%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL830-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 11:56:47 AM UTC 2026
% Result : Unsatisfiable 4.85s 1.67s
% Output : Refutation 4.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 8 ( 8 unt; 0 def)
% Number of atoms : 8 ( 2 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-5 aty)
% Number of variables : 11 ( 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f567,axiom,
! [X2,X3,X0,X1,X4] : c_List_Omap(X0,c_List_Olist_OCons(X1,X2,X3),X3,X4) = c_List_Olist_OCons(hAPP(X0,X1),c_List_Omap(X0,X2,X3,X4),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).
fof(f572,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),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),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f573,negated_conjecture,
~ c_List_Olistsp(c_InductTermi_OIT,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_OCons(v_a____,v_as____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f601,axiom,
! [X2,X3,X0,X1,X4,X5] : hAPP(c_COMBC(X0,X1,X2,X3,X4),X5) = hAPP(hAPP(X0,X5),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
fof(f606,plain,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(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_a____),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),
inference(forward_demodulation,[],[f573,f567]) ).
fof(f607,plain,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_a____),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),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
inference(forward_demodulation,[],[f606,f601]) ).
fof(f608,plain,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),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),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
inference(forward_demodulation,[],[f607,f601]) ).
fof(f609,plain,
$false,
inference(forward_subsumption_resolution,[],[f608,f572]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL830-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n007.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 16:56:10 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 4.85/1.67 % (1651438)Input is clausal, will run a generic CNF schedule.
% 4.85/1.67 % (1651447)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2427450984:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.85/1.67 % (1651445)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2957403959:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.85/1.67 % (1651443)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=3724109162:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.85/1.67 % (1651444)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3512068685:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.85/1.67 % (1651446)lrs+10_1_sil=8000:sp=occurrence:random_seed=3394811003:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.85/1.67 % (1651447)Instruction limit reached!
% 4.85/1.67 % (1651447)------------------------------
% 4.85/1.67 % (1651447)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.67 % (1651447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.67 % (1651447)CaDiCaL version: 2.1.3
% 4.85/1.67 % (1651447)Termination reason: Instruction limit
% 4.85/1.67 % (1651447)Termination phase: Saturation
% 4.85/1.67 % (1651447)Time elapsed: 0.039 s
% 4.85/1.67 % (1651447)Peak memory usage: 89 MB
% 4.85/1.67 % (1651447)Instructions burned: 115 (million)
% 4.85/1.67 % (1651449)dis-21_1_sil=8000:lcm=predicate:random_seed=1319248110: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)
% 4.85/1.67 % (1651448)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=526596655:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.85/1.67 % (1651446)Instruction limit reached!
% 4.85/1.67 % (1651446)------------------------------
% 4.85/1.67 % (1651446)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.67 % (1651446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.67 % (1651446)CaDiCaL version: 2.1.3
% 4.85/1.67 % (1651446)Termination reason: Instruction limit
% 4.85/1.67 % (1651446)Termination phase: Saturation
% 4.85/1.67 % (1651446)Time elapsed: 0.070 s
% 4.85/1.67 % (1651446)Peak memory usage: 88 MB
% 4.85/1.67 % (1651446)Instructions burned: 107 (million)
% 4.85/1.67 % (1651449)Instruction limit reached!
% 4.85/1.67 % (1651449)------------------------------
% 4.85/1.67 % (1651449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.67 % (1651449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.67 % (1651449)CaDiCaL version: 2.1.3
% 4.85/1.67 % (1651449)Termination reason: Instruction limit
% 4.85/1.67 % (1651449)Termination phase: Saturation
% 4.85/1.67 % (1651449)Time elapsed: 0.063 s
% 4.85/1.67 % (1651449)Peak memory usage: 89 MB
% 4.85/1.67 % (1651449)Instructions burned: 117 (million)
% 4.85/1.67 % (1651455)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=3343480034:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 4.85/1.67 % (1651455)Refutation not found, incomplete strategy
% 4.85/1.67 % (1651455)------------------------------
% 4.85/1.67 % (1651455)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.67 % (1651455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.67 % (1651455)CaDiCaL version: 2.1.3
% 4.85/1.67 % (1651455)Termination reason: Refutation not found, incomplete strategy
% 4.85/1.67 % (1651455)Time elapsed: 0.003 s
% 4.85/1.67 % (1651455)Peak memory usage: 88 MB
% 4.85/1.67 % (1651455)Instructions burned: 7 (million)
% 4.85/1.67 % (1651448)Instruction limit reached!
