%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN008-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 10:19:07 AM UTC 2026
% Result : Unsatisfiable 4.28s 1.64s
% Output : Refutation 4.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 38 ( 13 unt; 2 def)
% Number of atoms : 80 ( 7 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 89 ( 47 ~; 40 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal) ).
fof(f2,axiom,
! [X0,X1] :
( ~ quotient(X0,X1,zero)
| less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_equal_quotient) ).
fof(f4,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ quotient(X5,X4,X6)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X3,X5)
| ~ quotient(X0,X1,X2)
| ~ quotient(X2,X3,X7)
| less_equal(X6,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_property) ).
fof(f5,axiom,
! [X0] : less_equal(zero,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_is_smallest) ).
fof(f6,axiom,
! [X0,X1] :
( ~ less_equal(X1,X0)
| ~ less_equal(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_equal_and_equal) ).
fof(f8,axiom,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2)
| X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_defined) ).
fof(f10,axiom,
less_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLEb) ).
fof(f11,axiom,
quotient(a,c,aQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aQc) ).
fof(f12,axiom,
quotient(b,c,bQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bQc) ).
fof(f13,negated_conjecture,
~ less_equal(aQc,bQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_aQcLEbQc) ).
fof(f20,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| divide(X0,X1) = X2 ),
inference(resolution,[],[f9,f8]) ).
fof(f56,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ quotient(X5,X1,X6)
| ~ quotient(X3,X1,X4)
| ~ quotient(X3,X0,X5)
| ~ quotient(X0,X1,X2)
| less_equal(divide(X4,X2),X6) ),
inference(resolution,[],[f4,f8]) ).
fof(f88,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| zero = divide(X0,X1) ),
inference(resolution,[],[f42,f1]) ).
fof(f154,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ quotient(X3,X1,X5)
| ~ quotient(X0,X3,X4)
| ~ quotient(X0,X1,X2)
| less_equal(divide(X2,X5),zero)
| ~ less_equal(X4,X1) ),
inference(resolution,[],[f56,f1]) ).
fof(f203,plain,
zero = divide(a,b),
inference(resolution,[],[f88,f10]) ).
fof(f307,plain,
! [X2,X0,X1] :
( ~ quotient(X0,c,X2)
| ~ quotient(X0,b,X1)
| less_equal(divide(X2,bQc),zero)
| ~ less_equal(X1,c) ),
inference(resolution,[],[f154,f12]) ).
fof(f614,plain,
! [X0] :
( ~ quotient(a,b,X0)
| less_equal(divide(aQc,bQc),zero)
| ~ less_equal(X0,c) ),
inference(resolution,[],[f307,f11]) ).
fof(f622,definition,
( spl0_32
<=> less_equal(divide(aQc,bQc),zero) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f624,plain,
( less_equal(divide(aQc,bQc),zero)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f622]) ).
fof(f626,definition,
( spl0_33
<=> ! [X0] :
( ~ quotient(a,b,X0)
| ~ less_equal(X0,c) ) ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f627,plain,
( ! [X0] :
( ~ quotient(a,b,X0)
| ~ less_equal(X0,c) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f626]) ).
fof(f628,plain,
( spl0_32
| spl0_33 ),
inference(avatar_split_clause,[],[f614,f626,f622]) ).
fof(f629,plain,
( zero = divide(aQc,bQc)
| ~ spl0_32 ),
inference(resolution,[],[f624,f20]) ).
fof(f659,plain,
( quotient(aQc,bQc,zero)
| ~ spl0_32 ),
inference(superposition,[],[f8,f629]) ).
fof(f681,plain,
( less_equal(aQc,bQc)
| ~ spl0_32 ),
inference(resolution,[],[f659,f2]) ).
fof(f698,plain,
( $false
| ~ spl0_32 ),
inference(forward_subsumption_resolution,[],[f681,f13]) ).
fof(f699,plain,
~ spl0_32,
inference(avatar_contradiction_clause,[],[f698]) ).
fof(f755,plain,
( ~ less_equal(divide(a,b),c)
| ~ spl0_33 ),
inference(resolution,[],[f627,f8]) ).
fof(f758,plain,
( ~ less_equal(zero,c)
| ~ spl0_33 ),
inference(forward_demodulation,[],[f755,f203]) ).
fof(f763,plain,
( $false
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f758,f5]) ).
fof(f764,plain,
~ spl0_33,
inference(avatar_contradiction_clause,[],[f763]) ).
cnf(s23,plain,
( spl0_32
| spl0_33 ),
inference(sat_conversion,[],[f628]) ).
cnf(s24,plain,
~ spl0_32,
inference(sat_conversion,[],[f699]) ).
cnf(s29,plain,
~ spl0_33,
inference(sat_conversion,[],[f764]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s23,s29,s24]) ).
fof(f765,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n026.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 10:53:41 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 4.28/1.64 % (2659551)Input is clausal, will run a generic CNF schedule.
