%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW337+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:30:08 PM UTC 2026
% Result : Theorem 4.29s 1.71s
% Output : Refutation 4.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 8 unt; 1 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 69 ( 29 ~; 20 |; 7 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 56 ( 52 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X2),X1))
=> ( hBOOL(hAPP(X2,X0))
=> hBOOL(hAPP(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate1D) ).
fof(f666,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
<=> hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
fof(f5225,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_G)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f5226,conjecture,
! [X0] :
( ! [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1) )
=> ! [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f5227,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1) )
=> ! [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f5226]) ).
fof(f5228,plain,
~ ! [X0] :
( ! [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1) )
=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X2) ) ),
inference(rectify,[],[f5227]) ).
fof(f5231,plain,
? [X0] :
( ? [X2] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X2)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_ts)) )
& ! [X1] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) ) ),
inference(ennf_transformation,[],[f5228]) ).
fof(f5244,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(X1,X0))
| ~ hBOOL(hAPP(X2,X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X2),X1)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f5245,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(X1,X0))
| ~ hBOOL(hAPP(X2,X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X2),X1)) ),
inference(flattening,[],[f5244]) ).
fof(f5268,plain,
? [X0] :
( ? [X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_ts)) )
& ! [X2] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G)) ) ),
inference(rectify,[],[f5231]) ).
fof(f5269,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,sK0,sK1)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK1),v_ts))
& ! [X2] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,sK0,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f5268]) ).
fof(f5276,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| ~ hBOOL(hAPP(X0,X1)) )
& ( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0)) ) ),
inference(nnf_transformation,[],[f666]) ).
fof(f5277,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_G)),
inference(cnf_transformation,[],[f5225]) ).
fof(f5278,plain,
! [X2] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G))
| c_Hoare__Mirabelle_Otriple__valid(t_a,sK0,X2) ),
inference(cnf_transformation,[],[f5269]) ).
fof(f5279,plain,
hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK1),v_ts)),
inference(cnf_transformation,[],[f5269]) ).
fof(f5280,plain,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,sK0,sK1),
inference(cnf_transformation,[],[f5269]) ).
fof(f5291,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X1,X0))
| ~ hBOOL(hAPP(X2,X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X2),X1)) ),
inference(cnf_transformation,[],[f5245]) ).
fof(f5311,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f5276]) ).
fof(f5312,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f5276]) ).
fof(f5342,plain,
! [X2,X3,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X2),X1))
| sP7(X2,X1) ),
inference(cnf_transformation,[],[f5342_D]) ).
fof(f5342_D,definition,
! [X1,X2] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X2),X1))
<=> ~ sP7(X2,X1) ),
introduced(definition,[new_symbols(definition,[sP7])],[general_splitting_component_introduction]) ).
fof(f5343,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X0))
| hBOOL(hAPP(X1,X0))
| ~ sP7(X2,X1) ),
inference(general_splitting,[],[f5291,f5342_D]) ).
fof(f5346,plain,
hBOOL(hAPP(v_ts,sK1)),
inference(resolution,[],[f5279,f5311]) ).
fof(f5351,plain,
! [X0] :
( hBOOL(hAPP(X0,sK1))
| ~ sP7(v_ts,X0) ),
inference(resolution,[],[f5346,f5343]) ).
fof(f5354,plain,
! [X0] :
( ~ hBOOL(hAPP(v_G,X0))
| c_Hoare__Mirabelle_Otriple__valid(t_a,sK0,X0) ),
inference(resolution,[],[f5278,f5312]) ).
fof(f5380,plain,
sP7(v_ts,v_G),
inference(resolution,[],[f5277,f5342]) ).
fof(f5415,plain,
( c_Hoare__Mirabelle_Otriple__valid(t_a,sK0,sK1)
| ~ sP7(v_ts,v_G) ),
inference(resolution,[],[f5354,f5351]) ).
fof(f5416,plain,
~ sP7(v_ts,v_G),
inference(forward_subsumption_resolution,[],[f5415,f5280]) ).
fof(f5418,plain,
$false,
inference(forward_subsumption_resolution,[],[f5416,f5380]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW337+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n010.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 13:37:32 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.29/1.71 % (1927094)Detected formulas, will run a generic FOF schedule.
