TSTP Solution File: KLE048+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE048+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 17:09:10 EDT 2023
% Result : Theorem 0.12s 0.49s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 67 ( 41 unt; 0 def)
% Number of atoms : 119 ( 59 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 82 ( 30 ~; 23 |; 18 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 90 (; 83 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13050,plain,
$false,
inference(subsumption_resolution,[],[f13049,f45]) ).
fof(f45,plain,
one != star(sK0),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
( one != star(sK0)
& test(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f29,f34]) ).
fof(f34,plain,
( ? [X0] :
( one != star(X0)
& test(X0) )
=> ( one != star(sK0)
& test(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
? [X0] :
( one != star(X0)
& test(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
~ ! [X0] :
( test(X0)
=> one = star(X0) ),
inference(rectify,[],[f22]) ).
fof(f22,negated_conjecture,
~ ! [X3] :
( test(X3)
=> one = star(X3) ),
inference(negated_conjecture,[],[f21]) ).
fof(f21,conjecture,
! [X3] :
( test(X3)
=> one = star(X3) ),
file('/export/starexec/sandbox/tmp/tmp.JNVSkERg7R/Vampire---4.8_12118',goals) ).
fof(f13049,plain,
one = star(sK0),
inference(forward_demodulation,[],[f13047,f11151]) ).
fof(f11151,plain,
one = addition(one,star(sK0)),
inference(superposition,[],[f11148,f57]) ).
fof(f57,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.JNVSkERg7R/Vampire---4.8_12118',additive_commutativity) ).
fof(f11148,plain,
one = addition(star(sK0),one),
inference(unit_resulting_resolution,[],[f11147,f64]) ).
fof(f64,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/tmp/tmp.JNVSkERg7R/Vampire---4.8_12118',order) ).
fof(f11147,plain,
leq(star(sK0),one),
inference(superposition,[],[f11126,f50]) ).
fof(f50,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/tmp/tmp.JNVSkERg7R/Vampire---4.8_12118',multiplicative_left_identity) ).
fof(f11126,plain,
! [X9] : leq(multiplication(X9,star(sK0)),X9),
inference(subsumption_resolution,[],[f11090,f92]) ).
fof(f92,plain,
! [X0] : leq(X0,X0),
inference(unit_resulting_resolution,[],[f51,f65]) ).
fof(f65,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f51,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/tmp/tmp.JNVSkERg7R/Vampire---4.8_12118',additive_idempotence) ).
fof(f11090,plain,
! [X9] :
( ~ leq(X9,X9)
| leq(multiplication(X9,star(sK0)),X9) ),
inference(superposition,[],[f70,f5670]) ).
fof(f5670,plain,
! [X0] : addition(multiplication(X0,sK0),X0) = X0,
inference(unit_resulting_resolution,[],[f5662,f64]) ).
fof(f5662,plain,
! [X58] : leq(multiplication(X58,sK0),X58),
inference(forward_demodulation,[],[f5638,f49]) ).
fof(f49,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/tmp/tmp.JNVSkERg7R/Vampire---4.8_12118',multiplicative_right_identity) ).
fof(f5638,plain,
! [X58] : leq(multiplication(X58,sK0),multiplication(X58,one)),
inference(superposition,[],[f3749,f365]) ).
fof(f365,plain,
one = addition(sK0,one),
inference(superposition,[],[f328,f89]) ).
fof(f89,plain,
one = addition(sK0,sK1(sK0)),
inference(unit_resulting_resolution,[],[f72,f62]) ).
fof(f62,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
( ( complement(X1,X0)
| addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1) )
& ( ( addition(X0,X1) = one
& zero = multiplication(X1,X0)
& zero = multiplication(X0,X1) )
| ~ complement(X1,X0) ) ),
inference(flattening,[],[f41]) ).
fof(f41,plain,
! [X0,X1] :
( ( complement(X1,X0)
| addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1) )
& ( ( addition(X0,X1) = one
& zero = multiplication(X1,X0)
& zero = multiplication(X0,X1) )
| ~ complement(X1,X0) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& zero = multiplication(X1,X0)
& zero = multiplication(X0,X1) ) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X3,X4] :
( complement(X4,X3)
<=> ( one = addition(X3,X4)
& zero = multiplication(X4,X3)
& zero = multiplication(X3,X4) ) ),
file('/export/starexec/sandbox/tmp/tmp.JNVSkERg7R/Vampire---4.8_12118',test_2) ).
fof(f72,plain,
complement(sK1(sK0),sK0),
inference(unit_resulting_resolution,[],[f44,f55]) ).
fof(f55,plain,
! [X0] :
( ~ test(X0)
| complement(sK1(X0),X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( complement(sK1(X0),X0)
| ~ test(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f37,f38]) ).
