%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE055+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 11:40:13 AM UTC 2026
% Result : Theorem 4.59s 1.44s
% Output : Refutation 4.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 28 unt; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 36 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
fof(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
fof(f18,conjecture,
! [X0] :
( addition(X0,one) = one
=> addition(X0,domain(X0)) = domain(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f19,negated_conjecture,
~ ! [X0] :
( addition(X0,one) = one
=> addition(X0,domain(X0)) = domain(X0) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0] :
( domain(X0) != addition(X0,domain(X0))
& addition(X0,one) = one ),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
( domain(sK0) != addition(sK0,domain(sK0))
& one = addition(sK0,one) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f20]) ).
fof(f22,plain,
one = addition(sK0,one),
inference(cnf_transformation,[],[f21]) ).
fof(f23,plain,
domain(sK0) != addition(sK0,domain(sK0)),
inference(cnf_transformation,[],[f21]) ).
fof(f26,plain,
! [X0] : one = addition(domain(X0),one),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f31,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f32,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f33,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f34,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f39,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f40,plain,
! [X0] : one = addition(one,domain(X0)),
inference(forward_demodulation,[],[f26,f39]) ).
fof(f41,plain,
one = addition(one,sK0),
inference(forward_demodulation,[],[f22,f39]) ).
fof(f169,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f31,f33]) ).
fof(f204,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f32,f34]) ).
fof(f1388,plain,
! [X0] : multiplication(domain(X0),X0) = multiplication(addition(one,domain(X0)),X0),
inference(superposition,[],[f28,f169]) ).
fof(f1405,plain,
! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0),
inference(forward_demodulation,[],[f1388,f40]) ).
fof(f1422,plain,
! [X0] : multiplication(domain(X0),X0) = X0,
inference(forward_demodulation,[],[f1405,f33]) ).
fof(f1595,plain,
! [X0] : multiplication(X0,one) = addition(X0,multiplication(X0,sK0)),
inference(superposition,[],[f204,f41]) ).
fof(f1668,plain,
! [X0] : addition(X0,multiplication(X0,sK0)) = X0,
inference(forward_demodulation,[],[f1595,f34]) ).
fof(f6076,plain,
domain(sK0) = addition(domain(sK0),sK0),
inference(superposition,[],[f1668,f1422]) ).
fof(f6077,plain,
domain(sK0) = addition(sK0,domain(sK0)),
inference(forward_demodulation,[],[f6076,f39]) ).
fof(f6106,plain,
$false,
inference(forward_subsumption_resolution,[],[f6077,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE055+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n026.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 13:10:26 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 4.59/1.44 % (2837387)Detected formulas, will run a generic FOF schedule.
% 4.59/1.44 % (2837396)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2884439202:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.59/1.44 % (2837392)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=1266451519:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.59/1.44 % (2837394)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=803392189:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.59/1.44 % (2837393)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=1094235458:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.59/1.44 % (2837395)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2021662922:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.59/1.44 % (2837398)dis-21_1_sil=8000:lcm=predicate:random_seed=1171512500: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)
% 4.59/1.44 % (2837397)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=117462297:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.59/1.44 % (2837398)Refutation not found, incomplete strategy
% 4.59/1.44 % (2837398)------------------------------
% 4.59/1.44 % (2837398)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.44 % (2837398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.44 % (2837398)CaDiCaL version: 2.1.3
% 4.59/1.44 % (2837398)Termination reason: Refutation not found, incomplete strategy
% 4.59/1.44 % (2837398)Time elapsed: 0.001 s
% 4.59/1.44 % (2837398)Peak memory usage: 88 MB
% 4.59/1.44 % (2837398)Instructions burned: 1 (million)
% 4.59/1.44 % (2837395)Instruction limit reached!
