TSTP Solution File: KLE044+2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : KLE044+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 : 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 : Thu Aug 31 05:36:34 EDT 2023
% Result : Theorem 0.23s 0.50s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 68 ( 35 unt; 0 def)
% Number of atoms : 105 ( 41 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 71 ( 34 ~; 28 |; 4 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 80 (; 78 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2538,plain,
$false,
inference(avatar_sat_refutation,[],[f51,f2528,f2537]) ).
fof(f2537,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f2536]) ).
fof(f2536,plain,
( $false
| spl1_2 ),
inference(subsumption_resolution,[],[f2535,f1033]) ).
fof(f1033,plain,
! [X3] : star(addition(one,X3)) = multiplication(star(addition(one,X3)),addition(one,X3)),
inference(superposition,[],[f999,f77]) ).
fof(f77,plain,
! [X2,X3] : addition(X2,X3) = addition(X2,addition(X2,X3)),
inference(superposition,[],[f39,f33]) ).
fof(f33,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/tmp/tmp.tohoSe5oWm/Vampire---4.8_1036',additive_idempotence) ).
fof(f39,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f20]) ).
fof(f20,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/sandbox2/tmp/tmp.tohoSe5oWm/Vampire---4.8_1036',additive_associativity) ).
fof(f999,plain,
! [X15] : star(X15) = multiplication(star(X15),addition(one,X15)),
inference(forward_demodulation,[],[f998,f77]) ).
fof(f998,plain,
! [X15] : star(X15) = multiplication(star(X15),addition(one,addition(one,X15))),
inference(forward_demodulation,[],[f997,f844]) ).
fof(f844,plain,
! [X2,X3] : multiplication(X2,addition(one,X3)) = addition(X2,multiplication(X2,X3)),
inference(superposition,[],[f41,f31]) ).
fof(f31,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/tmp/tmp.tohoSe5oWm/Vampire---4.8_1036',multiplicative_right_identity) ).
fof(f41,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/sandbox2/tmp/tmp.tohoSe5oWm/Vampire---4.8_1036',right_distributivity) ).
fof(f997,plain,
! [X15] : star(X15) = addition(star(X15),multiplication(star(X15),addition(one,X15))),
inference(forward_demodulation,[],[f989,f36]) ).
fof(f36,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/sandbox2/tmp/tmp.tohoSe5oWm/Vampire---4.8_1036',additive_commutativity) ).
fof(f989,plain,
! [X15] : star(X15) = addition(multiplication(star(X15),addition(one,X15)),star(X15)),
inference(superposition,[],[f107,f871]) ).
fof(f871,plain,
! [X0] : star(X0) = addition(one,multiplication(star(X0),addition(one,X0))),
inference(backward_demodulation,[],[f94,f844]) ).
fof(f94,plain,
! [X0] : star(X0) = addition(one,addition(star(X0),multiplication(star(X0),X0))),
inference(backward_demodulation,[],[f74,f92]) ).
fof(f92,plain,
! [X6,X4,X5] : addition(X4,addition(X5,X6)) = addition(X5,addition(X4,X6)),
inference(forward_demodulation,[],[f78,f39]) ).
fof(f78,plain,
! [X6,X4,X5] : addition(X4,addition(X5,X6)) = addition(addition(X5,X4),X6),
inference(superposition,[],[f39,f36]) ).
fof(f74,plain,
! [X0] : star(X0) = addition(star(X0),addition(one,multiplication(star(X0),X0))),
inference(forward_demodulation,[],[f71,f36]) ).
fof(f71,plain,
! [X0] : star(X0) = addition(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(resolution,[],[f35,f37]) ).
fof(f37,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,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/sandbox2/tmp/tmp.tohoSe5oWm/Vampire---4.8_1036',order) ).
fof(f35,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
file('/export/starexec/sandbox2/tmp/tmp.tohoSe5oWm/Vampire---4.8_1036',star_unfold_left) ).
fof(f107,plain,
! [X2,X1] : addition(X2,X1) = addition(X1,addition(X2,X1)),
inference(superposition,[],[f77,f36]) ).
fof(f2535,plain,
( star(addition(one,sK0)) != multiplication(star(addition(one,sK0)),addition(one,sK0))
| spl1_2 ),
inference(forward_demodulation,[],[f2534,f844]) ).
fof(f2534,plain,
( star(addition(one,sK0)) != addition(star(addition(one,sK0)),multiplication(star(addition(one,sK0)),sK0))
| spl1_2 ),
inference(forward_demodulation,[],[f2533,f1001]) ).
