%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN006-7 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 10:19:06 AM UTC 2026
% Result : Unsatisfiable 8.39s 2.10s
% Output : Refutation 8.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 24 ( 19 unt; 0 def)
% Number of atoms : 34 ( 3 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal) ).
fof(f2,axiom,
! [X0,X1] :
( ~ quotient(X0,X1,zero)
| less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_quotient) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| less_equal(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor_existence) ).
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/sandbox/benchmark/theBenchmark.p',quotient_property) ).
fof(f5,axiom,
! [X0] : less_equal(zero,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_smallest) ).
fof(f6,axiom,
! [X0,X1] :
( ~ less_equal(X1,X0)
| ~ less_equal(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_and_equal) ).
fof(f8,axiom,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure) ).
fof(f11,axiom,
! [X0] : quotient(zero,X0,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
fof(f13,axiom,
! [X0] : quotient(X0,zero,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
fof(f14,axiom,
quotient(x,y,xQy),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQy) ).
fof(f15,axiom,
less_equal(xQy,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQyLEz) ).
fof(f16,axiom,
quotient(x,z,xQz),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQz) ).
fof(f17,negated_conjecture,
~ less_equal(xQz,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_xQzLEy) ).
fof(f73,plain,
quotient(xQy,z,zero),
inference(unit_resulting_resolution,[],[f1,f15]) ).
fof(f83,plain,
less_equal(divide(xQz,divide(y,z)),zero),
inference(unit_resulting_resolution,[],[f4,f14,f16,f8,f8,f73]) ).
fof(f1760,plain,
zero = divide(xQz,divide(y,z)),
inference(unit_resulting_resolution,[],[f6,f5,f83]) ).
fof(f1764,plain,
quotient(xQz,divide(y,z),zero),
inference(superposition,[],[f8,f1760]) ).
fof(f1766,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(unit_resulting_resolution,[],[f3,f8]) ).
fof(f1775,plain,
! [X0,X1] : quotient(divide(X0,X1),X0,zero),
inference(unit_resulting_resolution,[],[f1,f1766]) ).
fof(f1777,plain,
~ quotient(xQz,y,zero),
inference(unit_resulting_resolution,[],[f2,f17]) ).
fof(f3756,plain,
less_equal(divide(xQz,y),zero),
inference(unit_resulting_resolution,[],[f4,f11,f13,f8,f1775,f1764]) ).
fof(f4010,plain,
zero = divide(xQz,y),
inference(unit_resulting_resolution,[],[f6,f5,f3756]) ).
fof(f4017,plain,
quotient(xQz,y,zero),
inference(superposition,[],[f8,f4010]) ).
fof(f4018,plain,
$false,
inference(forward_subsumption_resolution,[],[f4017,f1777]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN006-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n011.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 10:50:51 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 6.72/1.99 % (2215712)Input is clausal, will run a generic CNF schedule.
% 6.72/1.99 % (2215819)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3830333378:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.72/1.99 % (2215813)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1562795275:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.72/1.99 % (2215814)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=830145403:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.72/1.99 % (2215812)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=1451377487:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.72/1.99 % (2215818)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2448266072:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.72/1.99 % (2215821)dis-21_1_sil=8000:lcm=predicate:random_seed=3733989071: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)
% 6.72/1.99 % (2215816)lrs+10_1_sil=8000:sp=occurrence:random_seed=2930329079:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.72/1.99 % (2215816)Refutation not found, incomplete strategy
% 6.72/1.99 % (2215816)------------------------------
% 6.72/1.99 % (2215816)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.72/1.99 % (2215816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.72/1.99 % (2215816)CaDiCaL version: 2.1.3
% 6.72/1.99 % (2215816)Termination reason: Refutation not found, incomplete strategy
% 6.72/1.99 % (2215816)Time elapsed: 0.001 s
% 6.72/1.99 % (2215816)Peak memory usage: 88 MB
% 6.72/1.99 % (2215818)Refutation not found, incomplete strategy
% 6.72/1.99 % (2215818)------------------------------
% 6.72/1.99 % (2215818)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.72/1.99 % (2215818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.72/1.99 % (2215818)CaDiCaL version: 2.1.3
% 6.72/1.99 % (2215818)Termination reason: Refutation not found, incomplete strategy
% 6.72/1.99 % (2215818)Time elapsed: 0.010 s
% 6.72/1.99 % (2215818)Peak memory usage: 88 MB
% 6.72/1.99 % (2215818)Instructions burned: 14 (million)
% 6.72/1.99 % (2215819)Instruction limit reached!
