%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL755-1 : 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 : n002.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 11:56:28 AM UTC 2026
% Result : Unsatisfiable 3.37s 1.39s
% Output : Refutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 7 ( 6 unt; 0 def)
% Number of atoms : 8 ( 1 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 4 ~; 1 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 4 ( 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f116,axiom,
! [X0] : c_Suc(X0) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
fof(f845,axiom,
! [X0] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X0))
| ~ c_InductTermi_OIT(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).
fof(f860,negated_conjecture,
! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X0),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f861,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f892,plain,
~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Oplus__class_Oplus(v_ja,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))),
inference(definition_unfolding,[],[f861,f116,f116]) ).
fof(f1054,plain,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Oplus__class_Oplus(v_ja,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
inference(resolution,[],[f845,f892]) ).
fof(f1055,plain,
$false,
inference(forward_subsumption_resolution,[],[f1054,f860]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL755-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n002.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 16:47:07 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.37/1.39 % (3727743)Input is clausal, will run a generic CNF schedule.
% 3.37/1.39 % (3727749)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2025958784:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.37/1.39 % (3727751)lrs+10_1_sil=8000:sp=occurrence:random_seed=2136836700:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.37/1.39 % (3727748)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=2948354088:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.37/1.39 % (3727750)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3480342206:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.37/1.39 % (3727751)First to succeed.
% 3.37/1.39 % (3727751)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3727743"
% 3.37/1.39 % (3727753)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2094621922:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.37/1.39 % (3727752)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3850475150:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.37/1.39 % (3727754)dis-21_1_sil=8000:lcm=predicate:random_seed=219179651: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)
% 3.37/1.39 % (3727752)Also succeeded, but the first one will report.
% 3.37/1.39 % (3727753)Also succeeded, but the first one will report.
% 3.37/1.39 % (3727754)Also succeeded, but the first one will report.
% 3.37/1.39 % (3727751)Refutation found. Thanks to Tanya!
% 3.37/1.39 % SZS status Unsatisfiable for theBenchmark
% 3.37/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 3.37/1.39 % (3727751)------------------------------
% 3.37/1.39 % (3727751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.39 % (3727751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.39 % (3727751)CaDiCaL version: 2.1.3
% 3.37/1.39 % (3727751)Termination reason: Refutation
% 3.37/1.39 % (3727751)Time elapsed: 0.014 s
% 3.37/1.39 % (3727751)Peak memory usage: 89 MB
% 3.37/1.39 % (3727751)Instructions burned: 21 (million)
% 3.37/1.39 % (3727751)------------------------------
% 3.37/1.39 % (3727751)------------------------------
% 3.37/1.39 % (3727743)Success in time 0.437 s
% 3.37/1.39 % Vampire exiting
%------------------------------------------------------------------------------