%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL800-1 : 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 : n006.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 11:56:38 AM UTC 2026
% Result : Unsatisfiable 3.79s 1.43s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 9 ( 9 unt; 0 def)
% Number of atoms : 9 ( 4 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1 ( 1 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 13 ( 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f444,axiom,
! [X2,X3,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X1),X2,X3) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X0,X2,X3),c_Lambda_Osubst(X1,X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__App_0) ).
fof(f447,axiom,
! [X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,X0) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).
fof(f463,axiom,
! [X2,X0,X1] : c_Lambda_Osubst(c_Lambda_Olift(X0,X1),X2,X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).
fof(f468,axiom,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f469,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f520,plain,
! [X2,X3,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(X0,X1),X2),X3,X1) = c_Lambda_OdB_OApp(X0,c_Lambda_Osubst(X2,X3,X1)),
inference(superposition,[],[f444,f463]) ).
fof(f865,plain,
c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(superposition,[],[f468,f520]) ).
fof(f878,plain,
c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____))),
inference(forward_demodulation,[],[f865,f447]) ).
fof(f882,plain,
$false,
inference(forward_subsumption_resolution,[],[f878,f469]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL800-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n006.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 16:52:10 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 3.79/1.43 % (3167697)Input is clausal, will run a generic CNF schedule.
% 3.79/1.43 % (3167703)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=74671716:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.79/1.43 % (3167708)dis-21_1_sil=8000:lcm=predicate:random_seed=1168823455: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)
% 3.79/1.43 % (3167707)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1442123308:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.79/1.43 % (3167705)lrs+10_1_sil=8000:sp=occurrence:random_seed=2174996842:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.79/1.43 % (3167704)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3530593738:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.79/1.43 % (3167702)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=2995431539:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.79/1.43 % (3167706)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2989810859:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.79/1.43 % (3167707)First to succeed.
% 3.79/1.43 % (3167707)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3167697"
% 3.79/1.43 % (3167708)Instruction limit reached!
% 3.79/1.43 % (3167708)------------------------------
% 3.79/1.43 % (3167708)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.43 % (3167708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.43 % (3167708)CaDiCaL version: 2.1.3
% 3.79/1.43 % (3167708)Termination reason: Instruction limit
% 3.79/1.43 % (3167708)Termination phase: Saturation
% 3.79/1.43 % (3167708)Time elapsed: 0.063 s
% 3.79/1.43 % (3167708)Peak memory usage: 88 MB
% 3.79/1.43 % (3167708)Instructions burned: 119 (million)
% 3.79/1.43 % (3167705)Instruction limit reached!
% 3.79/1.43 % (3167705)------------------------------
% 3.79/1.43 % (3167705)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.43 % (3167705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.43 % (3167705)CaDiCaL version: 2.1.3
% 3.79/1.43 % (3167705)Termination reason: Instruction limit
% 3.79/1.43 % (3167705)Termination phase: Saturation
% 3.79/1.43 % (3167705)Time elapsed: 0.072 s
% 3.79/1.43 % (3167705)Peak memory usage: 88 MB
% 3.79/1.43 % (3167705)Instructions burned: 107 (million)
% 3.79/1.43 % (3167706)Instruction limit reached!
% 3.79/1.43 % (3167706)------------------------------
% 3.79/1.43 % (3167706)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.43 % (3167706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.43 % (3167706)CaDiCaL version: 2.1.3
% 3.79/1.43 % (3167706)Termination reason: Instruction limit
% 3.79/1.43 % (3167706)Termination phase: Saturation
% 3.79/1.43 % (3167706)Time elapsed: 0.073 s
% 3.79/1.43 % (3167706)Peak memory usage: 89 MB
% 3.79/1.43 % (3167706)Instructions burned: 115 (million)
% 3.79/1.43 % (3167716)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=3697286603:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.79/1.43 % (3167716)Refutation not found, incomplete strategy
% 3.79/1.43 % (3167716)------------------------------
% 3.79/1.43 % (3167716)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.43 % (3167716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.43 % (3167716)CaDiCaL version: 2.1.3
% 3.79/1.43 % (3167716)Termination reason: Refutation not found, incomplete strategy
% 3.79/1.43 % (3167716)Time elapsed: 0.003 s
% 3.79/1.43 % (3167716)Peak memory usage: 88 MB
% 3.79/1.43 % (3167716)Instructions burned: 3 (million)
% 3.79/1.43 % (3167718)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1101058863:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.79/1.43 % (3167717)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3277269591: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)
% 3.79/1.43 % (3167718)Refutation not found, incomplete strategy
% 3.79/1.43 % (3167718)------------------------------
% 3.79/1.43 % (3167718)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.43 % (3167718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.43 % (3167718)CaDiCaL version: 2.1.3
% 3.79/1.43 % (3167718)Termination reason: Refutation not found, incomplete strategy
% 3.79/1.43 % (3167718)Time elapsed: 0.006 s
% 3.79/1.43 % (3167718)Peak memory usage: 88 MB
% 3.79/1.43 % (3167718)Instructions burned: 9 (million)
% 3.79/1.43 % (3167717)Refutation not found, incomplete strategy
% 3.79/1.43 % (3167717)------------------------------
% 3.79/1.43 % (3167717)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.43 % (3167717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.43 % (3167717)CaDiCaL version: 2.1.3
% 3.79/1.43 % (3167717)Termination reason: Refutation not found, incomplete strategy
% 3.79/1.43 % (3167717)Time elapsed: 0.009 s
% 3.79/1.43 % (3167717)Peak memory usage: 88 MB
% 3.79/1.43 % (3167717)Instructions burned: 15 (million)
% 3.79/1.43 % (3167707)Refutation found. Thanks to Tanya!
% 3.79/1.43 % SZS status Unsatisfiable for theBenchmark
% 3.79/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 3.79/1.43 % (3167707)------------------------------
% 3.79/1.43 % (3167707)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.43 % (3167707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.43 % (3167707)CaDiCaL version: 2.1.3
% 3.79/1.43 % (3167707)Termination reason: Refutation
% 3.79/1.43 % (3167707)Time elapsed: 0.023 s
% 3.79/1.43 % (3167707)Peak memory usage: 88 MB
% 3.79/1.43 % (3167707)Instructions burned: 34 (million)
% 3.79/1.43 % (3167707)------------------------------
% 3.79/1.43 % (3167707)------------------------------
% 3.79/1.43 % (3167697)Success in time 0.469 s
% 3.79/1.43 % Vampire exiting
%------------------------------------------------------------------------------