fof(f1001,plain,
! [X4,X5] : addition(star(X4),X5) = addition(one,addition(star(X4),X5)),
inference(backward_demodulation,[],[f983,f999]) ).
fof(f983,plain,
! [X4,X5] : addition(one,addition(multiplication(star(X4),addition(one,X4)),X5)) = addition(star(X4),X5),
inference(superposition,[],[f39,f871]) ).
fof(f2533,plain,
( star(addition(one,sK0)) != addition(one,addition(star(addition(one,sK0)),multiplication(star(addition(one,sK0)),sK0)))
| spl1_2 ),
inference(forward_demodulation,[],[f2532,f92]) ).
fof(f2532,plain,
( star(addition(one,sK0)) != addition(star(addition(one,sK0)),addition(one,multiplication(star(addition(one,sK0)),sK0)))
| spl1_2 ),
inference(forward_demodulation,[],[f2531,f36]) ).
fof(f2531,plain,
( star(addition(one,sK0)) != addition(addition(one,multiplication(star(addition(one,sK0)),sK0)),star(addition(one,sK0)))
| spl1_2 ),
inference(resolution,[],[f2529,f38]) ).
fof(f38,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f2529,plain,
( ~ leq(addition(one,multiplication(star(addition(one,sK0)),sK0)),star(addition(one,sK0)))
| spl1_2 ),
inference(resolution,[],[f50,f2515]) ).
fof(f2515,plain,
! [X28,X29] :
( leq(star(X28),X29)
| ~ leq(addition(one,multiplication(X29,X28)),X29) ),
inference(forward_demodulation,[],[f2497,f36]) ).
fof(f2497,plain,
! [X28,X29] :
( leq(star(X28),X29)
| ~ leq(addition(multiplication(X29,X28),one),X29) ),
inference(superposition,[],[f43,f32]) ).
fof(f32,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/tmp/tmp.tohoSe5oWm/Vampire---4.8_1036',multiplicative_left_identity) ).
fof(f43,plain,
! [X2,X0,X1] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,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/sandbox2/tmp/tmp.tohoSe5oWm/Vampire---4.8_1036',star_induction_right) ).
fof(f50,plain,
( ~ leq(star(sK0),star(addition(one,sK0)))
| spl1_2 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f49,plain,
( spl1_2
<=> leq(star(sK0),star(addition(one,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
fof(f2528,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f2527]) ).
fof(f2527,plain,
( $false
| spl1_1 ),
inference(subsumption_resolution,[],[f2524,f33]) ).
fof(f2524,plain,
( star(sK0) != addition(star(sK0),star(sK0))
| spl1_1 ),
inference(resolution,[],[f2522,f38]) ).
fof(f2522,plain,
( ~ leq(star(sK0),star(sK0))
| spl1_1 ),
inference(forward_demodulation,[],[f2521,f999]) ).
fof(f2521,plain,
( ~ leq(multiplication(star(sK0),addition(one,sK0)),star(sK0))
| spl1_1 ),
inference(forward_demodulation,[],[f2519,f1348]) ).
fof(f1348,plain,
! [X38,X37] : multiplication(star(X37),addition(one,X38)) = addition(one,multiplication(star(X37),addition(one,X38))),
inference(superposition,[],[f1001,f844]) ).
fof(f2519,plain,
( ~ leq(addition(one,multiplication(star(sK0),addition(one,sK0))),star(sK0))
| spl1_1 ),
inference(resolution,[],[f2515,f47]) ).
fof(f47,plain,
( ~ leq(star(addition(one,sK0)),star(sK0))
| spl1_1 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f46,plain,
( spl1_1
<=> leq(star(addition(one,sK0)),star(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
fof(f51,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f27,f49,f46]) ).
fof(f27,plain,
( ~ leq(star(sK0),star(addition(one,sK0)))
| ~ leq(star(addition(one,sK0)),star(sK0)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
( ~ leq(star(sK0),star(addition(one,sK0)))
| ~ leq(star(addition(one,sK0)),star(sK0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f21,f24]) ).
