%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE048+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 11:40:45 AM UTC 2026
% Result : Theorem 0.16s 0.51s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 71 ( 40 unt; 1 def)
% Number of atoms : 124 ( 64 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 91 ( 38 ~; 32 |; 12 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 83 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',order) ).
fof(f13,axiom,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
fof(f15,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X1),X2),X1)
=> leq(multiplication(star(X0),X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_induction_left) ).
fof(f18,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(f19,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(f21,conjecture,
! [X0] :
( test(X0)
=> star(X0) = one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f22,negated_conjecture,
~ ! [X0] :
( test(X0)
=> star(X0) = one ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f25,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f27,plain,
? [X0] :
( one != star(X0)
& test(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f28,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f32,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,[],[f18]) ).
fof(f33,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,[],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f25]) ).
fof(f35,plain,
( one != star(sK1)
& test(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f27]) ).
fof(f36,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f37,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f39,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f41,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f42,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f44,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f47,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f28]) ).
fof(f48,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f49,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X0,X1),X2),X1)
| leq(multiplication(star(X0),X2),X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f55,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f33]) ).
fof(f59,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f62,plain,
test(sK1),
inference(cnf_transformation,[],[f35]) ).
fof(f63,plain,
one != star(sK1),
inference(cnf_transformation,[],[f35]) ).
fof(f64,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f59]) ).
fof(f76,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f48,f39]) ).
fof(f81,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f76]) ).
fof(f84,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f55,f64]) ).
fof(f85,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f84,f36]) ).
fof(f91,plain,
! [X0] : star(X0) = addition(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(resolution,[],[f49,f47]) ).
fof(f95,plain,
! [X0] : star(X0) = addition(star(X0),addition(one,multiplication(X0,star(X0)))),
inference(forward_demodulation,[],[f91,f36]) ).
fof(f109,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f37,f39]) ).
fof(f116,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X1,addition(X2,X0)),
inference(superposition,[],[f37,f36]) ).
fof(f200,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f44,f42]) ).
fof(f237,plain,
! [X2,X0,X1] :
( ~ leq(addition(X0,multiplication(X1,X2)),X2)
| leq(multiplication(star(X1),X0),X2) ),
inference(superposition,[],[f51,f36]) ).
fof(f300,plain,
one = addition(sK1,c(sK1)),
inference(resolution,[],[f85,f62]) ).
fof(f381,plain,
one = addition(sK1,one),
inference(superposition,[],[f109,f300]) ).
fof(f393,plain,
one = addition(one,sK1),
inference(forward_demodulation,[],[f381,f36]) ).
fof(f960,plain,
! [X0] : multiplication(one,X0) = addition(X0,multiplication(sK1,X0)),
inference(superposition,[],[f200,f393]) ).
fof(f1033,plain,
! [X0] : addition(X0,multiplication(sK1,X0)) = X0,
inference(forward_demodulation,[],[f960,f42]) ).
fof(f1363,plain,
! [X0] : star(X0) = addition(one,addition(multiplication(X0,star(X0)),star(X0))),
inference(forward_demodulation,[],[f95,f116]) ).
fof(f1364,plain,
! [X0] : star(X0) = addition(one,addition(star(X0),multiplication(X0,star(X0)))),
inference(forward_demodulation,[],[f1363,f36]) ).
fof(f1365,plain,
! [X0] : star(X0) = addition(one,multiplication(addition(one,X0),star(X0))),
inference(forward_demodulation,[],[f1364,f200]) ).
fof(f1376,plain,
star(sK1) = addition(one,multiplication(one,star(sK1))),
inference(superposition,[],[f1365,f393]) ).
fof(f1408,plain,
star(sK1) = addition(one,star(sK1)),
inference(forward_demodulation,[],[f1376,f42]) ).
fof(f1554,definition,
( spl2_26
<=> leq(star(sK1),one) ),
introduced(definition,[new_symbols(definition,[spl2_26])],[avatar_definition]) ).
fof(f1555,plain,
( leq(star(sK1),one)
| ~ spl2_26 ),
inference(avatar_component_clause,[],[f1554]) ).
