%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT171+1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:37:08 PM UTC 2026
% Result : Theorem 0.58s 1.03s
% Output : Refutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 12 unt; 2 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 19 ( 10 ~; 5 |; 1 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 26 ( 26 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f97,axiom,
hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
fof(f98,axiom,
( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p)))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_PW) ).
fof(f322,conjecture,
hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f323,negated_conjecture,
~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p))),
inference(negated_conjecture,[status(cth)],[f322]) ).
fof(f324,plain,
~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p))),
inference(flattening,[],[f323]) ).
fof(f644,plain,
( ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p)))
| ~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e)))))) )
& ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e))))))
| ~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p))) ) ),
inference(nnf_transformation,[],[f98]) ).
fof(f849,plain,
hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e)))))),
inference(cnf_transformation,[],[f97]) ).
fof(f851,plain,
( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p)))
| ~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e)))))) ),
inference(cnf_transformation,[],[f644]) ).
fof(f1182,plain,
~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p))),
inference(cnf_transformation,[],[f324]) ).
fof(f1412,definition,
( spl34_38
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p))) ),
introduced(definition,[new_symbols(definition,[spl34_38])],[avatar_definition]) ).
fof(f1416,definition,
( spl34_39
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e)))))) ),
introduced(definition,[new_symbols(definition,[spl34_39])],[avatar_definition]) ).
fof(f1420,plain,
( ~ spl34_39
| spl34_38 ),
inference(avatar_split_clause,[],[f851,f1412,f1416]) ).
fof(f1421,plain,
spl34_39,
inference(avatar_split_clause,[],[f849,f1416]) ).
fof(f1427,plain,
~ spl34_38,
inference(avatar_split_clause,[],[f1182,f1412]) ).
cnf(s42,plain,
( spl34_38
| ~ spl34_39 ),
inference(sat_conversion,[],[f1420]) ).
cnf(s43,plain,
spl34_39,
inference(sat_conversion,[],[f1421]) ).
cnf(s49,plain,
~ spl34_38,
inference(sat_conversion,[],[f1427]) ).
cnf(s50,plain,
$false,
inference(rat,[],[s42,s43,s49]) ).
fof(f1428,plain,
$false,
inference(avatar_sat_refutation,[],[s50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT171+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 00:00:01 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.58/1.03 % (2145551)Detected formulas, will run a generic FOF schedule.
% 0.58/1.03 % (2145561)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=840058512:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.58/1.03 % (2145561)First to succeed.
% 0.58/1.03 % (2145561)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2145551"
% 0.58/1.03 % (2145556)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=915920383:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.58/1.03 % (2145562)dis-21_1_sil=8000:lcm=predicate:random_seed=3605432928:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.58/1.03 % (2145558)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=3988674932:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.58/1.03 % (2145560)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2642706957:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.58/1.03 % (2145559)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2514393546:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.58/1.03 % (2145557)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=1146194490:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.58/1.03 % (2145559)Refutation not found, incomplete strategy
% 0.58/1.03 % (2145559)------------------------------
% 0.58/1.03 % (2145559)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.58/1.03 % (2145559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/1.03 % (2145559)CaDiCaL version: 2.1.3
% 0.58/1.03 % (2145559)Termination reason: Refutation not found, incomplete strategy
% 0.58/1.03 % (2145559)Time elapsed: 0.007 s
% 0.58/1.03 % (2145559)Peak memory usage: 88 MB
% 0.58/1.03 % (2145559)Instructions burned: 12 (million)
% 0.58/1.03 % (2145562)Also succeeded, but the first one will report.
% 0.58/1.03 % (2145560)Instruction limit reached!
% 0.58/1.03 % (2145560)------------------------------
% 0.58/1.03 % (2145560)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.58/1.03 % (2145560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/1.03 % (2145560)CaDiCaL version: 2.1.3
% 0.58/1.03 % (2145560)Termination reason: Instruction limit
% 0.58/1.03 % (2145560)Termination phase: Saturation
% 0.58/1.03 % (2145560)Time elapsed: 0.062 s
% 0.58/1.03 % (2145560)Peak memory usage: 88 MB
% 0.58/1.03 % (2145560)Instructions burned: 119 (million)
% 0.58/1.03 % (2145561)Refutation found. Thanks to Tanya!
% 0.58/1.03 % SZS status Theorem for theBenchmark
% 0.58/1.03 % SZS output start Proof for theBenchmark
% See solution above
% 0.58/1.03 % (2145561)------------------------------
% 0.58/1.03 % (2145561)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.58/1.03 % (2145561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/1.03 % (2145561)CaDiCaL version: 2.1.3
% 0.58/1.03 % (2145561)Termination reason: Refutation
% 0.58/1.03 % (2145561)Time elapsed: 0.009 s
% 0.58/1.03 % (2145561)Peak memory usage: 90 MB
% 0.58/1.03 % (2145561)Instructions burned: 31 (million)
% 0.58/1.03 % (2145561)------------------------------
% 0.58/1.03 % (2145561)------------------------------
% 0.58/1.03 % (2145551)Success in time 0.323 s
% 0.58/1.03 % Vampire exiting
%------------------------------------------------------------------------------