TSTP Solution File: BOO009-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : BOO009-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n010.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 13:43:28 EDT 2023
% Result : Unsatisfiable 0.21s 0.55s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 40 ( 17 unt; 0 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 114 ( 61 ~; 47 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 130 (; 130 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14520,plain,
$false,
inference(unit_resulting_resolution,[],[f19,f2868,f4486,f51]) ).
fof(f51,plain,
! [X0,X1,X6,X4,X5] :
( ~ sP13(X4,X0,X6,X1)
| ~ sP12(X4,X0,X5,X1)
| ~ product(X5,X0,X6) ),
inference(general_splitting,[],[f49,f50_D]) ).
fof(f50,plain,
! [X3,X0,X1,X6,X4] :
( ~ product(X1,X0,X3)
| sum(X3,X4,X6)
| sP13(X4,X0,X6,X1) ),
inference(cnf_transformation,[],[f50_D]) ).
fof(f50_D,plain,
! [X1,X6,X0,X4] :
( ! [X3] :
( ~ product(X1,X0,X3)
| sum(X3,X4,X6) )
<=> ~ sP13(X4,X0,X6,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP13])]) ).
fof(f49,plain,
! [X3,X0,X1,X6,X4,X5] :
( ~ product(X5,X0,X6)
| ~ product(X1,X0,X3)
| sum(X3,X4,X6)
| ~ sP12(X4,X0,X5,X1) ),
inference(general_splitting,[],[f11,f48_D]) ).
fof(f48,plain,
! [X2,X0,X1,X4,X5] :
( ~ product(X2,X0,X4)
| ~ sum(X1,X2,X5)
| sP12(X4,X0,X5,X1) ),
inference(cnf_transformation,[],[f48_D]) ).
fof(f48_D,plain,
! [X1,X5,X0,X4] :
( ! [X2] :
( ~ product(X2,X0,X4)
| ~ sum(X1,X2,X5) )
<=> ~ sP12(X4,X0,X5,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP12])]) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sum(X1,X2,X5)
| ~ product(X5,X0,X6)
| ~ product(X2,X0,X4)
| ~ product(X1,X0,X3)
| sum(X3,X4,X6) ),
file('/export/starexec/sandbox/tmp/tmp.eXoX2FtdY3/Vampire---4.8_8808',distributivity3) ).
fof(f4486,plain,
sP13(additive_identity,y,additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f2,f4129,f50]) ).
fof(f4129,plain,
~ sum(multiply(additive_identity,y),additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f681,f3870,f31]) ).
fof(f31,plain,
! [X0,X1,X6,X4,X5] :
( ~ sP3(X4,X0,X6,X1)
| ~ sP2(X5,X0,X4,X1)
| ~ sum(X5,X0,X6) ),
inference(general_splitting,[],[f29,f30_D]) ).
fof(f30,plain,
! [X3,X0,X1,X6,X4] :
( ~ sum(X1,X0,X3)
| product(X3,X4,X6)
| sP3(X4,X0,X6,X1) ),
inference(cnf_transformation,[],[f30_D]) ).
fof(f30_D,plain,
! [X1,X6,X0,X4] :
( ! [X3] :
( ~ sum(X1,X0,X3)
| product(X3,X4,X6) )
<=> ~ sP3(X4,X0,X6,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP3])]) ).
fof(f29,plain,
! [X3,X0,X1,X6,X4,X5] :
( ~ sum(X1,X0,X3)
| ~ sum(X5,X0,X6)
| product(X3,X4,X6)
| ~ sP2(X5,X0,X4,X1) ),
inference(general_splitting,[],[f15,f28_D]) ).
fof(f28,plain,
! [X2,X0,X1,X4,X5] :
( ~ product(X1,X2,X5)
| ~ sum(X2,X0,X4)
| sP2(X5,X0,X4,X1) ),
inference(cnf_transformation,[],[f28_D]) ).
fof(f28_D,plain,
! [X1,X4,X0,X5] :
( ! [X2] :
( ~ product(X1,X2,X5)
| ~ sum(X2,X0,X4) )
<=> ~ sP2(X5,X0,X4,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).
fof(f15,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sum(X1,X0,X3)
| ~ sum(X5,X0,X6)
| ~ sum(X2,X0,X4)
| ~ product(X1,X2,X5)
| product(X3,X4,X6) ),
file('/export/starexec/sandbox/tmp/tmp.eXoX2FtdY3/Vampire---4.8_8808',distributivity7) ).
fof(f3870,plain,
sP3(y,additive_identity,additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f3853,f949]) ).
fof(f949,plain,
! [X3,X4,X5] :
( sP3(X4,additive_identity,X5,X3)
| product(X3,X4,X5) ),
inference(resolution,[],[f30,f6]) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox/tmp/tmp.eXoX2FtdY3/Vampire---4.8_8808',additive_identity2) ).
fof(f3853,plain,
~ product(additive_identity,y,additive_identity),
inference(unit_resulting_resolution,[],[f3852,f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| product(X1,X0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.eXoX2FtdY3/Vampire---4.8_8808',commutativity_of_multiplication) ).
fof(f3852,plain,
~ product(y,additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f6,f3749,f24]) ).