fof(f24,plain,
( ? [X0] :
( ~ leq(star(X0),star(addition(one,X0)))
| ~ leq(star(addition(one,X0)),star(X0)) )
=> ( ~ leq(star(sK0),star(addition(one,sK0)))
| ~ leq(star(addition(one,sK0)),star(sK0)) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
? [X0] :
( ~ leq(star(X0),star(addition(one,X0)))
| ~ leq(star(addition(one,X0)),star(X0)) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
~ ! [X0] :
( leq(star(X0),star(addition(one,X0)))
& leq(star(addition(one,X0)),star(X0)) ),
inference(rectify,[],[f18]) ).
fof(f18,negated_conjecture,
~ ! [X3] :
( leq(star(X3),star(addition(one,X3)))
& leq(star(addition(one,X3)),star(X3)) ),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
! [X3] :
( leq(star(X3),star(addition(one,X3)))
& leq(star(addition(one,X3)),star(X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.tohoSe5oWm/Vampire---4.8_1036',goals) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KLE044+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n026.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Aug 29 12:51:50 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.tohoSe5oWm/Vampire---4.8_1036
% 0.15/0.36 % (1204)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.42 % (1206)lrs-11_28_aac=none:afr=on:anc=none:bs=on:drc=off:fde=unused:gs=on:nm=2:nwc=1.3:sp=frequency:stl=188_1092 on Vampire---4 for (1092ds/0Mi)
% 0.23/0.42 % (1205)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_1169 on Vampire---4 for (1169ds/0Mi)
% 0.23/0.42 % (1208)lrs+3_20_av=off:bd=preordered:drc=off:fsd=off:fsr=off:fde=unused:irw=on:lcm=reverse:sos=theory:stl=315_961 on Vampire---4 for (961ds/0Mi)
% 0.23/0.42 % (1209)ott+1003_4:1_av=off:cond=on:drc=off:fsd=off:fsr=off:fde=none:gsp=on:nm=2:nwc=1.5:sos=all:sp=reverse_arity:tgt=full_871 on Vampire---4 for (871ds/0Mi)
% 0.23/0.42 % (1210)lrs-11_32_av=off:bd=off:bs=on:bsr=on:drc=off:flr=on:fsd=off:fsr=off:fde=none:gsp=on:irw=on:lcm=predicate:nm=4:sp=scramble:stl=125_825 on Vampire---4 for (825ds/0Mi)
% 0.23/0.42 % (1207)ott-4_11_av=off:bd=preordered:bce=on:drc=off:flr=on:fsr=off:lma=on:nwc=2.0:sp=occurrence:tgt=ground:urr=ec_only_1010 on Vampire---4 for (1010ds/0Mi)
% 0.23/0.42 % (1211)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_501 on Vampire---4 for (501ds/0Mi)
% 0.23/0.43 % (1209)Refutation not found, incomplete strategy% (1209)------------------------------
% 0.23/0.43 % (1209)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.43 % (1209)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.43 % (1209)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.43
% 0.23/0.43 % (1209)Memory used [KB]: 895
% 0.23/0.43 % (1209)Time elapsed: 0.004 s
% 0.23/0.43 % (1209)------------------------------
% 0.23/0.43 % (1209)------------------------------
% 0.23/0.49 % (1212)ott+4_40_av=off:bce=on:fsd=off:fde=unused:nm=4:nwc=1.1:sos=all:sp=frequency_375 on Vampire---4 for (375ds/0Mi)
% 0.23/0.49 % (1212)Refutation not found, incomplete strategy% (1212)------------------------------
% 0.23/0.49 % (1212)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.49 % (1212)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.49 % (1212)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.49
% 0.23/0.49 % (1212)Memory used [KB]: 895
% 0.23/0.49 % (1212)Time elapsed: 0.004 s
% 0.23/0.49 % (1212)------------------------------
% 0.23/0.49 % (1212)------------------------------
% 0.23/0.50 % (1206)First to succeed.
% 0.23/0.50 % (1206)Refutation found. Thanks to Tanya!
% 0.23/0.50 % SZS status Theorem for Vampire---4
% 0.23/0.50 % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.50 % (1206)------------------------------
% 0.23/0.50 % (1206)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.50 % (1206)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.50 % (1206)Termination reason: Refutation
% 0.23/0.50
% 0.23/0.50 % (1206)Memory used [KB]: 12537
% 0.23/0.50 % (1206)Time elapsed: 0.077 s
% 0.23/0.50 % (1206)------------------------------
% 0.23/0.50 % (1206)------------------------------
% 0.23/0.50 % (1204)Success in time 0.133 s
% 0.23/0.50 % Vampire---4.8 exiting
%------------------------------------------------------------------------------