TSTP Solution File: HEN010-2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : HEN010-2 : 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 : n026.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 15:58:48 EDT 2023
% Result : Unsatisfiable 0.22s 0.55s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of formulae : 45 ( 24 unt; 0 def)
% Number of atoms : 93 ( 3 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 107 ( 59 ~; 43 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 103 (; 103 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8458,plain,
$false,
inference(unit_resulting_resolution,[],[f3715,f7862,f7024,f35]) ).
fof(f35,plain,
! [X2,X0,X1,X7,X5] :
( ~ sP5(X1,X0,X2,X7)
| ~ quotient(X0,X2,X5)
| sP6(X7,X5,X2,X1) ),
inference(cnf_transformation,[],[f35_D]) ).
fof(f35_D,plain,
! [X1,X2,X5,X7] :
( ! [X0] :
( ~ sP5(X1,X0,X2,X7)
| ~ quotient(X0,X2,X5) )
<=> ~ sP6(X7,X5,X2,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP6])]) ).
fof(f7024,plain,
sP5(idQa,identity,idQ_idQa,zero),
inference(unit_resulting_resolution,[],[f20,f12,f33]) ).
fof(f33,plain,
! [X2,X3,X0,X1,X7] :
( ~ quotient(X3,X2,X7)
| ~ quotient(X0,X1,X3)
| sP5(X1,X0,X2,X7) ),
inference(cnf_transformation,[],[f33_D]) ).
fof(f33_D,plain,
! [X7,X2,X0,X1] :
( ! [X3] :
( ~ quotient(X3,X2,X7)
| ~ quotient(X0,X1,X3) )
<=> ~ sP5(X1,X0,X2,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP5])]) ).
fof(f12,axiom,
! [X0] : quotient(X0,X0,zero),
file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',x_divide_x_is_zero) ).
fof(f20,axiom,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',identity_divide_idQa) ).
fof(f7862,plain,
~ sP6(zero,idQa,idQ_idQa,idQa),
inference(unit_resulting_resolution,[],[f21,f5480,f36]) ).
fof(f36,plain,
! [X2,X1,X7,X4,X5] :
( ~ sP6(X7,X5,X2,X1)
| ~ sP4(X5,X4,X7)
| ~ quotient(X1,X2,X4) ),
inference(general_splitting,[],[f34,f35_D]) ).
fof(f34,plain,
! [X2,X0,X1,X7,X4,X5] :
( ~ quotient(X0,X2,X5)
| ~ quotient(X1,X2,X4)
| ~ sP4(X5,X4,X7)
| ~ sP5(X1,X0,X2,X7) ),
inference(general_splitting,[],[f32,f33_D]) ).
fof(f32,plain,
! [X2,X3,X0,X1,X7,X4,X5] :
( ~ quotient(X3,X2,X7)
| ~ quotient(X0,X2,X5)
| ~ quotient(X1,X2,X4)
| ~ quotient(X0,X1,X3)
| ~ sP4(X5,X4,X7) ),
inference(general_splitting,[],[f4,f31_D]) ).
fof(f31,plain,
! [X6,X7,X4,X5] :
( ~ quotient(X5,X4,X6)
| less_equal(X6,X7)
| sP4(X5,X4,X7) ),
inference(cnf_transformation,[],[f31_D]) ).
fof(f31_D,plain,
! [X7,X4,X5] :
( ! [X6] :
( ~ quotient(X5,X4,X6)
| less_equal(X6,X7) )
<=> ~ sP4(X5,X4,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP4])]) ).
fof(f4,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( less_equal(X6,X7)
| ~ quotient(X3,X2,X7)
| ~ quotient(X5,X4,X6)
| ~ quotient(X0,X2,X5)
| ~ quotient(X1,X2,X4)
| ~ quotient(X0,X1,X3) ),
file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',quotient_property) ).
fof(f5480,plain,
sP4(idQa,idQa_Q__idQ_idQa,zero),
inference(unit_resulting_resolution,[],[f2270,f8,f31]) ).
fof(f8,axiom,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',closure) ).
fof(f2270,plain,
~ less_equal(divide(idQa,idQa_Q__idQ_idQa),zero),
inference(unit_resulting_resolution,[],[f13,f1734,f23]) ).
fof(f23,plain,
! [X2,X10,X0,X9] :
( ~ quotient(X0,X2,X10)
| ~ less_equal(X9,X2)
| sP0(X10,X0,X9) ),
inference(cnf_transformation,[],[f23_D]) ).
fof(f23_D,plain,
! [X9,X0,X10] :
( ! [X2] :
( ~ quotient(X0,X2,X10)
| ~ less_equal(X9,X2) )
<=> ~ sP0(X10,X0,X9) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP0])]) ).
fof(f1734,plain,
! [X0] : ~ sP0(idQa,X0,divide(X0,idQa_Q__idQ_idQa)),
inference(unit_resulting_resolution,[],[f101,f8,f24]) ).
fof(f24,plain,
! [X10,X0,X1,X9] :
( ~ sP0(X10,X0,X9)
| ~ quotient(X0,X1,X9)
| less_equal(X10,X1) ),
inference(general_splitting,[],[f15,f23_D]) ).
