%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE064+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 : n013.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 11:40:14 AM UTC 2026
% Result : Theorem 5.77s 1.93s
% Output : Refutation 5.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 30 unt; 0 def)
% Number of atoms : 38 ( 37 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 40 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
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(f17,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain5) ).
fof(f18,conjecture,
! [X0,X1] :
( addition(domain(X0),domain(X1)) = domain(X1)
=> addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f19,negated_conjecture,
~ ! [X0,X1] :
( addition(domain(X0),domain(X1)) = domain(X1)
=> addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0,X1] :
( multiplication(domain(X1),X0) != addition(X0,multiplication(domain(X1),X0))
& addition(domain(X0),domain(X1)) = domain(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
( multiplication(domain(sK1),sK0) != addition(sK0,multiplication(domain(sK1),sK0))
& domain(sK1) = addition(domain(sK0),domain(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f20]) ).
fof(f22,plain,
domain(sK1) = addition(domain(sK0),domain(sK1)),
inference(cnf_transformation,[],[f21]) ).
fof(f23,plain,
multiplication(domain(sK1),sK0) != addition(sK0,multiplication(domain(sK1),sK0)),
inference(cnf_transformation,[],[f21]) ).
fof(f26,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
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(f33,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f36,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[],[f17]) ).
fof(f38,plain,
! [X0] : one = addition(domain(X0),one),
inference(cnf_transformation,[],[f15]) ).
fof(f40,plain,
domain(sK1) = domain(addition(sK0,sK1)),
inference(forward_demodulation,[],[f22,f36]) ).
fof(f50,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f31,f33]) ).
fof(f97,plain,
! [X0] : one = addition(one,domain(X0)),
inference(superposition,[],[f26,f38]) ).
fof(f130,plain,
! [X0] : multiplication(domain(X0),X0) = multiplication(addition(one,domain(X0)),X0),
inference(superposition,[],[f28,f50]) ).
fof(f134,plain,
multiplication(domain(sK1),sK0) != multiplication(addition(one,domain(sK1)),sK0),
inference(superposition,[],[f23,f50]) ).
fof(f135,plain,
multiplication(domain(sK1),sK0) != multiplication(one,sK0),
inference(forward_demodulation,[],[f134,f97]) ).
fof(f137,plain,
! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0),
inference(forward_demodulation,[],[f130,f97]) ).
fof(f141,plain,
sK0 != multiplication(domain(sK1),sK0),
inference(forward_demodulation,[],[f135,f33]) ).
fof(f142,plain,
! [X0] : multiplication(domain(X0),X0) = X0,
inference(forward_demodulation,[],[f137,f33]) ).
fof(f154,plain,
! [X0,X1] : addition(X0,multiplication(X1,X0)) = multiplication(addition(domain(X0),X1),X0),
inference(superposition,[],[f31,f142]) ).
fof(f155,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = multiplication(addition(domain(X0),X1),X0),
inference(forward_demodulation,[],[f154,f50]) ).
fof(f1030,plain,
! [X0,X1] : multiplication(domain(addition(X0,X1)),X0) = multiplication(addition(one,domain(X1)),X0),
inference(superposition,[],[f155,f36]) ).
fof(f1087,plain,
! [X0,X1] : multiplication(one,X0) = multiplication(domain(addition(X0,X1)),X0),
inference(forward_demodulation,[],[f1030,f97]) ).
fof(f1099,plain,
! [X0,X1] : multiplication(domain(addition(X0,X1)),X0) = X0,
inference(forward_demodulation,[],[f1087,f33]) ).
fof(f1136,plain,
sK0 = multiplication(domain(sK1),sK0),
inference(superposition,[],[f1099,f40]) ).
fof(f1165,plain,
$false,
inference(forward_subsumption_resolution,[],[f1136,f141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE064+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.52 % Computer : n013.cluster.edu
% 0.10/0.52 % Model : x86_64 x86_64
% 0.10/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.52 % Memory : 8046.5625MB
% 0.10/0.52 % OS : Linux 6.8.0-71-generic
% 0.10/0.52 % CPULimit : 300
% 0.10/0.52 % WCLimit : 300
% 0.10/0.52 % DateTime : Sun Sep 27 13:08:07 UTC 2026
% 0.10/0.52 % CPUTime :
% 0.10/0.52 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.56 Running first-order theorem proving
% 0.14/0.56 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
% 5.77/1.93 % (212830)Detected formulas, will run a generic FOF schedule.
% 5.77/1.93 % (212836)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=4062269940:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.77/1.93 % (212838)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1719038796:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.77/1.93 % (212840)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=70993265:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.77/1.93 % (212835)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=3813778650:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.77/1.93 % (212837)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=3719347346:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.77/1.93 % (212841)dis-21_1_sil=8000:lcm=predicate:random_seed=2297728963: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)
% 5.77/1.93 % (212839)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1519035708:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.77/1.93 % (212841)Refutation not found, incomplete strategy
% 5.77/1.93 % (212841)------------------------------
% 5.77/1.93 % (212841)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.77/1.93 % (212841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/1.93 % (212841)CaDiCaL version: 2.1.3
% 5.77/1.93 % (212841)Termination reason: Refutation not found, incomplete strategy
% 5.77/1.93 % (212841)Time elapsed: 0.001 s
% 5.77/1.93 % (212841)Peak memory usage: 88 MB
% 5.77/1.93 % (212841)Instructions burned: 1 (million)
% 5.77/1.93 % (212839)Instruction limit reached!