% 6.72/1.99 % (2215819)------------------------------
% 6.72/1.99 % (2215819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.72/1.99 % (2215819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.72/1.99 % (2215819)CaDiCaL version: 2.1.3
% 6.72/1.99 % (2215819)Termination reason: Instruction limit
% 6.72/1.99 % (2215819)Termination phase: Saturation
% 6.72/1.99 % (2215819)Time elapsed: 0.048 s
% 6.72/1.99 % (2215819)Peak memory usage: 88 MB
% 6.72/1.99 % (2215819)Instructions burned: 181 (million)
% 6.72/1.99 % (2215821)Instruction limit reached!
% 6.72/1.99 % (2215821)------------------------------
% 6.72/1.99 % (2215821)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.72/1.99 % (2215821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.72/1.99 % (2215821)CaDiCaL version: 2.1.3
% 6.72/1.99 % (2215821)Termination reason: Instruction limit
% 6.72/1.99 % (2215821)Termination phase: Saturation
% 6.72/1.99 % (2215821)Time elapsed: 0.057 s
% 6.72/1.99 % (2215821)Peak memory usage: 88 MB
% 6.72/1.99 % (2215821)Instructions burned: 118 (million)
% 6.72/1.99 % (2215884)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=4002908815:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 6.72/1.99 % (2215884)Refutation not found, incomplete strategy
% 6.72/1.99 % (2215884)------------------------------
% 6.72/1.99 % (2215884)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.72/1.99 % (2215884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.72/1.99 % (2215884)CaDiCaL version: 2.1.3
% 6.72/1.99 % (2215884)Termination reason: Refutation not found, incomplete strategy
% 6.72/1.99 % (2215884)Time elapsed: 0.006 s
% 6.72/1.99 % (2215884)Peak memory usage: 88 MB
% 6.72/1.99 % (2215884)Instructions burned: 7 (million)
% 6.72/1.99 % (2215885)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=644791416: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)
% 8.39/2.10 % (2215818)------------------------------
% 8.39/2.10 % (2215818)------------------------------
% 8.39/2.10 % (2215816)------------------------------
% 8.39/2.10 % (2215816)------------------------------
% 8.39/2.10 % (2215885)Instruction limit reached!
% 8.39/2.10 % (2215885)------------------------------
% 8.39/2.10 % (2215885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.10 % (2215885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.10 % (2215885)CaDiCaL version: 2.1.3
% 8.39/2.10 % (2215885)Termination reason: Instruction limit
% 8.39/2.10 % (2215885)Termination phase: Saturation
% 8.39/2.10 % (2215885)Time elapsed: 0.096 s
% 8.39/2.10 % (2215885)Peak memory usage: 88 MB
% 8.39/2.10 % (2215885)Instructions burned: 189 (million)
% 8.39/2.10 % (2215889)lrs+10_64_to=lpo:sil=8000:random_seed=3702057039:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 8.39/2.10 % (2215888)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1782325703:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 8.39/2.10 % (2215884)------------------------------
% 8.39/2.10 % (2215884)------------------------------
% 8.39/2.10 % (2215888)Refutation not found, incomplete strategy
% 8.39/2.10 % (2215888)------------------------------
% 8.39/2.10 % (2215888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.10 % (2215888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.10 % (2215888)CaDiCaL version: 2.1.3
% 8.39/2.10 % (2215888)Termination reason: Refutation not found, incomplete strategy
% 8.39/2.10 % (2215888)Time elapsed: 0.003 s
% 8.39/2.10 % (2215888)Peak memory usage: 88 MB
% 8.39/2.10 % (2215888)Instructions burned: 2 (million)
% 8.39/2.10 % (2215889)Instruction limit reached!