% 4.59/1.44 % (2837395)------------------------------
% 4.59/1.44 % (2837395)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.44 % (2837395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.44 % (2837395)CaDiCaL version: 2.1.3
% 4.59/1.44 % (2837395)Termination reason: Instruction limit
% 4.59/1.44 % (2837395)Termination phase: Saturation
% 4.59/1.44 % (2837395)Time elapsed: 0.063 s
% 4.59/1.44 % (2837395)Peak memory usage: 88 MB
% 4.59/1.44 % (2837395)Instructions burned: 111 (million)
% 4.59/1.44 % (2837396)Instruction limit reached!
% 4.59/1.44 % (2837396)------------------------------
% 4.59/1.44 % (2837396)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.44 % (2837396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.44 % (2837396)CaDiCaL version: 2.1.3
% 4.59/1.44 % (2837396)Termination reason: Instruction limit
% 4.59/1.44 % (2837396)Termination phase: Saturation
% 4.59/1.44 % (2837396)Time elapsed: 0.066 s
% 4.59/1.44 % (2837396)Peak memory usage: 88 MB
% 4.59/1.44 % (2837396)Instructions burned: 120 (million)
% 4.59/1.44 % (2837397)Instruction limit reached!
% 4.59/1.44 % (2837397)------------------------------
% 4.59/1.44 % (2837397)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.44 % (2837397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.44 % (2837397)CaDiCaL version: 2.1.3
% 4.59/1.44 % (2837397)Termination reason: Instruction limit
% 4.59/1.44 % (2837397)Termination phase: Saturation
% 4.59/1.44 % (2837397)Time elapsed: 0.080 s
% 4.59/1.44 % (2837397)Peak memory usage: 89 MB
% 4.59/1.44 % (2837397)Instructions burned: 140 (million)
% 4.59/1.44 % (2837406)lrs+10_1_sil=8000:sp=occurrence:random_seed=3289534277:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.59/1.44 % (2837407)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2807419008:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.59/1.44 % (2837408)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3228933950:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.59/1.44 % (2837398)------------------------------
% 4.59/1.44 % (2837398)------------------------------
% 4.59/1.44 % (2837407)Instruction limit reached!
% 4.59/1.44 % (2837407)------------------------------
% 4.59/1.44 % (2837407)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.44 % (2837407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.44 % (2837407)CaDiCaL version: 2.1.3
% 4.59/1.44 % (2837407)Termination reason: Instruction limit
% 4.59/1.44 % (2837407)Termination phase: Saturation
% 4.59/1.44 % (2837407)Time elapsed: 0.089 s
% 4.59/1.44 % (2837407)Peak memory usage: 89 MB
% 4.59/1.44 % (2837407)Instructions burned: 157 (million)
% 4.59/1.44 % (2837408)First to succeed.
% 4.59/1.44 % (2837408)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2837387"
% 4.59/1.44 % (2837406)Also succeeded, but the first one will report.
% 4.59/1.44 % (2837412)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=687373511:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 4.59/1.44 % (2837413)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=347396696:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.59/1.44 % (2837413)Also succeeded, but the first one will report.
% 4.59/1.44 % (2837408)Refutation found. Thanks to Tanya!
% 4.59/1.44 % SZS status Theorem for theBenchmark
% 4.59/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 4.59/1.44 % (2837408)------------------------------
% 4.59/1.44 % (2837408)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.44 % (2837408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.44 % (2837408)CaDiCaL version: 2.1.3
% 4.59/1.44 % (2837408)Termination reason: Refutation
% 4.59/1.44 % (2837408)Time elapsed: 0.080 s
% 4.59/1.44 % (2837408)Peak memory usage: 91 MB
% 4.59/1.44 % (2837408)Instructions burned: 203 (million)
% 4.59/1.44 % (2837408)------------------------------
% 4.59/1.44 % (2837408)------------------------------
% 4.59/1.44 % (2837387)Success in time 0.588 s
% 4.59/1.44 % Vampire exiting
%------------------------------------------------------------------------------