%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL784-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 12:00:35 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 7 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-5 aty)
% Number of variables : 13 ( 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f109,axiom,
! [X2,X0,X1] : c_List_Olist_ONil(X0) = c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).
fof(f272,axiom,
! [X0,X1] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X0)),X1),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
fof(f300,axiom,
! [X2,X3,X0,X1] : c_List_Ofoldl(X0,X1,c_List_Olist_ONil(X2),X3,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
fof(f304,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_True_0) ).
fof(f313,axiom,
! [X2,X3,X0,X1] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2),X3) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X2),X3),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__map_0) ).
fof(f362,axiom,
v_rs____ = c_List_Olist_ONil(tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f363,plain,
c_List_Olist_ONil(tc_Lambda_OdB) = v_rs____,
inference(reorient_equations,[],[f362]) ).
fof(f365,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
fof(f366,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f394,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
inference(definition_unfolding,[],[f366,f304]) ).
fof(f401,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
inference(superposition,[],[f394,f363]) ).
fof(f402,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),v_i____),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(forward_demodulation,[],[f401,f313]) ).
fof(f403,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),v_i____),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(forward_demodulation,[],[f402,f109]) ).
fof(f404,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),v_i____))),
inference(forward_demodulation,[],[f403,f300]) ).
fof(f405,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(forward_demodulation,[],[f404,f272]) ).
fof(f406,plain,
$false,
inference(forward_subsumption_resolution,[],[f405,f365]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL784-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n026.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 16:52:57 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.47 % (3058851)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (3058861)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2253093289:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (3058857)% WARNING: option uhcvi not known.
% 0.17/0.47 % (3058861) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3058851-3058861"...
% 0.17/0.47 % (3058856)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4168680708_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (3058861)...printing done.
% 0.17/0.47 % (3058857)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2953297613:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (3058858)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2222833230:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (3058859)dis+10_1_sil=32000:sp=arity:random_seed=2732356369:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (3058860)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3827754832:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (3058861)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (3058861)------------------------------
% 0.17/0.47 % (3058861)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (3058861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (3058861)CaDiCaL version: 2.1.3
% 0.17/0.47 % (3058861)Termination reason: Refutation
% 0.17/0.47 % (3058861)Time elapsed: 0.006 s
% 0.17/0.47 % (3058861)Peak memory usage: 12 MB
% 0.17/0.47 % (3058861)Instructions burned: 17 (million)
% 0.17/0.47 % (3058851)Success in time 0.05 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------