%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL812-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 11:56:42 AM UTC 2026
% Result : Unsatisfiable 0.14s 1.51s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of formulae : 5 ( 4 unt; 0 def)
% Number of atoms : 6 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 4 ( 3 ~; 1 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-5 aty)
% Number of variables : 2 ( 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f709,axiom,
! [X0,X1] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0),X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
fof(f735,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),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),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f736,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),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),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2017,plain,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),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),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(resolution,[],[f709,f736]) ).
fof(f2019,plain,
$false,
inference(forward_subsumption_resolution,[],[f2017,f735]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL812-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 16:53:59 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.14/1.51 % (2249368)Input is clausal, will run a generic CNF schedule.
% 0.14/1.51 % (2249374)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2928791516:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.14/1.51 % (2249378)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1993099379:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.14/1.51 % (2249379)dis-21_1_sil=8000:lcm=predicate:random_seed=3115786002:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 0.14/1.51 % (2249373)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=908579682:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.14/1.51 % (2249376)lrs+10_1_sil=8000:sp=occurrence:random_seed=421289174:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.14/1.51 % (2249375)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2780890255:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.14/1.51 % (2249377)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1392437747:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.14/1.51 % (2249376)First to succeed.
% 0.14/1.51 % (2249376)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2249368"
% 0.14/1.51 % (2249379)Instruction limit reached!
% 0.14/1.51 % (2249379)------------------------------
% 0.14/1.51 % (2249379)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.51 % (2249379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.51 % (2249379)CaDiCaL version: 2.1.3
% 0.14/1.51 % (2249379)Termination reason: Instruction limit
% 0.14/1.51 % (2249379)Termination phase: Saturation
% 0.14/1.51 % (2249379)Time elapsed: 0.067 s
% 0.14/1.51 % (2249379)Peak memory usage: 89 MB
% 0.14/1.51 % (2249379)Instructions burned: 119 (million)
% 0.14/1.51 % (2249377)Instruction limit reached!
% 0.14/1.51 % (2249377)------------------------------
% 0.14/1.51 % (2249377)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.51 % (2249377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.51 % (2249377)CaDiCaL version: 2.1.3
% 0.14/1.51 % (2249377)Termination reason: Instruction limit
% 0.14/1.51 % (2249377)Termination phase: Saturation
% 0.14/1.51 % (2249377)Time elapsed: 0.070 s
% 0.14/1.51 % (2249377)Peak memory usage: 89 MB
% 0.14/1.51 % (2249377)Instructions burned: 115 (million)
% 0.14/1.51 % (2249378)Instruction limit reached!
% 0.14/1.51 % (2249378)------------------------------
% 0.14/1.51 % (2249378)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.51 % (2249378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.51 % (2249378)CaDiCaL version: 2.1.3
% 0.14/1.51 % (2249378)Termination reason: Instruction limit
% 0.14/1.51 % (2249378)Termination phase: Saturation
% 0.14/1.51 % (2249378)Time elapsed: 0.120 s
% 0.14/1.51 % (2249378)Peak memory usage: 90 MB
% 0.14/1.51 % (2249378)Instructions burned: 180 (million)
% 0.14/1.51 % (2249388)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1757789470:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 0.14/1.51 % (2249387)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=169397061:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.14/1.51 % (2249387)Refutation not found, incomplete strategy
% 0.14/1.51 % (2249387)------------------------------
% 0.14/1.51 % (2249387)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.51 % (2249387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.51 % (2249387)CaDiCaL version: 2.1.3
% 0.14/1.51 % (2249387)Termination reason: Refutation not found, incomplete strategy
% 0.14/1.51 % (2249387)Time elapsed: 0.012 s
% 0.14/1.51 % (2249387)Peak memory usage: 88 MB
% 0.14/1.51 % (2249387)Instructions burned: 18 (million)
% 0.14/1.51 % (2249388)Also succeeded, but the first one will report.
% 0.14/1.51 % (2249389)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1502466801:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 0.14/1.51 % (2249376)Refutation found. Thanks to Tanya!
% 0.14/1.51 % SZS status Unsatisfiable for theBenchmark
% 0.14/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/1.51 % (2249376)------------------------------
% 0.14/1.51 % (2249376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.51 % (2249376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.51 % (2249376)CaDiCaL version: 2.1.3
% 0.14/1.51 % (2249376)Termination reason: Refutation
% 0.14/1.51 % (2249376)Time elapsed: 0.039 s
% 0.14/1.51 % (2249376)Peak memory usage: 89 MB
% 0.14/1.51 % (2249376)Instructions burned: 61 (million)
% 0.14/1.51 % (2249376)------------------------------
% 0.14/1.51 % (2249376)------------------------------
% 0.14/1.51 % (2249368)Success in time 0.484 s
% 0.14/1.51 % Vampire exiting
%------------------------------------------------------------------------------