%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL767-1 : 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 11:56:30 AM UTC 2026
% Result : Unsatisfiable 9.44s 2.55s
% Output : Refutation 9.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 14 ( 11 unt; 0 def)
% Number of atoms : 20 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 9 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-5 aty)
% Number of variables : 49 ( 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f151,axiom,
! [X0,X1] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
fof(f231,axiom,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
fof(f232,axiom,
! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
fof(f286,axiom,
! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
fof(f312,axiom,
! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
fof(f639,axiom,
! [X2,X3,X0,X1,X4,X5] : hAPP(c_COMBS(X0,X1,X2,X3,X4),X5) = hAPP(hAPP(X0,X5),hAPP(X1,X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBS__def_0) ).
fof(f641,axiom,
! [X2,X3,X0,X1,X4,X5] : hAPP(c_COMBB(X0,X1,X2,X3,X4),X5) = hAPP(X0,hAPP(X1,X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
fof(f790,plain,
! [X2,X3,X0,X1,X4] : ~ c_HOL_Oord__class_Oless(hAPP(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),X0,X1,X2,X3),X4),hAPP(X0,X4),tc_nat),
inference(superposition,[],[f151,f639]) ).
fof(f987,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X0
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X0,tc_nat) ),
inference(superposition,[],[f231,f312]) ).
fof(f993,plain,
! [X2,X3,X0,X1,X4] : hAPP(c_COMBS(X1,hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2,X3,X4),X0) = hAPP(hAPP(X1,X0),X0),
inference(superposition,[],[f639,f312]) ).
fof(f1011,plain,
! [X2,X3,X0,X1] : hAPP(c_COMBS(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1,X2,X3),X0) = hAPP(X0,X0),
inference(superposition,[],[f993,f312]) ).
fof(f1057,plain,
! [X2,X3,X0,X1,X6,X4,X5] : ~ c_HOL_Oord__class_Oless(hAPP(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),c_COMBS(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1,X2,X3),X4,X5,X6),X0),hAPP(X0,X0),tc_nat),
inference(superposition,[],[f790,f1011]) ).
fof(f1395,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1) != X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(superposition,[],[f987,f232]) ).
fof(f1477,plain,
$false,
inference(unit_resulting_resolution,[],[f1395,f286,f1057,f641]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL767-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 % Computer : n005.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.44 % DateTime : Sun Sep 27 16:45:02 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 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
% 9.44/2.55 % (4042)Input is clausal, will run a generic CNF schedule.
% 9.44/2.55 % (4051)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3683309604:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 9.44/2.55 % (4050)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=784593712:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 9.44/2.55 % (4052)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3128828778:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 9.44/2.55 % (4053)lrs+10_1_sil=8000:sp=occurrence:random_seed=2907115279:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 9.44/2.55 % (4056)dis-21_1_sil=8000:lcm=predicate:random_seed=2350581830: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)
% 9.44/2.55 % (4054)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3470855210:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 9.44/2.55 % (4055)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1956667257:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 9.44/2.55 % (4053)Instruction limit reached!
% 9.44/2.55 % (4053)------------------------------
% 9.44/2.55 % (4053)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.44/2.55 % (4053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.44/2.55 % (4053)CaDiCaL version: 2.1.3
% 9.44/2.55 % (4053)Termination reason: Instruction limit
% 9.44/2.55 % (4053)Termination phase: Saturation
% 9.44/2.55 % (4053)Time elapsed: 0.110 s
% 9.44/2.55 % (4053)Peak memory usage: 89 MB
% 9.44/2.55 % (4053)Instructions burned: 107 (million)
% 9.44/2.55 % (4056)Instruction limit reached!
% 9.44/2.55 % (4056)------------------------------
% 9.44/2.55 % (4056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.44/2.55 % (4056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.44/2.55 % (4056)CaDiCaL version: 2.1.3
% 9.44/2.55 % (4056)Termination reason: Instruction limit
% 9.44/2.55 % (4056)Termination phase: Saturation
% 9.44/2.55 % (4056)Time elapsed: 0.114 s
% 9.44/2.55 % (4056)Peak memory usage: 89 MB
% 9.44/2.55 % (4056)Instructions burned: 118 (million)
% 9.44/2.55 % (4054)Instruction limit reached!
% 9.44/2.55 % (4054)------------------------------
% 9.44/2.55 % (4054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.44/2.55 % (4054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.44/2.55 % (4054)CaDiCaL version: 2.1.3
% 9.44/2.55 % (4054)Termination reason: Instruction limit
% 9.44/2.55 % (4054)Termination phase: Saturation
% 9.44/2.55 % (4054)Time elapsed: 0.116 s
% 9.44/2.55 % (4054)Peak memory usage: 89 MB
% 9.44/2.55 % (4054)Instructions burned: 114 (million)
% 9.44/2.55 % (4055)Instruction limit reached!
