%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE090-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 11:40:18 AM UTC 2026
% Result : Unsatisfiable 6.35s 1.78s
% Output : Refutation 6.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 50 ( 50 unt; 0 def)
% Number of atoms : 50 ( 49 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f4,axiom,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f5,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f6,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f8,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f9,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f10,axiom,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f11,axiom,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
fof(f19,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f20,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(reorient_equations,[],[f19]) ).
fof(f21,axiom,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
fof(f22,plain,
! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(reorient_equations,[],[f21]) ).
fof(f23,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
fof(f24,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(reorient_equations,[],[f23]) ).
fof(f35,negated_conjecture,
addition(sK2_goals_X0,sK1_goals_X1) = sK1_goals_X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f36,plain,
sK1_goals_X1 = addition(sK2_goals_X0,sK1_goals_X1),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) != antidomain(sK2_goals_X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_1) ).
fof(f38,plain,
antidomain(sK2_goals_X0) != addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)),
inference(reorient_equations,[],[f37]) ).
fof(f39,plain,
antidomain(sK2_goals_X0) != addition(antidomain(sK2_goals_X0),antidomain(sK1_goals_X1)),
inference(backward_demodulation,[],[f38,f3]) ).
fof(f40,plain,
! [X0] : one = addition(antidomain(X0),antidomain(antidomain(X0))),
inference(backward_demodulation,[],[f24,f3]) ).
fof(f54,plain,
! [X0,X1] : addition(X1,X0) = addition(X1,addition(X1,X0)),
inference(superposition,[],[f4,f6]) ).
fof(f56,plain,
zero = antidomain(one),
inference(superposition,[],[f8,f20]) ).
fof(f62,plain,
! [X0] : one = addition(antidomain(X0),one),
inference(superposition,[],[f54,f40]) ).
fof(f70,plain,
! [X0] : one = addition(one,antidomain(X0)),
inference(forward_demodulation,[],[f62,f3]) ).
fof(f80,plain,
one = addition(zero,antidomain(zero)),
inference(superposition,[],[f40,f56]) ).
fof(f93,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(multiplication(antidomain(X0),X1),zero),
inference(superposition,[],[f10,f20]) ).
fof(f104,plain,
! [X0,X1] : multiplication(antidomain(X0),X1) = multiplication(antidomain(X0),addition(X1,X0)),
inference(forward_demodulation,[],[f93,f5]) ).
fof(f111,plain,
! [X2,X0,X1] : multiplication(antidomain(multiplication(X1,X0)),multiplication(X1,X2)) = multiplication(antidomain(multiplication(X1,X0)),multiplication(X1,addition(X2,X0))),
inference(superposition,[],[f104,f10]) ).
fof(f114,plain,
multiplication(antidomain(sK1_goals_X1),sK2_goals_X0) = multiplication(antidomain(sK1_goals_X1),sK1_goals_X1),
inference(superposition,[],[f104,f36]) ).
fof(f120,plain,
zero = multiplication(antidomain(sK1_goals_X1),sK2_goals_X0),
inference(forward_demodulation,[],[f114,f20]) ).
fof(f138,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f3,f5]) ).
fof(f140,plain,
one = antidomain(zero),
inference(backward_demodulation,[],[f80,f138]) ).
fof(f148,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f11,f9]) ).
fof(f154,plain,
! [X0,X1] : multiplication(addition(X1,antidomain(X0)),X0) = addition(multiplication(X1,X0),zero),
inference(superposition,[],[f11,f20]) ).
fof(f168,plain,
! [X0,X1] : multiplication(X1,X0) = multiplication(addition(X1,antidomain(X0)),X0),
inference(forward_demodulation,[],[f154,f5]) ).
fof(f178,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,antidomain(antidomain(X1)))) = multiplication(antidomain(multiplication(X0,antidomain(antidomain(X1)))),multiplication(X0,antidomain(antidomain(X1)))),
inference(superposition,[],[f168,f22]) ).
fof(f189,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,antidomain(antidomain(X1)))),
inference(forward_demodulation,[],[f178,f20]) ).
fof(f346,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X1,antidomain(antidomain(X0)))),multiplication(X1,antidomain(X0))) = multiplication(antidomain(multiplication(X1,antidomain(antidomain(X0)))),multiplication(X1,one)),
inference(superposition,[],[f111,f40]) ).
fof(f365,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X1,antidomain(antidomain(X0)))),multiplication(X1,antidomain(X0))) = multiplication(antidomain(multiplication(X1,antidomain(antidomain(X0)))),X1),
inference(forward_demodulation,[],[f346,f8]) ).
fof(f412,plain,
zero = multiplication(antidomain(zero),multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))),
inference(superposition,[],[f189,f120]) ).
fof(f431,plain,
zero = multiplication(one,multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))),
inference(forward_demodulation,[],[f412,f140]) ).
fof(f442,plain,
zero = multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))),
inference(forward_demodulation,[],[f431,f9]) ).
fof(f450,plain,
multiplication(antidomain(zero),multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0))) = multiplication(antidomain(zero),antidomain(sK1_goals_X1)),
inference(superposition,[],[f365,f442]) ).
fof(f465,plain,
multiplication(one,multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0))) = multiplication(one,antidomain(sK1_goals_X1)),
inference(forward_demodulation,[],[f450,f140]) ).
fof(f468,plain,
antidomain(sK1_goals_X1) = multiplication(one,multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0))),
inference(forward_demodulation,[],[f465,f9]) ).
fof(f471,plain,
antidomain(sK1_goals_X1) = multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)),
inference(forward_demodulation,[],[f468,f9]) ).
