%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE114+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 : 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 11:40:22 AM UTC 2026
% Result : Theorem 8.56s 2.45s
% Output : Refutation 8.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 45 unt; 0 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 15 ( 15 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 35 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
fof(f21,axiom,
! [X0] : c(X0) = antidomain(domain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement) ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',forward_diamond) ).
fof(f25,axiom,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',forward_box) ).
fof(f27,conjecture,
! [X0] : forward_box(X0,one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f28,negated_conjecture,
~ ! [X0] : forward_box(X0,one) = one,
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0] : one != forward_box(X0,one),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
one != forward_box(sK0,one),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f29]) ).
fof(f31,plain,
one != forward_box(sK0,one),
inference(cnf_transformation,[],[f30]) ).
fof(f33,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f35,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f36,plain,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
inference(cnf_transformation,[],[f25]) ).
fof(f41,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f46,plain,
! [X0] : c(X0) = antidomain(domain(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f47,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f49,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f52,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f55,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f56,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f57,plain,
! [X0] : c(X0) = antidomain(antidomain(antidomain(X0))),
inference(definition_unfolding,[],[f46,f47]) ).
fof(f61,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f52,f47,f47]) ).
fof(f62,plain,
! [X0,X1] : forward_box(X0,X1) = antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(X0,antidomain(antidomain(antidomain(antidomain(antidomain(X1))))))))))),
inference(definition_unfolding,[],[f36,f57,f61,f57]) ).
fof(f63,plain,
one != antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(antidomain(one))))))))))),
inference(definition_unfolding,[],[f31,f62]) ).
fof(f64,plain,
! [X0] : one = addition(antidomain(X0),antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f33,f41]) ).
fof(f70,plain,
zero = antidomain(one),
inference(superposition,[],[f35,f49]) ).
fof(f71,plain,
one != antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(zero)))))))))),
inference(superposition,[],[f63,f70]) ).
fof(f76,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f56,f41]) ).
fof(f77,plain,
one = addition(zero,antidomain(zero)),
inference(superposition,[],[f64,f70]) ).
fof(f78,plain,
one = antidomain(zero),
inference(forward_demodulation,[],[f77,f76]) ).
fof(f79,plain,
one != antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(one))))))))),
inference(superposition,[],[f71,f78]) ).
fof(f83,plain,
one != antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(zero)))))))),
inference(forward_demodulation,[],[f79,f70]) ).
fof(f84,plain,
one != antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK0,antidomain(one))))))),
inference(forward_demodulation,[],[f83,f78]) ).
fof(f85,plain,
one != antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK0,zero)))))),
inference(forward_demodulation,[],[f84,f70]) ).
fof(f86,plain,
one != antidomain(antidomain(antidomain(antidomain(antidomain(zero))))),
inference(forward_demodulation,[],[f85,f55]) ).
fof(f87,plain,
one != antidomain(antidomain(antidomain(antidomain(one)))),
inference(forward_demodulation,[],[f86,f78]) ).
fof(f88,plain,
one != antidomain(antidomain(antidomain(zero))),
inference(forward_demodulation,[],[f87,f70]) ).
fof(f89,plain,
one != antidomain(antidomain(one)),
inference(forward_demodulation,[],[f88,f78]) ).
fof(f90,plain,
one != antidomain(zero),
inference(forward_demodulation,[],[f89,f70]) ).
fof(f91,plain,
$false,
inference(forward_subsumption_resolution,[],[f90,f78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE114+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 % Computer : n015.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 27 13:14:15 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.47 Running first-order theorem proving
% 0.15/0.47 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
% 8.56/2.45 % (1666253)Detected formulas, will run a generic FOF schedule.
% 8.56/2.45 % (1666259)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=2245224483:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.56/2.45 % (1666258)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=3708372363:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.56/2.45 % (1666263)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2577834773:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.56/2.45 % (1666260)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=309047592:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.56/2.45 % (1666261)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3736101386:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.56/2.45 % (1666261)Refutation not found, incomplete strategy
% 8.56/2.45 % (1666261)------------------------------
% 8.56/2.45 % (1666261)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.56/2.45 % (1666261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.56/2.45 % (1666261)CaDiCaL version: 2.1.3
% 8.56/2.45 % (1666261)Termination reason: Refutation not found, incomplete strategy
% 8.56/2.45 % (1666261)Time elapsed: 0.002 s
% 8.56/2.45 % (1666261)Peak memory usage: 88 MB
% 8.56/2.45 % (1666262)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3257080412:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.56/2.45 % (1666264)dis-21_1_sil=8000:lcm=predicate:random_seed=2510089867: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)
% 8.56/2.45 % (1666264)Refutation not found, incomplete strategy
% 8.56/2.45 % (1666264)------------------------------
% 8.56/2.45 % (1666264)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.56/2.45 % (1666264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.56/2.45 % (1666264)CaDiCaL version: 2.1.3
% 8.56/2.45 % (1666264)Termination reason: Refutation not found, incomplete strategy
% 8.56/2.45 % (1666264)Time elapsed: 0.003 s
% 8.56/2.45 % (1666264)Peak memory usage: 88 MB
% 8.56/2.45 % (1666264)Instructions burned: 1 (million)
% 8.56/2.45 % (1666263)Instruction limit reached!