% 4.29/1.71 % (1927102)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=660461344:i=141695:sd=1:nm=32:gsp=on:ss=included_2995 on theBenchmark for (2995ds/141695Mi)
% 4.29/1.71 % (1927100)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1670302296:i=141193_2995 on theBenchmark for (2995ds/141193Mi)
% 4.29/1.71 % (1927105)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2845764251:s2a=on:i=139:gtg=position_2995 on theBenchmark for (2995ds/139Mi)
% 4.29/1.71 % (1927101)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2152453930:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2995 on theBenchmark for (2995ds/134677Mi)
% 4.29/1.71 % (1927104)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2171048641:i=119:av=off:ss=axioms_2995 on theBenchmark for (2995ds/119Mi)
% 4.29/1.71 % (1927103)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3062359329:i=109:sd=1:ins=1:gsp=on:ss=axioms_2995 on theBenchmark for (2995ds/109Mi)
% 4.29/1.71 % (1927106)dis-21_1_sil=8000:lcm=predicate:random_seed=3786151737:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2995 on theBenchmark for (2995ds/129Mi)
% 4.29/1.71 % (1927103)First to succeed.
% 4.29/1.71 % (1927103)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1927094"
% 4.29/1.71 % (1927105)Instruction limit reached!
% 4.29/1.71 % (1927105)------------------------------
% 4.29/1.71 % (1927105)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.29/1.71 % (1927105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.71 % (1927105)CaDiCaL version: 2.1.3
% 4.29/1.71 % (1927105)Termination reason: Instruction limit
% 4.29/1.71 % (1927105)Termination phase: SInE selection
% 4.29/1.71 % (1927105)Time elapsed: 0.058 s
% 4.29/1.71 % (1927105)Peak memory usage: 90 MB
% 4.29/1.71 % (1927105)Instructions burned: 140 (million)
% 4.29/1.71 % (1927104)Instruction limit reached!
% 4.29/1.71 % (1927104)------------------------------
% 4.29/1.71 % (1927104)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.29/1.71 % (1927104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.71 % (1927104)CaDiCaL version: 2.1.3
% 4.29/1.71 % (1927104)Termination reason: Instruction limit
% 4.29/1.71 % (1927104)Termination phase: Saturation
% 4.29/1.71 % (1927104)Time elapsed: 0.067 s
% 4.29/1.71 % (1927104)Peak memory usage: 94 MB
% 4.29/1.71 % (1927104)Instructions burned: 120 (million)
% 4.29/1.71 % (1927106)Instruction limit reached!
% 4.29/1.71 % (1927106)------------------------------
% 4.29/1.71 % (1927106)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.29/1.71 % (1927106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.71 % (1927106)CaDiCaL version: 2.1.3
% 4.29/1.71 % (1927106)Termination reason: Instruction limit
% 4.29/1.71 % (1927106)Termination phase: Preprocessing 3
% 4.29/1.71 % (1927106)Time elapsed: 0.095 s
% 4.29/1.71 % (1927106)Peak memory usage: 93 MB
% 4.29/1.71 % (1927106)Instructions burned: 130 (million)
% 4.29/1.71 % (1927114)lrs+10_1_sil=8000:sp=occurrence:random_seed=1985302865:i=285:sd=3:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/285Mi)
% 4.29/1.71 % (1927115)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3938306072:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/157Mi)
% 4.29/1.71 % (1927116)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3601467335:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 4.29/1.71 % (1927103)Refutation found. Thanks to Tanya!
% 4.29/1.71 % SZS status Theorem for theBenchmark
% 4.29/1.71 % SZS output start Proof for theBenchmark
% See solution above
% 4.29/1.71 % (1927103)------------------------------
% 4.29/1.71 % (1927103)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.29/1.71 % (1927103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.71 % (1927103)CaDiCaL version: 2.1.3
% 4.29/1.71 % (1927103)Termination reason: Refutation
% 4.29/1.71 % (1927103)Time elapsed: 0.029 s
% 4.29/1.71 % (1927103)Peak memory usage: 94 MB
% 4.29/1.71 % (1927103)Instructions burned: 38 (million)
% 4.29/1.71 % (1927103)------------------------------
% 4.29/1.71 % (1927103)------------------------------
% 4.29/1.71 % (1927094)Success in time 0.857 s
% 4.29/1.71 % Vampire exiting
%------------------------------------------------------------------------------