fof(f857,plain,
addition(antidomain(sK2_goals_X0),antidomain(sK1_goals_X1)) = multiplication(addition(one,antidomain(sK1_goals_X1)),antidomain(sK2_goals_X0)),
inference(superposition,[],[f148,f471]) ).
fof(f859,plain,
addition(antidomain(sK2_goals_X0),antidomain(sK1_goals_X1)) = multiplication(one,antidomain(sK2_goals_X0)),
inference(forward_demodulation,[],[f857,f70]) ).
fof(f864,plain,
antidomain(sK2_goals_X0) = addition(antidomain(sK2_goals_X0),antidomain(sK1_goals_X1)),
inference(forward_demodulation,[],[f859,f9]) ).
fof(f866,plain,
$false,
inference(forward_subsumption_resolution,[],[f864,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE090-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 13:12:46 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 4.45/1.69 % (1663065)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.45/1.69 % (1663112)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2833106564:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.45/1.69 % (1663110)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1053453043:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.45/1.69 % (1663109)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1983620314:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.45/1.69 % (1663111)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3973491100:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.45/1.69 % (1663108)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=3234485163:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.45/1.69 % (1663114)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3398264567:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.45/1.69 % (1663113)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3484401142:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.45/1.69 % (1663112)Instruction limit reached!
% 4.45/1.69 % (1663112)------------------------------
% 4.45/1.69 % (1663112)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.69 % (1663112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.69 % (1663112)CaDiCaL version: 2.1.3
% 4.45/1.69 % (1663112)Termination reason: Instruction limit
% 4.45/1.69 % (1663112)Termination phase: Saturation
% 4.45/1.69 % (1663112)Time elapsed: 0.063 s
% 4.45/1.69 % (1663112)Peak memory usage: 90 MB
% 4.45/1.69 % (1663112)Instructions burned: 184 (million)
% 4.45/1.69 % (1663111)Instruction limit reached!
% 4.45/1.69 % (1663111)------------------------------
% 4.45/1.69 % (1663111)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.69 % (1663111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.69 % (1663111)CaDiCaL version: 2.1.3
% 4.45/1.69 % (1663111)Termination reason: Instruction limit
% 4.45/1.69 % (1663111)Termination phase: Saturation
% 4.45/1.69 % (1663111)Time elapsed: 0.081 s
% 4.45/1.69 % (1663111)Peak memory usage: 89 MB
% 4.45/1.69 % (1663111)Instructions burned: 137 (million)
% 4.45/1.69 % (1663157)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3146688699:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 4.45/1.69 % (1663113)Instruction limit reached!
% 4.45/1.69 % (1663113)------------------------------
% 4.45/1.69 % (1663113)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.69 % (1663113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.69 % (1663113)CaDiCaL version: 2.1.3
% 4.45/1.69 % (1663113)Termination reason: Instruction limit
% 4.45/1.69 % (1663113)Termination phase: Saturation
% 4.45/1.69 % (1663113)Time elapsed: 0.169 s
% 4.45/1.69 % (1663113)Peak memory usage: 91 MB
% 4.45/1.69 % (1663113)Instructions burned: 258 (million)
% 4.45/1.69 % (1663167)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1841644273:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 4.45/1.69 % (1663192)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2816311736:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 4.45/1.69 % (1663192)Instruction limit reached!
% 4.45/1.69 % (1663192)------------------------------
% 4.45/1.69 % (1663192)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.69 % (1663192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.69 % (1663192)CaDiCaL version: 2.1.3
% 4.45/1.69 % (1663192)Termination reason: Instruction limit
% 4.45/1.69 % (1663192)Termination phase: Saturation
% 4.45/1.69 % (1663192)Time elapsed: 0.115 s
% 6.35/1.78 % (1663192)Peak memory usage: 93 MB
% 6.35/1.78 % (1663192)Instructions burned: 216 (million)
% 6.35/1.78 % (1663157)First to succeed.
% 6.35/1.78 % (1663157)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1663065"
% 6.35/1.78 % (1663233)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=911916206:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 6.35/1.78 % (1663114)Instruction limit reached!
% 6.35/1.78 % (1663114)------------------------------
% 6.35/1.78 % (1663114)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.35/1.78 % (1663114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.35/1.78 % (1663114)CaDiCaL version: 2.1.3
% 6.35/1.78 % (1663114)Termination reason: Instruction limit
% 6.35/1.78 % (1663114)Termination phase: Saturation
% 6.35/1.78 % (1663114)Time elapsed: 0.642 s
% 6.35/1.78 % (1663114)Peak memory usage: 100 MB
% 6.35/1.78 % (1663114)Instructions burned: 1188 (million)
% 6.35/1.78 % (1663157)Refutation found. Thanks to Tanya!
% 6.35/1.78 % SZS status Unsatisfiable for theBenchmark
% 6.35/1.78 % SZS output start Proof for theBenchmark
% See solution above
% 6.35/1.78 % (1663157)------------------------------
% 6.35/1.78 % (1663157)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.35/1.78 % (1663157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.35/1.78 % (1663157)CaDiCaL version: 2.1.3
% 6.35/1.78 % (1663157)Termination reason: Refutation
% 6.35/1.78 % (1663157)Time elapsed: 0.407 s
% 6.35/1.78 % (1663157)Peak memory usage: 131 MB
% 6.35/1.78 % (1663157)Instructions burned: 1110 (million)
% 6.35/1.78 % (1663157)------------------------------
% 6.35/1.78 % (1663157)------------------------------
% 6.35/1.78 % (1663065)Success in time 0.829 s
% 6.35/1.78 % Vampire exiting
%------------------------------------------------------------------------------