%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE004+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 : n014.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 11:40:00 AM UTC 2026
% Result : Theorem 3.51s 1.38s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 18 unt; 0 def)
% Number of atoms : 107 ( 52 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 106 ( 46 ~; 42 |; 12 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 51 ( 48 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
fof(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
fof(f13,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_1) ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).
fof(f16,axiom,
! [X0] :
( ~ test(X0)
=> c(X0) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_4) ).
fof(f17,conjecture,
c(zero) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
c(zero) != one,
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
one != c(zero),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0] :
( c(X0) = zero
| test(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f21,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f22,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f21]) ).
fof(f23,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f24,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X2] : complement(X2,X0)
| ~ test(X0) ) ),
inference(rectify,[],[f23]) ).
fof(f25,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( complement(sK0(X0),X0)
| ~ test(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0))],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ( complement(X1,X0)
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0)
| addition(X0,X1) != one )
& ( ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one )
| ~ complement(X1,X0) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X0,X1] :
( ( complement(X1,X0)
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0)
| addition(X0,X1) != one )
& ( ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one )
| ~ complement(X1,X0) ) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
one != c(zero),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f30,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f31,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f32,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f34,plain,
! [X0] :
( zero = c(X0)
| test(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f44,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| test(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f45,plain,
! [X0,X1] :
( addition(X0,X1) = one
| ~ complement(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f46,plain,
! [X0,X1] :
( zero = multiplication(X1,X0)
| ~ complement(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
! [X0,X1] :
( zero != multiplication(X1,X0)
| zero != multiplication(X0,X1)
| complement(X1,X0)
| addition(X0,X1) != one ),
inference(cnf_transformation,[],[f27]) ).
fof(f49,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f35]) ).
fof(f52,plain,
! [X0] :
( test(c(X0))
| ~ test(X0) ),
inference(resolution,[],[f49,f44]) ).
fof(f63,plain,
! [X0] :
( ~ complement(zero,X0)
| one = X0 ),
inference(superposition,[],[f45,f31]) ).
fof(f74,plain,
! [X0] :
( ~ complement(one,X0)
| zero = X0 ),
inference(superposition,[],[f46,f32]) ).
fof(f77,plain,
( one = c(zero)
| ~ test(zero) ),
inference(resolution,[],[f63,f49]) ).
fof(f78,plain,
~ test(zero),
inference(forward_subsumption_resolution,[],[f77,f28]) ).
fof(f135,plain,
( zero = c(one)
| ~ test(one) ),
inference(resolution,[],[f74,f49]) ).
fof(f136,plain,
zero = c(one),
inference(forward_subsumption_resolution,[],[f135,f34]) ).
fof(f175,plain,
( test(zero)
| ~ test(one) ),
inference(superposition,[],[f52,f136]) ).
fof(f177,plain,
~ test(one),
inference(forward_subsumption_resolution,[],[f175,f78]) ).
fof(f228,plain,
! [X0] :
( zero != zero
| zero != multiplication(X0,zero)
| complement(zero,X0)
| addition(X0,zero) != one ),
inference(superposition,[],[f48,f29]) ).
fof(f231,plain,
! [X0] :
( zero != multiplication(X0,zero)
| complement(zero,X0)
| addition(X0,zero) != one ),
inference(trivial_inequality_removal,[],[f228]) ).
fof(f236,plain,
! [X0] :
( complement(zero,X0)
| addition(X0,zero) != one ),
inference(forward_subsumption_resolution,[],[f231,f30]) ).
fof(f241,plain,
! [X0] :
( one != X0
| complement(zero,X0) ),
inference(forward_demodulation,[],[f236,f31]) ).
fof(f243,plain,
complement(zero,one),
inference(equality_resolution,[],[f241]) ).
fof(f246,plain,
test(one),
inference(resolution,[],[f243,f44]) ).
fof(f247,plain,
$false,
inference(forward_subsumption_resolution,[],[f246,f177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE004+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 12:57:46 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.51/1.38 % (795863)Detected formulas, will run a generic FOF schedule.
% 3.51/1.38 % (795869)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=3957926706:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.51/1.38 % (795873)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1978629762:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.51/1.38 % (795871)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1747950721:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.51/1.38 % (795874)dis-21_1_sil=8000:lcm=predicate:random_seed=3525110580: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)
% 3.51/1.38 % (795868)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=1419530097:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.51/1.38 % (795870)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=2968922844:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.51/1.38 % (795872)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1083320132:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.51/1.38 % (795871)Refutation not found, incomplete strategy
% 3.51/1.38 % (795871)------------------------------
% 3.51/1.38 % (795871)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.38 % (795871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.38 % (795871)CaDiCaL version: 2.1.3
% 3.51/1.38 % (795871)Termination reason: Refutation not found, incomplete strategy
% 3.51/1.38 % (795871)Time elapsed: 0.001 s
% 3.51/1.38 % (795871)Peak memory usage: 88 MB
% 3.51/1.38 % (795874)Refutation not found, incomplete strategy
% 3.51/1.38 % (795874)------------------------------
% 3.51/1.38 % (795874)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.38 % (795874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.38 % (795874)CaDiCaL version: 2.1.3
% 3.51/1.38 % (795874)Termination reason: Refutation not found, incomplete strategy
% 3.51/1.38 % (795874)Time elapsed: 0.002 s
% 3.51/1.38 % (795874)Peak memory usage: 88 MB
% 3.51/1.38 % (795874)Instructions burned: 1 (million)
% 3.51/1.38 % (795872)First to succeed.
% 3.51/1.38 % (795872)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-795863"
% 3.51/1.38 % (795873)Also succeeded, but the first one will report.
% 3.51/1.38 % (795874)------------------------------
% 3.51/1.38 % (795874)------------------------------
% 3.51/1.38 % (795871)------------------------------
% 3.51/1.38 % (795871)------------------------------
% 3.51/1.38 % (795872)Refutation found. Thanks to Tanya!
% 3.51/1.38 % SZS status Theorem for theBenchmark
% 3.51/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.38 % (795872)------------------------------
% 3.51/1.38 % (795872)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.38 % (795872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.38 % (795872)CaDiCaL version: 2.1.3
% 3.51/1.38 % (795872)Termination reason: Refutation
% 3.51/1.38 % (795872)Time elapsed: 0.007 s
% 3.51/1.38 % (795872)Peak memory usage: 88 MB
% 3.51/1.38 % (795872)Instructions burned: 8 (million)
% 3.51/1.38 % (795872)------------------------------
% 3.51/1.38 % (795872)------------------------------
% 3.51/1.38 % (795863)Success in time 0.432 s
% 3.51/1.38 % Vampire exiting
%------------------------------------------------------------------------------