% 4.85/1.67 % (1651448)------------------------------
% 4.85/1.67 % (1651448)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.67 % (1651448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.67 % (1651448)CaDiCaL version: 2.1.3
% 4.85/1.67 % (1651448)Termination reason: Instruction limit
% 4.85/1.67 % (1651448)Termination phase: Saturation
% 4.85/1.67 % (1651448)Time elapsed: 0.124 s
% 4.85/1.67 % (1651448)Peak memory usage: 90 MB
% 4.85/1.67 % (1651448)Instructions burned: 180 (million)
% 4.85/1.67 % (1651458)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3393076155: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)
% 4.85/1.67 % (1651459)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2351449944:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.85/1.67 % (1651459)First to succeed.
% 4.85/1.67 % (1651459)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1651438"
% 4.85/1.67 % (1651455)------------------------------
% 4.85/1.67 % (1651455)------------------------------
% 4.85/1.67 % (1651461)lrs+10_64_to=lpo:sil=8000:random_seed=919649563:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 4.85/1.67 % (1651458)Instruction limit reached!
% 4.85/1.67 % (1651458)------------------------------
% 4.85/1.67 % (1651458)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.67 % (1651458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.67 % (1651458)CaDiCaL version: 2.1.3
% 4.85/1.67 % (1651458)Termination reason: Instruction limit
% 4.85/1.67 % (1651458)Termination phase: Saturation
% 4.85/1.67 % (1651458)Time elapsed: 0.105 s
% 4.85/1.67 % (1651458)Peak memory usage: 89 MB
% 4.85/1.67 % (1651458)Instructions burned: 190 (million)
% 4.85/1.67 % (1651464)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=508006289:avsq=on:i=194:fgj=on:bd=preordered_2996 on theBenchmark for (2996ds/194Mi)
% 4.85/1.67 % (1651461)Instruction limit reached!
% 4.85/1.67 % (1651461)------------------------------
% 4.85/1.67 % (1651461)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.67 % (1651461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.67 % (1651461)CaDiCaL version: 2.1.3
% 4.85/1.67 % (1651461)Termination reason: Instruction limit
% 4.85/1.67 % (1651461)Termination phase: Saturation
% 4.85/1.67 % (1651461)Time elapsed: 0.080 s
% 4.85/1.67 % (1651461)Peak memory usage: 89 MB
% 4.85/1.67 % (1651461)Instructions burned: 126 (million)
% 4.85/1.67 % (1651464)Instruction limit reached!
% 4.85/1.67 % (1651464)------------------------------
% 4.85/1.67 % (1651464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.67 % (1651464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.67 % (1651464)CaDiCaL version: 2.1.3
% 4.85/1.67 % (1651464)Termination reason: Instruction limit
% 4.85/1.67 % (1651464)Termination phase: Saturation
% 4.85/1.67 % (1651464)Time elapsed: 0.060 s
% 4.85/1.67 % (1651464)Peak memory usage: 90 MB
% 4.85/1.67 % (1651464)Instructions burned: 195 (million)
% 4.85/1.67 % (1651466)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=989299246:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 4.85/1.67 % (1651459)Refutation found. Thanks to Tanya!
% 4.85/1.67 % SZS status Unsatisfiable for theBenchmark
% 4.85/1.67 % SZS output start Proof for theBenchmark
% See solution above
% 4.85/1.67 % (1651459)------------------------------
% 4.85/1.67 % (1651459)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.67 % (1651459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.67 % (1651459)CaDiCaL version: 2.1.3
% 4.85/1.67 % (1651459)Termination reason: Refutation
% 4.85/1.67 % (1651459)Time elapsed: 0.013 s
% 4.85/1.67 % (1651459)Peak memory usage: 88 MB
% 4.85/1.67 % (1651459)Instructions burned: 19 (million)
% 4.85/1.67 % (1651459)------------------------------
% 4.85/1.67 % (1651459)------------------------------
% 4.85/1.67 % (1651438)Success in time 0.616 s
% 4.85/1.67 % Vampire exiting
%------------------------------------------------------------------------------