fof(f15,axiom,
! [X2,X10,X0,X1,X9] :
( ~ less_equal(X9,X2)
| less_equal(X10,X1)
| ~ quotient(X0,X2,X10)
| ~ quotient(X0,X1,X9) ),
file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',xQyLEz_implies_xQzLEy) ).
fof(f101,plain,
~ less_equal(idQa,idQa_Q__idQ_idQa),
inference(unit_resulting_resolution,[],[f22,f70,f6]) ).
fof(f6,axiom,
! [X0,X1] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',less_equal_and_equal) ).
fof(f70,plain,
less_equal(idQa_Q__idQ_idQa,idQa),
inference(unit_resulting_resolution,[],[f21,f3]) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| less_equal(X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',divisor_existence) ).
fof(f22,axiom,
idQa != idQa_Q__idQ_idQa,
file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',prove_idQa_equals_idQa_Q__idQ_idQa) ).
fof(f13,axiom,
! [X0] : quotient(X0,zero,X0),
file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',x_divde_zero_is_x) ).
fof(f21,axiom,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',identity_divide_idQ_idQa) ).
fof(f3715,plain,
quotient(identity,idQ_idQa,idQa),
inference(superposition,[],[f8,f3524]) ).
fof(f3524,plain,
idQa = divide(identity,idQ_idQa),
inference(unit_resulting_resolution,[],[f1820,f3423,f6]) ).
fof(f3423,plain,
less_equal(idQa,divide(identity,idQ_idQa)),
inference(unit_resulting_resolution,[],[f8,f2885,f25]) ).
fof(f25,plain,
! [X2,X10,X0,X9] :
( ~ quotient(X2,X0,X10)
| less_equal(X9,X10)
| sP1(X2,X0,X9) ),
inference(cnf_transformation,[],[f25_D]) ).
fof(f25_D,plain,
! [X9,X0,X2] :
( ! [X10] :
( ~ quotient(X2,X0,X10)
| less_equal(X9,X10) )
<=> ~ sP1(X2,X0,X9) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).
fof(f2885,plain,
~ sP1(identity,idQ_idQa,idQa),
inference(unit_resulting_resolution,[],[f1894,f19,f26]) ).
fof(f26,plain,
! [X2,X0,X1,X9] :
( ~ sP1(X2,X0,X9)
| ~ quotient(X2,X1,X9)
| ~ less_equal(X0,X1) ),
inference(general_splitting,[],[f16,f25_D]) ).
fof(f16,axiom,
! [X2,X10,X0,X1,X9] :
( ~ less_equal(X0,X1)
| less_equal(X9,X10)
| ~ quotient(X2,X0,X10)
| ~ quotient(X2,X1,X9) ),
file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',xLEy_implies_zQyLEzQx) ).
fof(f19,axiom,
quotient(identity,a,idQa),
file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',identity_divide_a) ).
fof(f1894,plain,
less_equal(idQ_idQa,a),
inference(unit_resulting_resolution,[],[f19,f1576,f24]) ).
fof(f1576,plain,
sP0(idQ_idQa,identity,idQa),
inference(unit_resulting_resolution,[],[f54,f20,f23]) ).
fof(f54,plain,
! [X0] : less_equal(X0,X0),
inference(unit_resulting_resolution,[],[f12,f2]) ).
fof(f2,axiom,
! [X0,X1] :
( ~ quotient(X0,X1,zero)
| less_equal(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',less_equal_quotient) ).
fof(f1820,plain,
less_equal(divide(identity,idQ_idQa),idQa),
inference(unit_resulting_resolution,[],[f20,f1552,f24]) ).
fof(f1552,plain,
! [X0,X1] : sP0(divide(X0,X1),X0,X1),
inference(unit_resulting_resolution,[],[f54,f8,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : HEN010-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.37 % Computer : n026.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Wed Aug 30 14:53:36 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.43 % (4102)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (4133)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.22/0.43 % (4132)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.22/0.43 % (4135)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.22/0.43 % (4134)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)
% 0.22/0.43 % (4136)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)
% 0.22/0.43 % (4137)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)
% 0.22/0.43 % (4138)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)
% 0.22/0.43 TRYING [1]
% 0.22/0.44 TRYING [2]
% 0.22/0.44 TRYING [3]
% 0.22/0.44 TRYING [1]
% 0.22/0.44 TRYING [2]
% 0.22/0.44 TRYING [4]
% 0.22/0.45 TRYING [3]
% 0.22/0.45 TRYING [5]
% 0.22/0.46 TRYING [4]
% 0.22/0.48 TRYING [6]
% 0.22/0.51 TRYING [5]
% 0.22/0.55 TRYING [7]
% 0.22/0.55 % (4138)First to succeed.
% 0.22/0.55 % (4138)Refutation found. Thanks to Tanya!
% 0.22/0.55 % SZS status Unsatisfiable for Vampire---4
% 0.22/0.55 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.55 % (4138)------------------------------
% 0.22/0.55 % (4138)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.55 % (4138)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.55 % (4138)Termination reason: Refutation
% 0.22/0.55
% 0.22/0.55 % (4138)Memory used [KB]: 3326
% 0.22/0.55 % (4138)Time elapsed: 0.118 s
% 0.22/0.55 % (4138)------------------------------
% 0.22/0.55 % (4138)------------------------------
% 0.22/0.55 % (4102)Success in time 0.179 s
% 0.22/0.55 % Vampire---4.8 exiting
%------------------------------------------------------------------------------