%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG369-1 : 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 : n017.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 09:19:52 AM UTC 2026
% Result : Unsatisfiable 2.64s 1.08s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 19 ( 10 unt; 2 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 21 ~; 14 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 3 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f642,axiom,
! [X0] :
( v_thesis____
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).
fof(f706,axiom,
c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_2) ).
fof(f707,axiom,
c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_1) ).
fof(f708,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_e,v_m____),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f709,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f768,definition,
( spl0_1
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f769,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f768]) ).
fof(f771,definition,
( spl0_2
<=> v_thesis____ ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f774,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f642,f771,f768]) ).
fof(f775,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f709,f771]) ).
fof(f777,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_e,v_m____),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_1 ),
inference(resolution,[],[f769,f706]) ).
fof(f778,plain,
( ~ c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f777,f708]) ).
fof(f779,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f778,f707]) ).
fof(f780,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f779]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f774]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f775]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f780]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f781,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG369-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 20:09:06 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 2.64/1.08 % (3961906)Input is clausal, will run a generic CNF schedule.
% 2.64/1.08 % (3961914)lrs+10_1_sil=8000:sp=occurrence:random_seed=409551115:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.64/1.08 % (3961914)First to succeed.
% 2.64/1.08 % (3961914)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3961906"
% 2.64/1.08 % (3961913)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1676236071:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.64/1.08 % (3961917)dis-21_1_sil=8000:lcm=predicate:random_seed=3374556673: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)
% 2.64/1.08 % (3961916)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2917786231:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.64/1.08 % (3961915)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2838237812:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.64/1.08 % (3961912)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=669434114:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.64/1.08 % (3961911)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=626162672:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.64/1.08 % (3961917)Also succeeded, but the first one will report.
% 2.64/1.08 % (3961916)Also succeeded, but the first one will report.
% 2.64/1.08 % (3961915)Instruction limit reached!
% 2.64/1.08 % (3961915)------------------------------
% 2.64/1.08 % (3961915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.08 % (3961915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.08 % (3961915)CaDiCaL version: 2.1.3
% 2.64/1.08 % (3961915)Termination reason: Instruction limit
% 2.64/1.08 % (3961915)Termination phase: Saturation
% 2.64/1.08 % (3961915)Time elapsed: 0.079 s
% 2.64/1.08 % (3961915)Peak memory usage: 89 MB
% 2.64/1.08 % (3961915)Instructions burned: 115 (million)
% 2.64/1.08 % (3961914)Refutation found. Thanks to Tanya!
% 2.64/1.08 % SZS status Unsatisfiable for theBenchmark
% 2.64/1.08 % SZS output start Proof for theBenchmark
% See solution above
% 2.64/1.08 % (3961914)------------------------------
% 2.64/1.08 % (3961914)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.08 % (3961914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.08 % (3961914)CaDiCaL version: 2.1.3
% 2.64/1.08 % (3961914)Termination reason: Refutation
% 2.64/1.08 % (3961914)Time elapsed: 0.004 s
% 2.64/1.08 % (3961914)Peak memory usage: 90 MB
% 2.64/1.08 % (3961914)Instructions burned: 10 (million)
% 2.64/1.08 % (3961914)------------------------------
% 2.64/1.08 % (3961914)------------------------------
% 2.64/1.08 % (3961906)Success in time 0.316 s
% 2.64/1.08 % Vampire exiting
%------------------------------------------------------------------------------