TSTP Solution File: KLE025+2 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE025+2 : 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 : n008.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 17:09:06 EDT 2023
% Result : Theorem 0.17s 0.49s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 67 ( 30 unt; 0 def)
% Number of atoms : 158 ( 88 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 143 ( 52 ~; 42 |; 32 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 86 (; 72 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2803,plain,
$false,
inference(trivial_inequality_removal,[],[f2794]) ).
fof(f2794,plain,
multiplication(sK1,sK0) != multiplication(sK1,sK0),
inference(superposition,[],[f223,f2780]) ).
fof(f2780,plain,
multiplication(sK1,sK0) = multiplication(sK1,multiplication(sK0,sK2)),
inference(forward_demodulation,[],[f2779,f54]) ).
fof(f54,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/tmp/tmp.aJTLiMcvhg/Vampire---4.8_7914',multiplicative_right_identity) ).
fof(f2779,plain,
multiplication(sK1,multiplication(sK0,sK2)) = multiplication(sK1,multiplication(sK0,one)),
inference(forward_demodulation,[],[f2764,f72]) ).
fof(f72,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/tmp/tmp.aJTLiMcvhg/Vampire---4.8_7914',multiplicative_associativity) ).
fof(f2764,plain,
multiplication(sK1,multiplication(sK0,sK2)) = multiplication(multiplication(sK1,sK0),one),
inference(superposition,[],[f358,f1501]) ).
fof(f1501,plain,
one = addition(c(sK2),sK2),
inference(backward_demodulation,[],[f1204,f1466]) ).
fof(f1466,plain,
c(sK2) = sK3(sK2),
inference(resolution,[],[f1203,f48]) ).
fof(f48,plain,
test(sK2),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
( multiplication(sK1,sK0) != multiplication(multiplication(sK1,sK0),sK2)
& zero = multiplication(multiplication(sK1,sK0),c(sK2))
& test(sK2)
& test(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f30,f37]) ).
fof(f37,plain,
( ? [X0,X1,X2] :
( multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2)
& zero = multiplication(multiplication(X1,X0),c(X2))
& test(X2)
& test(X1) )
=> ( multiplication(sK1,sK0) != multiplication(multiplication(sK1,sK0),sK2)
& zero = multiplication(multiplication(sK1,sK0),c(sK2))
& test(sK2)
& test(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
? [X0,X1,X2] :
( multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2)
& zero = multiplication(multiplication(X1,X0),c(X2))
& test(X2)
& test(X1) ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
? [X0,X1,X2] :
( multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2)
& zero = multiplication(multiplication(X1,X0),c(X2))
& test(X2)
& test(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( zero = multiplication(multiplication(X1,X0),c(X2))
=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X3,X4,X5] :
( ( test(X5)
& test(X4) )
=> ( zero = multiplication(multiplication(X4,X3),c(X5))
=> multiplication(X4,X3) = multiplication(multiplication(X4,X3),X5) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X3,X4,X5] :
( ( test(X5)
& test(X4) )
=> ( zero = multiplication(multiplication(X4,X3),c(X5))
=> multiplication(X4,X3) = multiplication(multiplication(X4,X3),X5) ) ),
file('/export/starexec/sandbox/tmp/tmp.aJTLiMcvhg/Vampire---4.8_7914',goals) ).
fof(f1203,plain,
( ~ test(sK2)
| c(sK2) = sK3(sK2) ),
inference(resolution,[],[f1169,f62]) ).
fof(f62,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| c(X0) = X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X3,X4] :
( test(X3)
=> ( c(X3) = X4
<=> complement(X3,X4) ) ),
file('/export/starexec/sandbox/tmp/tmp.aJTLiMcvhg/Vampire---4.8_7914',test_3) ).
fof(f1169,plain,
complement(sK2,sK3(sK2)),
inference(trivial_inequality_removal,[],[f1168]) ).
fof(f1168,plain,
( zero != zero
| complement(sK2,sK3(sK2)) ),
inference(forward_demodulation,[],[f1167,f108]) ).
fof(f108,plain,
zero = multiplication(sK3(sK2),sK2),
inference(resolution,[],[f95,f48]) ).
fof(f95,plain,
! [X0] :
( ~ test(X0)
| zero = multiplication(sK3(X0),X0) ),
inference(resolution,[],[f68,f58]) ).
fof(f58,plain,
! [X0] :
( complement(sK3(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( complement(sK3(X0),X0)
| ~ test(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f40,f41]) ).
fof(f41,plain,
! [X0] :
( ? [X2] : complement(X2,X0)
=> complement(sK3(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X2] : complement(X2,X0)
| ~ test(X0) ) ),
inference(rectify,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X3] :
( test(X3)
<=> ? [X4] : complement(X4,X3) ),
file('/export/starexec/sandbox/tmp/tmp.aJTLiMcvhg/Vampire---4.8_7914',test_1) ).
fof(f68,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X1,X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,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,[],[f45]) ).
fof(f45,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,[],[f14]) ).
fof(f14,axiom,
! [X3,X4] :
( complement(X4,X3)
<=> ( one = addition(X3,X4)
& zero = multiplication(X4,X3)
& zero = multiplication(X3,X4) ) ),
file('/export/starexec/sandbox/tmp/tmp.aJTLiMcvhg/Vampire---4.8_7914',test_2) ).
