%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL837-1 : 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 : n016.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 11:56:48 AM UTC 2026
% Result : Unsatisfiable 3.75s 1.44s
% Output : Refutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 14 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 8 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 11 con; 0-5 aty)
% Number of variables : 11 ( 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f70,axiom,
! [X0] : c_Suc(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
fof(f667,axiom,
! [X2,X3,X0,X1,X4] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),hAPP(hAPP(c_Lambda_Olift,X1),X2)),c_Suc(X3))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X4),X1),X3)),X2) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X4),X2)),X1),X3)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__subst_0) ).
fof(f740,axiom,
! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
fof(f798,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/sandbox2/benchmark/theBenchmark.p',cls_subst__map_0) ).
fof(f805,axiom,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f806,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),hAPP(hAPP(c_Lambda_Olift,v_u____),c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(v_i____))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),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_conjecture_0) ).
fof(f843,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat))),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)))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_i____),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(superposition,[],[f806,f667]) ).
fof(f844,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_i____),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(forward_demodulation,[],[f843,f798]) ).
fof(f845,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_i____),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(forward_subsumption_resolution,[],[f844,f805]) ).
fof(f846,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(v_i____),tc_nat),
inference(forward_demodulation,[],[f845,f70]) ).
fof(f847,plain,
$false,
inference(forward_subsumption_resolution,[],[f846,f740]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL837-1 : 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 : n016.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 17:03:47 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
% 3.75/1.44 % (2848392)Input is clausal, will run a generic CNF schedule.
% 3.75/1.44 % (2848400)lrs+10_1_sil=8000:sp=occurrence:random_seed=1938563236:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.75/1.44 % (2848400)Instruction limit reached!
% 3.75/1.44 % (2848400)------------------------------
% 3.75/1.44 % (2848400)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.44 % (2848400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.44 % (2848400)CaDiCaL version: 2.1.3
% 3.75/1.44 % (2848400)Termination reason: Instruction limit
% 3.75/1.44 % (2848400)Termination phase: Saturation
% 3.75/1.44 % (2848400)Time elapsed: 0.038 s
% 3.75/1.44 % (2848400)Peak memory usage: 89 MB
% 3.75/1.44 % (2848400)Instructions burned: 108 (million)
% 3.75/1.44 % (2848398)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3550707607:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.75/1.44 % (2848399)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3244749148:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.75/1.44 % (2848397)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=20533917:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.75/1.44 % (2848402)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=216565786:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.75/1.44 % (2848403)dis-21_1_sil=8000:lcm=predicate:random_seed=1039250264: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)
% 3.75/1.44 % (2848401)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3983636084:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.75/1.44 % (2848403)Instruction limit reached!
% 3.75/1.44 % (2848403)------------------------------
% 3.75/1.44 % (2848403)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.44 % (2848403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.44 % (2848403)CaDiCaL version: 2.1.3
% 3.75/1.44 % (2848403)Termination reason: Instruction limit
% 3.75/1.44 % (2848403)Termination phase: Saturation
% 3.75/1.44 % (2848403)Time elapsed: 0.066 s
% 3.75/1.44 % (2848403)Peak memory usage: 89 MB
% 3.75/1.44 % (2848403)Instructions burned: 118 (million)
% 3.75/1.44 % (2848401)Instruction limit reached!
% 3.75/1.44 % (2848401)------------------------------
% 3.75/1.44 % (2848401)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.44 % (2848401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.44 % (2848401)CaDiCaL version: 2.1.3
% 3.75/1.44 % (2848401)Termination reason: Instruction limit
% 3.75/1.44 % (2848401)Termination phase: Saturation
% 3.75/1.44 % (2848401)Time elapsed: 0.074 s
% 3.75/1.44 % (2848401)Peak memory usage: 89 MB
% 3.75/1.44 % (2848401)Instructions burned: 115 (million)
% 3.75/1.44 % (2848408)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=1805482245:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.75/1.44 % (2848402)Instruction limit reached!
% 3.75/1.44 % (2848402)------------------------------
% 3.75/1.44 % (2848402)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.44 % (2848402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.44 % (2848402)CaDiCaL version: 2.1.3
% 3.75/1.44 % (2848402)Termination reason: Instruction limit
% 3.75/1.44 % (2848402)Termination phase: Saturation
% 3.75/1.44 % (2848402)Time elapsed: 0.117 s
% 3.75/1.44 % (2848402)Peak memory usage: 90 MB
% 3.75/1.44 % (2848402)Instructions burned: 181 (million)
% 3.75/1.44 % (2848408)First to succeed.
% 3.75/1.44 % (2848408)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2848392"
% 3.75/1.44 % (2848412)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3847128066: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)
% 3.75/1.44 % (2848413)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=517095795:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.75/1.44 % (2848412)Also succeeded, but the first one will report.
% 3.75/1.44 % (2848413)Refutation not found, incomplete strategy
% 3.75/1.44 % (2848413)------------------------------
% 3.75/1.44 % (2848413)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.44 % (2848413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.44 % (2848413)CaDiCaL version: 2.1.3
% 3.75/1.44 % (2848413)Termination reason: Refutation not found, incomplete strategy
% 3.75/1.44 % (2848413)Time elapsed: 0.028 s
% 3.75/1.44 % (2848413)Peak memory usage: 88 MB
% 3.75/1.44 % (2848413)Instructions burned: 46 (million)
% 3.75/1.44 % (2848408)Refutation found. Thanks to Tanya!
% 3.75/1.44 % SZS status Unsatisfiable for theBenchmark
% 3.75/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 3.75/1.44 % (2848408)------------------------------
% 3.75/1.44 % (2848408)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.44 % (2848408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.44 % (2848408)CaDiCaL version: 2.1.3
% 3.75/1.44 % (2848408)Termination reason: Refutation
% 3.75/1.44 % (2848408)Time elapsed: 0.007 s
% 3.75/1.44 % (2848408)Peak memory usage: 89 MB
% 3.75/1.44 % (2848408)Instructions burned: 18 (million)
% 3.75/1.44 % (2848408)------------------------------
% 3.75/1.44 % (2848408)------------------------------
% 3.75/1.44 % (2848392)Success in time 0.475 s
% 3.75/1.44 % Vampire exiting
%------------------------------------------------------------------------------