% 9.44/2.55 % (4055)------------------------------
% 9.44/2.55 % (4055)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.44/2.55 % (4055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.44/2.55 % (4055)CaDiCaL version: 2.1.3
% 9.44/2.55 % (4055)Termination reason: Instruction limit
% 9.44/2.55 % (4055)Termination phase: Saturation
% 9.44/2.55 % (4055)Time elapsed: 0.187 s
% 9.44/2.55 % (4055)Peak memory usage: 90 MB
% 9.44/2.55 % (4055)Instructions burned: 180 (million)
% 9.44/2.55 % (4065)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=4263883613:i=143:sd=2:aac=none:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/143Mi)
% 9.44/2.55 % (4065)Refutation not found, incomplete strategy
% 9.44/2.55 % (4065)------------------------------
% 9.44/2.55 % (4065)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.44/2.55 % (4065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.44/2.55 % (4065)CaDiCaL version: 2.1.3
% 9.44/2.55 % (4065)Termination reason: Refutation not found, incomplete strategy
% 9.44/2.55 % (4065)Time elapsed: 0.013 s
% 9.44/2.55 % (4065)Peak memory usage: 88 MB
% 9.44/2.55 % (4065)Instructions burned: 10 (million)
% 9.44/2.55 % (4069)lrs+10_64_to=lpo:sil=8000:random_seed=2967842905:i=126:bd=preordered_2994 on theBenchmark for (2994ds/126Mi)
% 9.44/2.55 % (4066)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2801779097:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2995 on theBenchmark for (2995ds/189Mi)
% 9.44/2.55 % (4067)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1256391669:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 9.44/2.55 % (4067)Refutation not found, incomplete strategy
% 9.44/2.55 % (4067)------------------------------
% 9.44/2.55 % (4067)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.44/2.55 % (4067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.44/2.55 % (4067)CaDiCaL version: 2.1.3
% 9.44/2.55 % (4067)Termination reason: Refutation not found, incomplete strategy
% 9.44/2.55 % (4067)Time elapsed: 0.020 s
% 9.44/2.55 % (4067)Peak memory usage: 88 MB
% 9.44/2.55 % (4067)Instructions burned: 19 (million)
% 9.44/2.55 % (4069)Instruction limit reached!
% 9.44/2.55 % (4069)------------------------------
% 9.44/2.55 % (4069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.44/2.55 % (4069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.44/2.55 % (4069)CaDiCaL version: 2.1.3
% 9.44/2.55 % (4069)Termination reason: Instruction limit
% 9.44/2.55 % (4069)Termination phase: Saturation
% 9.44/2.55 % (4069)Time elapsed: 0.092 s
% 9.44/2.55 % (4069)Peak memory usage: 89 MB
% 9.44/2.55 % (4069)Instructions burned: 126 (million)
% 9.44/2.55 % (4066)Instruction limit reached!
% 9.44/2.55 % (4066)------------------------------
% 9.44/2.55 % (4066)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.44/2.55 % (4066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.44/2.55 % (4066)CaDiCaL version: 2.1.3
% 9.44/2.55 % (4066)Termination reason: Instruction limit
% 9.44/2.55 % (4066)Termination phase: Saturation
% 9.44/2.55 % (4066)Time elapsed: 0.173 s
% 9.44/2.55 % (4066)Peak memory usage: 90 MB
% 9.44/2.55 % (4066)Instructions burned: 189 (million)
% 9.44/2.55 % (4075)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=44540177:avsq=on:i=194:fgj=on:bd=preordered_2992 on theBenchmark for (2992ds/194Mi)
% 9.44/2.55 % (4051)First to succeed.
% 9.44/2.55 % (4051)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4042"
% 9.44/2.55 % (4065)------------------------------
% 9.44/2.55 % (4065)------------------------------
% 9.44/2.55 % (4067)------------------------------
% 9.44/2.55 % (4067)------------------------------
% 9.44/2.55 % (4076)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=1270569363:i=157:gtg=all_2991 on theBenchmark for (2991ds/157Mi)
% 9.44/2.55 % (4075)Instruction limit reached!
% 9.44/2.55 % (4075)------------------------------
% 9.44/2.55 % (4075)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.44/2.55 % (4075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.44/2.55 % (4075)CaDiCaL version: 2.1.3
% 9.44/2.55 % (4075)Termination reason: Instruction limit
% 9.44/2.55 % (4075)Termination phase: Saturation
% 9.44/2.55 % (4075)Time elapsed: 0.201 s
% 9.44/2.55 % (4075)Peak memory usage: 90 MB
% 9.44/2.55 % (4075)Instructions burned: 194 (million)
% 9.44/2.55 % (4051)Refutation found. Thanks to Tanya!
% 9.44/2.55 % SZS status Unsatisfiable for theBenchmark
% 9.44/2.55 % SZS output start Proof for theBenchmark
% See solution above
% 9.44/2.55 % (4051)------------------------------
% 9.44/2.55 % (4051)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.44/2.55 % (4051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.44/2.55 % (4051)CaDiCaL version: 2.1.3
% 9.44/2.55 % (4051)Termination reason: Refutation
% 9.44/2.55 % (4051)Time elapsed: 0.792 s
% 9.44/2.55 % (4051)Peak memory usage: 135 MB
% 9.44/2.55 % (4051)Instructions burned: 1384 (million)
% 9.44/2.55 % (4051)------------------------------
% 9.44/2.55 % (4051)------------------------------
% 9.44/2.55 % (4042)Success in time 1.266 s
% 9.44/2.55 % Vampire exiting
%------------------------------------------------------------------------------