fof(f1695,plain,
! [X0] :
( ~ leq(X0,X0)
| leq(multiplication(star(sK1),X0),X0) ),
inference(superposition,[],[f237,f1033]) ).
fof(f1709,plain,
! [X0] : leq(multiplication(star(sK1),X0),X0),
inference(forward_subsumption_resolution,[],[f1695,f81]) ).
fof(f1723,plain,
leq(star(sK1),one),
inference(superposition,[],[f1709,f41]) ).
fof(f1728,plain,
spl2_26,
inference(avatar_split_clause,[],[f1723,f1554]) ).
fof(f1729,plain,
( one = addition(star(sK1),one)
| ~ spl2_26 ),
inference(resolution,[],[f1555,f47]) ).
fof(f1730,plain,
( one = addition(one,star(sK1))
| ~ spl2_26 ),
inference(forward_demodulation,[],[f1729,f36]) ).
fof(f1786,plain,
( one = star(sK1)
| ~ spl2_26 ),
inference(superposition,[],[f1730,f1408]) ).
fof(f1826,plain,
( $false
| ~ spl2_26 ),
inference(forward_subsumption_resolution,[],[f1786,f63]) ).
fof(f1827,plain,
~ spl2_26,
inference(avatar_contradiction_clause,[],[f1826]) ).
cnf(s30,plain,
spl2_26,
inference(sat_conversion,[],[f1728]) ).
cnf(s33,plain,
~ spl2_26,
inference(sat_conversion,[],[f1827]) ).
cnf(s36,plain,
$false,
inference(rat,[],[s30,s33]) ).
fof(f1831,plain,
$false,
inference(avatar_sat_refutation,[],[s36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE048+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n007.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 13:03:55 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.51 % (1400343)Will run a generic schedule for satisfiability detection.
% 0.16/0.51 % (1400353)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=74194125:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.51 % (1400349)% WARNING: option uhcvi not known.
% 0.16/0.51 % (1400351)dis+10_1_sil=32000:sp=arity:random_seed=3646720179:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.51 % (1400348)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1373193309_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.51 % (1400349)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3664863246:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.51 % (1400350)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=728596817:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.51 % (1400352)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3836953716:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.51 % (1400354)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1509777783:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.51 % TRYING [1]
% 0.16/0.51 % TRYING [2]
% 0.16/0.51 % TRYING [3]
% 0.16/0.51 % TRYING [4]
% 0.16/0.51 % TRYING [5]
% 0.16/0.51 % (1400353)Instruction limit reached!
% 0.16/0.51 % (1400353)------------------------------
% 0.16/0.51 % (1400353)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.51 % (1400353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.51 % (1400353)CaDiCaL version: 2.1.3
% 0.16/0.51 % (1400353)Termination reason: Instruction limit
% 0.16/0.51 % (1400353)Termination phase: Saturation
% 0.16/0.51 % (1400353)Time elapsed: 0.043 s
% 0.16/0.51 % (1400353)Peak memory usage: 13 MB
% 0.16/0.51 % (1400353)Instructions burned: 132 (million)
% 0.16/0.51 % (1400351) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1400343-1400351"...
% 0.16/0.51 % (1400351)...printing done.
% 0.16/0.51 % (1400351)Refutation found. Thanks to Tanya!
% 0.16/0.51 % SZS status Theorem for theBenchmark
% 0.16/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.51 % (1400351)------------------------------
% 0.16/0.51 % (1400351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.51 % (1400351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.51 % (1400351)CaDiCaL version: 2.1.3
% 0.16/0.51 % (1400351)Termination reason: Refutation
% 0.16/0.51 % (1400351)Time elapsed: 0.042 s
% 0.16/0.51 % (1400351)Peak memory usage: 13 MB
% 0.16/0.51 % (1400351)Instructions burned: 64 (million)
% 0.16/0.51 % (1400343)Success in time 0.082 s
% 0.16/0.51 % Vampire exiting
%------------------------------------------------------------------------------