fof(f1167,plain,
( complement(sK2,sK3(sK2))
| zero != multiplication(sK3(sK2),sK2) ),
inference(trivial_inequality_removal,[],[f1166]) ).
fof(f1166,plain,
( one != one
| complement(sK2,sK3(sK2))
| zero != multiplication(sK3(sK2),sK2) ),
inference(forward_demodulation,[],[f1165,f121]) ).
fof(f121,plain,
one = addition(sK2,sK3(sK2)),
inference(resolution,[],[f96,f48]) ).
fof(f96,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,sK3(X0)) ),
inference(resolution,[],[f69,f58]) ).
fof(f69,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f46]) ).
fof(f1165,plain,
( one != addition(sK2,sK3(sK2))
| complement(sK2,sK3(sK2))
| zero != multiplication(sK3(sK2),sK2) ),
inference(forward_demodulation,[],[f1110,f60]) ).
fof(f60,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.aJTLiMcvhg/Vampire---4.8_7914',additive_commutativity) ).
fof(f1110,plain,
( one != addition(sK3(sK2),sK2)
| complement(sK2,sK3(sK2))
| zero != multiplication(sK3(sK2),sK2) ),
inference(trivial_inequality_removal,[],[f1095]) ).
fof(f1095,plain,
( zero != zero
| one != addition(sK3(sK2),sK2)
| complement(sK2,sK3(sK2))
| zero != multiplication(sK3(sK2),sK2) ),
inference(superposition,[],[f70,f105]) ).
fof(f105,plain,
zero = multiplication(sK2,sK3(sK2)),
inference(resolution,[],[f93,f48]) ).
fof(f93,plain,
! [X0] :
( ~ test(X0)
| zero = multiplication(X0,sK3(X0)) ),
inference(resolution,[],[f67,f58]) ).
fof(f67,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f70,plain,
! [X0,X1] :
( zero != multiplication(X1,X0)
| addition(X0,X1) != one
| complement(X1,X0)
| zero != multiplication(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f1204,plain,
one = addition(sK3(sK2),sK2),
inference(resolution,[],[f1169,f69]) ).
fof(f358,plain,
! [X6] : multiplication(multiplication(sK1,sK0),addition(c(sK2),X6)) = multiplication(sK1,multiplication(sK0,X6)),
inference(forward_demodulation,[],[f357,f72]) ).
fof(f357,plain,
! [X6] : multiplication(multiplication(sK1,sK0),addition(c(sK2),X6)) = multiplication(multiplication(sK1,sK0),X6),
inference(forward_demodulation,[],[f304,f76]) ).
fof(f76,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f60,f53]) ).
fof(f53,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/tmp/tmp.aJTLiMcvhg/Vampire---4.8_7914',additive_identity) ).
fof(f304,plain,
! [X6] : multiplication(multiplication(sK1,sK0),addition(c(sK2),X6)) = addition(zero,multiplication(multiplication(sK1,sK0),X6)),
inference(superposition,[],[f73,f49]) ).
fof(f49,plain,
zero = multiplication(multiplication(sK1,sK0),c(sK2)),
inference(cnf_transformation,[],[f38]) ).
fof(f73,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.aJTLiMcvhg/Vampire---4.8_7914',right_distributivity) ).
fof(f223,plain,
multiplication(sK1,sK0) != multiplication(sK1,multiplication(sK0,sK2)),
inference(superposition,[],[f50,f72]) ).
fof(f50,plain,
multiplication(sK1,sK0) != multiplication(multiplication(sK1,sK0),sK2),
inference(cnf_transformation,[],[f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : KLE025+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 30 17:48:02 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.17/0.41 % (8041)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.42 % (8044)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.17/0.42 % (8046)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.17/0.42 % (8043)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.17/0.42 % (8048)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)
% 0.17/0.42 % (8045)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)
% 0.17/0.42 % (8050)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)
% 0.17/0.42 % (8052)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)
% 0.17/0.42 TRYING [1]
% 0.17/0.42 TRYING [2]
% 0.17/0.42 TRYING [3]
% 0.17/0.42 TRYING [1]
% 0.17/0.42 TRYING [2]
% 0.17/0.43 TRYING [4]
% 0.17/0.43 TRYING [3]
% 0.17/0.46 TRYING [5]
% 0.17/0.47 TRYING [4]
% 0.17/0.49 % (8050)First to succeed.
% 0.17/0.49 % (8050)Refutation found. Thanks to Tanya!
% 0.17/0.49 % SZS status Theorem for Vampire---4
% 0.17/0.49 % SZS output start Proof for Vampire---4
% See solution above
% 0.17/0.50 % (8050)------------------------------
% 0.17/0.50 % (8050)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.17/0.50 % (8050)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.17/0.50 % (8050)Termination reason: Refutation
% 0.17/0.50
% 0.17/0.50 % (8050)Memory used [KB]: 2814
% 0.17/0.50 % (8050)Time elapsed: 0.076 s
% 0.17/0.50 % (8050)------------------------------
% 0.17/0.50 % (8050)------------------------------
% 0.17/0.50 % (8041)Success in time 0.137 s
% 0.17/0.50 % Vampire---4.8 exiting
%------------------------------------------------------------------------------