% 8.56/2.45 % (1666263)------------------------------
% 8.56/2.45 % (1666263)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.56/2.45 % (1666263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.56/2.45 % (1666263)CaDiCaL version: 2.1.3
% 8.56/2.45 % (1666263)Termination reason: Instruction limit
% 8.56/2.45 % (1666263)Termination phase: Saturation
% 8.56/2.45 % (1666263)Time elapsed: 0.126 s
% 8.56/2.45 % (1666263)Peak memory usage: 89 MB
% 8.56/2.45 % (1666263)Instructions burned: 139 (million)
% 8.56/2.45 % (1666262)Instruction limit reached!
% 8.56/2.45 % (1666262)------------------------------
% 8.56/2.45 % (1666262)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.56/2.45 % (1666262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.56/2.45 % (1666262)CaDiCaL version: 2.1.3
% 8.56/2.45 % (1666262)Termination reason: Instruction limit
% 8.56/2.45 % (1666262)Termination phase: Saturation
% 8.56/2.45 % (1666262)Time elapsed: 0.112 s
% 8.56/2.45 % (1666262)Peak memory usage: 88 MB
% 8.56/2.45 % (1666262)Instructions burned: 119 (million)
% 8.56/2.45 % (1666261)------------------------------
% 8.56/2.45 % (1666261)------------------------------
% 8.56/2.45 % (1666272)lrs+10_1_sil=8000:sp=occurrence:random_seed=3760880873:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 8.56/2.45 % (1666273)lrs+10_1_sil=32000:urr=on:br=off:random_seed=985100813:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 8.56/2.45 % (1666264)------------------------------
% 8.56/2.45 % (1666264)------------------------------
% 8.56/2.45 % (1666273)Refutation not found, incomplete strategy
% 8.56/2.45 % (1666273)------------------------------
% 8.56/2.45 % (1666273)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.56/2.45 % (1666273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.56/2.45 % (1666273)CaDiCaL version: 2.1.3
% 8.56/2.45 % (1666273)Termination reason: Refutation not found, incomplete strategy
% 8.56/2.45 % (1666273)Time elapsed: 0.002 s
% 8.56/2.45 % (1666273)Peak memory usage: 88 MB
% 8.56/2.45 % (1666273)Instructions burned: 1 (million)
% 8.56/2.45 % (1666272)First to succeed.
% 8.56/2.45 % (1666272)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1666253"
% 8.56/2.45 % (1666259)Also succeeded, but the first one will report.
% 8.56/2.45 % (1666274)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3228898187:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 8.56/2.45 % (1666274)Also succeeded, but the first one will report.
% 8.56/2.45 % (1666277)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=1513459994:s2a=on:i=248:s2at=1.23:gtg=position_2992 on theBenchmark for (2992ds/248Mi)
% 8.56/2.45 % (1666258)Also succeeded, but the first one will report.
% 8.56/2.45 % (1666272)Refutation found. Thanks to Tanya!
% 8.56/2.45 % SZS status Theorem for theBenchmark
% 8.56/2.45 % SZS output start Proof for theBenchmark
% See solution above
% 8.56/2.45 % (1666272)------------------------------
% 8.56/2.45 % (1666272)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.56/2.45 % (1666272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.56/2.45 % (1666272)CaDiCaL version: 2.1.3
% 8.56/2.45 % (1666272)Termination reason: Refutation
% 8.56/2.45 % (1666272)Time elapsed: 0.006 s
% 8.56/2.45 % (1666272)Peak memory usage: 89 MB
% 8.56/2.45 % (1666272)Instructions burned: 4 (million)
% 8.56/2.45 % (1666272)------------------------------
% 8.56/2.45 % (1666272)------------------------------
% 8.56/2.45 % (1666253)Success in time 1.094 s
% 8.56/2.45 % Vampire exiting
%------------------------------------------------------------------------------