% 8.39/2.10 % (2215889)------------------------------
% 8.39/2.10 % (2215889)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.10 % (2215889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.10 % (2215889)CaDiCaL version: 2.1.3
% 8.39/2.10 % (2215889)Termination reason: Instruction limit
% 8.39/2.10 % (2215889)Termination phase: Saturation
% 8.39/2.10 % (2215889)Time elapsed: 0.043 s
% 8.39/2.10 % (2215889)Peak memory usage: 88 MB
% 8.39/2.10 % (2215889)Instructions burned: 129 (million)
% 8.39/2.10 % (2215890)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3955384548:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 8.39/2.10 % (2215893)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=692349798:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 8.39/2.10 % (2215894)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3758926975:i=3394:sd=4:ss=included:sgt=64_2994 on theBenchmark for (2994ds/3394Mi)
% 8.39/2.10 % (2215893)Instruction limit reached!
% 8.39/2.10 % (2215893)------------------------------
% 8.39/2.10 % (2215893)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.10 % (2215893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.10 % (2215893)CaDiCaL version: 2.1.3
% 8.39/2.10 % (2215893)Termination reason: Instruction limit
% 8.39/2.10 % (2215893)Termination phase: Saturation
% 8.39/2.10 % (2215893)Time elapsed: 0.056 s
% 8.39/2.10 % (2215893)Peak memory usage: 90 MB
% 8.39/2.10 % (2215893)Instructions burned: 158 (million)
% 8.39/2.10 % (2215890)Instruction limit reached!
% 8.39/2.10 % (2215890)------------------------------
% 8.39/2.10 % (2215890)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.10 % (2215890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.10 % (2215890)CaDiCaL version: 2.1.3
% 8.39/2.10 % (2215890)Termination reason: Instruction limit
% 8.39/2.10 % (2215890)Termination phase: Saturation
% 8.39/2.10 % (2215890)Time elapsed: 0.120 s
% 8.39/2.10 % (2215890)Peak memory usage: 89 MB
% 8.39/2.10 % (2215890)Instructions burned: 195 (million)
% 8.39/2.10 % (2215888)------------------------------
% 8.39/2.10 % (2215888)------------------------------
% 8.39/2.10 % (2215813)First to succeed.
% 8.39/2.10 % (2215813)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2215712"
% 8.39/2.10 % (2215812)Also succeeded, but the first one will report.
% 8.39/2.10 % (2215899)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=3870582366:i=107_2992 on theBenchmark for (2992ds/107Mi)
% 8.39/2.10 % (2215899)Refutation not found, incomplete strategy
% 8.39/2.10 % (2215899)------------------------------
% 8.39/2.10 % (2215899)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.10 % (2215899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.10 % (2215899)CaDiCaL version: 2.1.3
% 8.39/2.10 % (2215899)Termination reason: Refutation not found, incomplete strategy
% 8.39/2.10 % (2215899)Time elapsed: 0.005 s
% 8.39/2.10 % (2215899)Peak memory usage: 88 MB
% 8.39/2.10 % (2215899)Instructions burned: 12 (million)
% 8.39/2.10 % (2215898)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=2449037896:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2992 on theBenchmark for (2992ds/106Mi)
% 8.39/2.10 % (2215898)Also succeeded, but the first one will report.
% 8.39/2.10 % (2215900)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=3762048478:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2991 on theBenchmark for (2991ds/242Mi)
% 8.39/2.10 % (2215899)------------------------------
% 8.39/2.10 % (2215899)------------------------------
% 8.39/2.10 % (2215813)Refutation found. Thanks to Tanya!
% 8.39/2.10 % SZS status Unsatisfiable for theBenchmark
% 8.39/2.10 % SZS output start Proof for theBenchmark
% See solution above
% 8.39/2.10 % (2215813)------------------------------
% 8.39/2.10 % (2215813)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.10 % (2215813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.10 % (2215813)CaDiCaL version: 2.1.3
% 8.39/2.10 % (2215813)Termination reason: Refutation
% 8.39/2.10 % (2215813)Time elapsed: 0.695 s
% 8.39/2.10 % (2215813)Peak memory usage: 127 MB
% 8.39/2.10 % (2215813)Instructions burned: 1065 (million)
% 8.39/2.10 % (2215813)------------------------------
% 8.39/2.10 % (2215813)------------------------------
% 8.39/2.10 % (2215712)Success in time 1.129 s
% 8.39/2.10 % Vampire exiting
%------------------------------------------------------------------------------