage: 89 MB
% 5.18/1.78 % (2543641)Instructions burned: 119 (million)
% 5.18/1.78 % (2543640)------------------------------
% 5.18/1.78 % (2543640)------------------------------
% 5.18/1.78 % (2543643)------------------------------
% 5.18/1.78 % (2543643)------------------------------
% 5.18/1.78 % (2543664)lrs+10_1_sil=8000:sp=occurrence:random_seed=2288150070:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.18/1.78 % (2543665)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1636815107:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.18/1.78 % (2543637)First to succeed.
% 5.18/1.78 % (2543637)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2543536"
% 5.18/1.78 % (2543664)Also succeeded, but the first one will report.
% 5.18/1.78 % (2543665)Instruction limit reached!
% 5.18/1.78 % (2543665)------------------------------
% 5.18/1.78 % (2543665)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.78 % (2543665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.78 % (2543665)CaDiCaL version: 2.1.3
% 5.18/1.78 % (2543665)Termination reason: Instruction limit
% 5.18/1.78 % (2543665)Termination phase: Saturation
% 5.18/1.78 % (2543665)Time elapsed: 0.105 s
% 5.18/1.78 % (2543665)Peak memory usage: 90 MB
% 5.18/1.78 % (2543665)Instructions burned: 157 (million)
% 5.18/1.78 % (2543666)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2947243418:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 5.18/1.78 % (2543667)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=2181006909:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 5.18/1.78 % (2543637)Refutation found. Thanks to Tanya!
% 5.18/1.78 % SZS status Theorem for theBenchmark
% 5.18/1.78 % SZS output start Proof for theBenchmark
% See solution above
% 5.18/1.78 % (2543637)------------------------------
% 5.18/1.78 % (2543637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.78 % (2543637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.78 % (2543637)CaDiCaL version: 2.1.3
% 5.18/1.78 % (2543637)Termination reason: Refutation
% 5.18/1.78 % (2543637)Time elapsed: 0.357 s
% 5.18/1.78 % (2543637)Peak memory usage: 129 MB
% 5.18/1.78 % (2543637)Instructions burned: 959 (million)
% 5.18/1.78 % (2543637)------------------------------
% 5.18/1.78 % (2543637)------------------------------
% 5.18/1.78 % (2543536)Success in time 0.656 s
% 5.18/1.78 % Vampire exiting
%------------------------------------------------------------------------------