%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL777-1 : 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 : n005.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 11:56:33 AM UTC 2026
% Result : Unsatisfiable 3.50s 1.47s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of formulae : 5 ( 5 unt; 0 def)
% Number of atoms : 5 ( 1 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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; 8 con; 0-5 aty)
% Number of variables : 3 ( 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f427,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2) = c_List_Ofoldl(c_Lambda_OdB_OApp,X0,c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__last_0) ).
fof(f492,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f495,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f521,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
inference(forward_demodulation,[],[f495,f427]) ).
fof(f523,plain,
$false,
inference(forward_subsumption_resolution,[],[f521,f492]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL777-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n005.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 16:47:47 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 3.50/1.47 % (9165)Input is clausal, will run a generic CNF schedule.
% 3.50/1.47 % (9170)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=73097316:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.50/1.47 % (9175)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=347538867:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.50/1.47 % (9171)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=980833567:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.50/1.47 % (9173)lrs+10_1_sil=8000:sp=occurrence:random_seed=3850624346:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.50/1.47 % (9174)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1722320339:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.50/1.47 % (9176)dis-21_1_sil=8000:lcm=predicate:random_seed=3843517907: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)
% 3.50/1.47 % (9172)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1144008974:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.50/1.47 % (9173)First to succeed.
% 3.50/1.47 % (9173)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-9165"
% 3.50/1.47 % (9175)Also succeeded, but the first one will report.
% 3.50/1.47 % (9176)Instruction limit reached!
% 3.50/1.47 % (9176)------------------------------
% 3.50/1.47 % (9176)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.47 % (9176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.47 % (9176)CaDiCaL version: 2.1.3
% 3.50/1.47 % (9176)Termination reason: Instruction limit
% 3.50/1.47 % (9176)Termination phase: Saturation
% 3.50/1.47 % (9176)Time elapsed: 0.072 s
% 3.50/1.47 % (9176)Peak memory usage: 89 MB
% 3.50/1.47 % (9176)Instructions burned: 119 (million)
% 3.50/1.47 % (9174)Instruction limit reached!
% 3.50/1.47 % (9174)------------------------------
% 3.50/1.47 % (9174)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.47 % (9174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.47 % (9174)CaDiCaL version: 2.1.3
% 3.50/1.47 % (9174)Termination reason: Instruction limit
% 3.50/1.47 % (9174)Termination phase: Saturation
% 3.50/1.47 % (9174)Time elapsed: 0.074 s
% 3.50/1.47 % (9174)Peak memory usage: 88 MB
% 3.50/1.47 % (9174)Instructions burned: 115 (million)
% 3.50/1.47 % (9185)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=483445886: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)
% 3.50/1.47 % (9184)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=386081171:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.50/1.47 % (9184)Also succeeded, but the first one will report.
% 3.50/1.47 % (9185)Also succeeded, but the first one will report.
% 3.50/1.47 % (9173)Refutation found. Thanks to Tanya!
% 3.50/1.47 % SZS status Unsatisfiable for theBenchmark
% 3.50/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.47 % (9173)------------------------------
% 3.50/1.47 % (9173)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.47 % (9173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.47 % (9173)CaDiCaL version: 2.1.3
% 3.50/1.47 % (9173)Termination reason: Refutation
% 3.50/1.47 % (9173)Time elapsed: 0.005 s
% 3.50/1.47 % (9173)Peak memory usage: 88 MB
% 3.50/1.47 % (9173)Instructions burned: 6 (million)
% 3.50/1.47 % (9173)------------------------------
% 3.50/1.47 % (9173)------------------------------
% 3.50/1.47 % (9165)Success in time 0.423 s
% 3.50/1.47 % Vampire exiting
%------------------------------------------------------------------------------