% 5.77/1.93 % (212839)------------------------------
% 5.77/1.93 % (212839)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.77/1.93 % (212839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/1.93 % (212839)CaDiCaL version: 2.1.3
% 5.77/1.93 % (212839)Termination reason: Instruction limit
% 5.77/1.93 % (212839)Termination phase: Saturation
% 5.77/1.93 % (212839)Time elapsed: 0.065 s
% 5.77/1.93 % (212839)Peak memory usage: 88 MB
% 5.77/1.93 % (212839)Instructions burned: 120 (million)
% 5.77/1.93 % (212838)Instruction limit reached!
% 5.77/1.93 % (212838)------------------------------
% 5.77/1.93 % (212838)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.77/1.93 % (212838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/1.93 % (212838)CaDiCaL version: 2.1.3
% 5.77/1.93 % (212838)Termination reason: Instruction limit
% 5.77/1.93 % (212838)Termination phase: Saturation
% 5.77/1.93 % (212838)Time elapsed: 0.067 s
% 5.77/1.93 % (212838)Peak memory usage: 89 MB
% 5.77/1.93 % (212838)Instructions burned: 110 (million)
% 5.77/1.93 % (212840)Instruction limit reached!
% 5.77/1.93 % (212840)------------------------------
% 5.77/1.93 % (212840)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.77/1.93 % (212840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/1.93 % (212840)CaDiCaL version: 2.1.3
% 5.77/1.93 % (212840)Termination reason: Instruction limit
% 5.77/1.93 % (212840)Termination phase: Saturation
% 5.77/1.93 % (212840)Time elapsed: 0.079 s
% 5.77/1.93 % (212840)Peak memory usage: 89 MB
% 5.77/1.93 % (212840)Instructions burned: 139 (million)
% 5.77/1.93 % (212850)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1075078531:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.77/1.93 % (212849)lrs+10_1_sil=8000:sp=occurrence:random_seed=2799172766:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.77/1.93 % (212851)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1488475269:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.77/1.93 % (212841)------------------------------
% 5.77/1.93 % (212841)------------------------------
% 5.77/1.93 % (212850)Instruction limit reached!
% 5.77/1.93 % (212850)------------------------------
% 5.77/1.93 % (212850)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.77/1.93 % (212850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/1.93 % (212850)CaDiCaL version: 2.1.3
% 5.77/1.93 % (212850)Termination reason: Instruction limit
% 5.77/1.93 % (212850)Termination phase: Saturation
% 5.77/1.93 % (212850)Time elapsed: 0.091 s
% 5.77/1.93 % (212850)Peak memory usage: 89 MB
% 5.77/1.93 % (212850)Instructions burned: 157 (million)
% 5.77/1.93 % (212836)First to succeed.
% 5.77/1.93 % (212836)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-212830"
% 5.77/1.93 % (212849)Instruction limit reached!
% 5.77/1.93 % (212849)------------------------------
% 5.77/1.93 % (212849)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.77/1.93 % (212849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/1.93 % (212849)CaDiCaL version: 2.1.3
% 5.77/1.93 % (212849)Termination reason: Instruction limit
% 5.77/1.93 % (212849)Termination phase: Saturation
% 5.77/1.93 % (212849)Time elapsed: 0.171 s
% 5.77/1.93 % (212849)Peak memory usage: 90 MB
% 5.77/1.93 % (212849)Instructions burned: 286 (million)
% 5.77/1.93 % (212855)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=2816880709:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 5.77/1.93 % (212851)Instruction limit reached!
% 5.77/1.93 % (212851)------------------------------
% 5.77/1.93 % (212851)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.77/1.93 % (212851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/1.93 % (212851)CaDiCaL version: 2.1.3
% 5.77/1.93 % (212851)Termination reason: Instruction limit
% 5.77/1.93 % (212851)Termination phase: Saturation
% 5.77/1.93 % (212851)Time elapsed: 0.195 s
% 5.77/1.93 % (212851)Peak memory usage: 91 MB
% 5.77/1.93 % (212851)Instructions burned: 325 (million)
% 5.77/1.93 % (212856)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4159378440:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.77/1.93 % (212857)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4161891910:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.77/1.93 % (212836)Refutation found. Thanks to Tanya!
% 5.77/1.93 % SZS status Theorem for theBenchmark
% 5.77/1.93 % SZS output start Proof for theBenchmark
% See solution above
% 5.77/1.93 % (212836)------------------------------
% 5.77/1.93 % (212836)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.77/1.93 % (212836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/1.93 % (212836)CaDiCaL version: 2.1.3
% 5.77/1.93 % (212836)Termination reason: Refutation
% 5.77/1.93 % (212836)Time elapsed: 0.430 s
% 5.77/1.93 % (212836)Peak memory usage: 130 MB
% 5.77/1.93 % (212836)Instructions burned: 1060 (million)
% 5.77/1.93 % (212836)------------------------------
% 5.77/1.93 % (212836)------------------------------
% 5.77/1.93 % (212830)Success in time 0.728 s
% 5.77/1.93 % Vampire exiting
%------------------------------------------------------------------------------