fof(f38,plain,
! [X0] :
( ? [X2] : complement(X2,X0)
=> complement(sK1(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X2] : complement(X2,X0)
| ~ test(X0) ) ),
inference(rectify,[],[f36]) ).
fof(f36,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X3] :
( test(X3)
<=> ? [X4] : complement(X4,X3) ),
file('/export/starexec/sandbox/tmp/tmp.JNVSkERg7R/Vampire---4.8_12118',test_1) ).
fof(f44,plain,
test(sK0),
inference(cnf_transformation,[],[f35]) ).
fof(f328,plain,
! [X2,X3] : addition(X2,X3) = addition(X2,addition(X2,X3)),
inference(superposition,[],[f66,f51]) ).
fof(f66,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2,X1,X0] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
file('/export/starexec/sandbox/tmp/tmp.JNVSkERg7R/Vampire---4.8_12118',additive_associativity) ).
fof(f3749,plain,
! [X21,X22,X23] : leq(multiplication(X21,X22),multiplication(X21,addition(X22,X23))),
inference(superposition,[],[f352,f68]) ).
fof(f68,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/tmp/tmp.JNVSkERg7R/Vampire---4.8_12118',right_distributivity) ).
fof(f352,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(unit_resulting_resolution,[],[f328,f65]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X0,X1),X2),X0)
| leq(multiplication(X2,star(X1)),X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X1),X2),X0)
=> leq(multiplication(X2,star(X1)),X0) ),
file('/export/starexec/sandbox/tmp/tmp.JNVSkERg7R/Vampire---4.8_12118',star_induction_right) ).
fof(f13047,plain,
star(sK0) = addition(one,star(sK0)),
inference(unit_resulting_resolution,[],[f12916,f64]) ).
fof(f12916,plain,
leq(one,star(sK0)),
inference(superposition,[],[f52,f12288]) ).
fof(f12288,plain,
one = addition(one,multiplication(sK0,star(sK0))),
inference(forward_demodulation,[],[f12185,f378]) ).
fof(f378,plain,
one = addition(one,sK0),
inference(superposition,[],[f365,f57]) ).
fof(f12185,plain,
addition(one,sK0) = addition(one,multiplication(sK0,star(sK0))),
inference(superposition,[],[f1105,f11143]) ).
fof(f11143,plain,
! [X0] : addition(multiplication(X0,star(sK0)),X0) = X0,
inference(unit_resulting_resolution,[],[f11126,f64]) ).
fof(f1105,plain,
! [X1] : addition(one,X1) = addition(one,addition(X1,sK0)),
inference(superposition,[],[f392,f57]) ).
fof(f392,plain,
! [X0] : addition(one,X0) = addition(one,addition(sK0,X0)),
inference(superposition,[],[f66,f378]) ).
fof(f52,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
file('/export/starexec/sandbox/tmp/tmp.JNVSkERg7R/Vampire---4.8_12118',star_unfold_right) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : KLE048+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.08 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.08/0.28 % Computer : n025.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Wed Aug 30 18:00:10 EDT 2023
% 0.08/0.28 % CPUTime :
% 0.12/0.34 % (12301)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.34 % (12316)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.12/0.34 % (12317)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.12/0.34 % (12319)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.12/0.34 % (12318)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.12/0.34 % (12320)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.12/0.34 % (12321)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.12/0.34 % (12322)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.12/0.35 TRYING [1]
% 0.12/0.35 TRYING [2]
% 0.12/0.35 TRYING [3]
% 0.12/0.35 TRYING [1]
% 0.12/0.35 TRYING [2]
% 0.12/0.36 TRYING [4]
% 0.12/0.37 TRYING [3]
% 0.12/0.40 TRYING [5]
% 0.12/0.41 TRYING [4]
% 0.12/0.48 TRYING [6]
% 0.12/0.49 % (12322)First to succeed.
% 0.12/0.49 % (12322)Refutation found. Thanks to Tanya!
% 0.12/0.49 % SZS status Theorem for Vampire---4
% 0.12/0.49 % SZS output start Proof for Vampire---4
% See solution above
% 0.12/0.49 % (12322)------------------------------
% 0.12/0.49 % (12322)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.12/0.49 % (12322)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.12/0.49 % (12322)Termination reason: Refutation
% 0.12/0.49
% 0.12/0.49 % (12322)Memory used [KB]: 4477
% 0.12/0.49 % (12322)Time elapsed: 0.144 s
% 0.12/0.49 % (12322)------------------------------
% 0.12/0.49 % (12322)------------------------------
% 0.12/0.49 % (12301)Success in time 0.204 s
% 0.12/0.49 % Vampire---4.8 exiting
%------------------------------------------------------------------------------