% 4.28/1.64 % (2659579)dis-21_1_sil=8000:lcm=predicate:random_seed=2100513224: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)
% 4.28/1.64 % (2659575)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1213327075:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.28/1.64 % (2659578)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2478683453:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.28/1.64 % (2659573)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=2724955548:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.28/1.64 % (2659574)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=542164757:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.28/1.64 % (2659577)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3099706969:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.28/1.64 % (2659576)lrs+10_1_sil=8000:sp=occurrence:random_seed=3534943151:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.28/1.64 % (2659577)Refutation not found, incomplete strategy
% 4.28/1.64 % (2659577)------------------------------
% 4.28/1.64 % (2659577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.28/1.64 % (2659577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.28/1.64 % (2659577)CaDiCaL version: 2.1.3
% 4.28/1.64 % (2659577)Termination reason: Refutation not found, incomplete strategy
% 4.28/1.64 % (2659577)Time elapsed: 0.001 s
% 4.28/1.64 % (2659577)Peak memory usage: 88 MB
% 4.28/1.64 % (2659577)Instructions burned: 3 (million)
% 4.28/1.64 % (2659576)First to succeed.
% 4.28/1.64 % (2659576)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2659551"
% 4.28/1.64 % (2659579)Instruction limit reached!
% 4.28/1.64 % (2659579)------------------------------
% 4.28/1.64 % (2659579)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.28/1.64 % (2659579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.28/1.64 % (2659579)CaDiCaL version: 2.1.3
% 4.28/1.64 % (2659579)Termination reason: Instruction limit
% 4.28/1.64 % (2659579)Termination phase: Saturation
% 4.28/1.64 % (2659579)Time elapsed: 0.057 s
% 4.28/1.64 % (2659579)Peak memory usage: 88 MB
% 4.28/1.64 % (2659579)Instructions burned: 118 (million)
% 4.28/1.64 % (2659578)Instruction limit reached!
% 4.28/1.64 % (2659578)------------------------------
% 4.28/1.64 % (2659578)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.28/1.64 % (2659578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.28/1.64 % (2659578)CaDiCaL version: 2.1.3
% 4.28/1.64 % (2659578)Termination reason: Instruction limit
% 4.28/1.64 % (2659578)Termination phase: Saturation
% 4.28/1.64 % (2659578)Time elapsed: 0.110 s
% 4.28/1.64 % (2659578)Peak memory usage: 89 MB
% 4.28/1.64 % (2659578)Instructions burned: 182 (million)
% 4.28/1.64 % (2659577)------------------------------
% 4.28/1.64 % (2659577)------------------------------
% 4.28/1.64 % (2659591)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=3585133423:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.28/1.64 % (2659591)Refutation not found, incomplete strategy
% 4.28/1.64 % (2659591)------------------------------
% 4.28/1.64 % (2659591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.28/1.64 % (2659591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.28/1.64 % (2659591)CaDiCaL version: 2.1.3
% 4.28/1.64 % (2659591)Termination reason: Refutation not found, incomplete strategy
% 4.28/1.64 % (2659591)Time elapsed: 0.004 s
% 4.28/1.64 % (2659591)Peak memory usage: 88 MB
% 4.28/1.64 % (2659591)Instructions burned: 4 (million)
% 4.28/1.64 % (2659592)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2440716286: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)
% 4.28/1.64 % (2659593)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1244196611:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 4.28/1.64 % (2659593)Refutation not found, incomplete strategy
% 4.28/1.64 % (2659593)------------------------------
% 4.28/1.64 % (2659593)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.28/1.64 % (2659593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.28/1.64 % (2659593)CaDiCaL version: 2.1.3
% 4.28/1.64 % (2659593)Termination reason: Refutation not found, incomplete strategy
% 4.28/1.64 % (2659593)Time elapsed: 0.002 s
% 4.28/1.64 % (2659593)Peak memory usage: 88 MB
% 4.28/1.64 % (2659593)Instructions burned: 3 (million)
% 4.28/1.64 % (2659576)Refutation found. Thanks to Tanya!
% 4.28/1.64 % SZS status Unsatisfiable for theBenchmark
% 4.28/1.64 % SZS output start Proof for theBenchmark
% See solution above
% 4.28/1.64 % (2659576)------------------------------
% 4.28/1.64 % (2659576)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.28/1.64 % (2659576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.28/1.64 % (2659576)CaDiCaL version: 2.1.3
% 4.28/1.64 % (2659576)Termination reason: Refutation
% 4.28/1.64 % (2659576)Time elapsed: 0.027 s
% 4.28/1.64 % (2659576)Peak memory usage: 89 MB
% 4.28/1.64 % (2659576)Instructions burned: 22 (million)
% 4.28/1.64 % (2659576)------------------------------
% 4.28/1.64 % (2659576)------------------------------
% 4.28/1.64 % (2659551)Success in time 0.501 s
% 4.28/1.64 % Vampire exiting
%------------------------------------------------------------------------------