fof(f24,plain,
! [X2,X0,X1,X4,X5] :
( ~ product(X1,X2,X5)
| ~ sum(X0,X2,X4)
| sP0(X5,X0,X4,X1) ),
inference(cnf_transformation,[],[f24_D]) ).
fof(f24_D,plain,
! [X1,X4,X0,X5] :
( ! [X2] :
( ~ product(X1,X2,X5)
| ~ sum(X0,X2,X4) )
<=> ~ sP0(X5,X0,X4,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP0])]) ).
fof(f3749,plain,
~ sP0(additive_identity,x,x,y),
inference(unit_resulting_resolution,[],[f6,f498,f27]) ).
fof(f27,plain,
! [X0,X1,X6,X4,X5] :
( ~ sP1(X4,X0,X6,X1)
| ~ sP0(X5,X0,X4,X1)
| ~ sum(X0,X5,X6) ),
inference(general_splitting,[],[f25,f26_D]) ).
fof(f26,plain,
! [X3,X0,X1,X6,X4] :
( ~ sum(X0,X1,X3)
| product(X3,X4,X6)
| sP1(X4,X0,X6,X1) ),
inference(cnf_transformation,[],[f26_D]) ).
fof(f26_D,plain,
! [X1,X6,X0,X4] :
( ! [X3] :
( ~ sum(X0,X1,X3)
| product(X3,X4,X6) )
<=> ~ sP1(X4,X0,X6,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).
fof(f25,plain,
! [X3,X0,X1,X6,X4,X5] :
( ~ sum(X0,X1,X3)
| ~ sum(X0,X5,X6)
| product(X3,X4,X6)
| ~ sP0(X5,X0,X4,X1) ),
inference(general_splitting,[],[f13,f24_D]) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sum(X0,X1,X3)
| ~ sum(X0,X5,X6)
| ~ sum(X0,X2,X4)
| ~ product(X1,X2,X5)
| product(X3,X4,X6) ),
file('/export/starexec/sandbox/tmp/tmp.eXoX2FtdY3/Vampire---4.8_8808',distributivity5) ).
fof(f498,plain,
sP1(x,x,x,y),
inference(unit_resulting_resolution,[],[f68,f1,f26]) ).
fof(f1,axiom,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
file('/export/starexec/sandbox/tmp/tmp.eXoX2FtdY3/Vampire---4.8_8808',closure_of_addition) ).
fof(f68,plain,
~ product(add(x,y),x,x),
inference(unit_resulting_resolution,[],[f23,f4]) ).
fof(f23,axiom,
~ product(x,add(x,y),x),
file('/export/starexec/sandbox/tmp/tmp.eXoX2FtdY3/Vampire---4.8_8808',prove_equations) ).
fof(f681,plain,
! [X0,X1] : sP2(multiply(X0,X1),additive_identity,X1,X0),
inference(unit_resulting_resolution,[],[f6,f2,f28]) ).
fof(f2,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/tmp/tmp.eXoX2FtdY3/Vampire---4.8_8808',closure_of_multiplication) ).
fof(f2868,plain,
! [X0] : sP12(additive_identity,X0,inverse(X0),additive_identity),
inference(unit_resulting_resolution,[],[f5,f19,f48]) ).
fof(f5,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox/tmp/tmp.eXoX2FtdY3/Vampire---4.8_8808',additive_identity1) ).
fof(f19,axiom,
! [X0] : product(inverse(X0),X0,additive_identity),
file('/export/starexec/sandbox/tmp/tmp.eXoX2FtdY3/Vampire---4.8_8808',multiplicative_inverse1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO009-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 30 16:04:33 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.41 % (9062)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (9091)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.21/0.42 % (9092)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.21/0.42 % (9094)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.21/0.42 % (9093)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)
% 0.21/0.42 % (9095)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)
% 0.21/0.42 % (9096)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)
% 0.21/0.42 % (9097)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)
% 0.21/0.42 TRYING [1]
% 0.21/0.42 TRYING [2]
% 0.21/0.42 TRYING [3]
% 0.21/0.43 TRYING [1]
% 0.21/0.43 TRYING [2]
% 0.21/0.44 TRYING [3]
% 0.21/0.45 TRYING [4]
% 0.21/0.50 TRYING [4]
% 0.21/0.51 TRYING [5]
% 0.21/0.55 % (9097)First to succeed.
% 0.21/0.55 % (9097)Refutation found. Thanks to Tanya!
% 0.21/0.55 % SZS status Unsatisfiable for Vampire---4
% 0.21/0.55 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.56 % (9097)------------------------------
% 0.21/0.56 % (9097)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.56 % (9097)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.56 % (9097)Termination reason: Refutation
% 0.21/0.56
% 0.21/0.56 % (9097)Memory used [KB]: 4605
% 0.21/0.56 % (9097)Time elapsed: 0.135 s
% 0.21/0.56 % (9097)------------------------------
% 0.21/0.56 % (9097)------------------------------
% 0.21/0.56 % (9062)Success in time 0.193 s
% 0.21/0.56 % Vampire---4.8 exiting
%------------------------------------------------------------------------------