%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN007-6 : 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 : n015.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 5.56s 1.71s
% Output : Refutation 5.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 24 ( 11 unt; 0 def)
% Number of atoms : 51 ( 3 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 55 ( 28 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 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 : 52 ( 52 !; 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(f3,axiom,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| less_equal(X2,X0) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',quotient_property) ).
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(f13,axiom,
! [X0] : quotient(X0,zero,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
fof(f14,axiom,
! [X2,X0,X1] :
( ~ less_equal(X1,X2)
| ~ less_equal(X0,X1)
| less_equal(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
fof(f15,axiom,
less_equal(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xLEy) ).
fof(f16,axiom,
quotient(z,y,zQy),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zQy) ).
fof(f17,axiom,
quotient(z,x,zQx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zQx) ).
fof(f18,negated_conjecture,
~ less_equal(zQy,zQx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_zQyLEzQx) ).
fof(f24,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ quotient(X4,X1,X5)
| ~ quotient(X2,X1,X3)
| ~ quotient(X2,X0,X4)
| ~ quotient(X0,X1,zero)
| less_equal(X3,X5) ),
inference(resolution,[],[f13,f4]) ).
fof(f27,plain,
! [X2,X3,X0,X1,X4] :
( ~ quotient(X3,X1,zero)
| ~ quotient(X0,X3,X4)
| ~ quotient(X0,X1,X2)
| less_equal(X2,divide(X4,X1)) ),
inference(resolution,[],[f24,f8]) ).
fof(f32,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[],[f3,f8]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| divide(X0,X1) = X2 ),
inference(resolution,[],[f9,f8]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ less_equal(X0,divide(X1,X2))
| less_equal(X0,X1) ),
inference(resolution,[],[f32,f14]) ).
fof(f87,plain,
zQy = divide(z,y),
inference(resolution,[],[f40,f16]) ).
fof(f101,plain,
! [X2,X3,X0,X1,X4] :
( ~ quotient(X0,X3,X4)
| ~ quotient(X0,X1,X2)
| less_equal(X4,divide(X2,X3))
| ~ less_equal(X1,X3) ),
inference(resolution,[],[f27,f1]) ).
fof(f266,plain,
! [X2,X3,X0,X1] :
( ~ quotient(X0,X1,X2)
| less_equal(divide(X0,X3),divide(X2,X3))
| ~ less_equal(X1,X3) ),
inference(resolution,[],[f101,f8]) ).
fof(f273,plain,
! [X0] :
( less_equal(divide(z,X0),divide(zQx,X0))
| ~ less_equal(x,X0) ),
inference(resolution,[],[f266,f17]) ).
fof(f330,plain,
( less_equal(zQy,divide(zQx,y))
| ~ less_equal(x,y) ),
inference(superposition,[],[f273,f87]) ).
fof(f347,plain,
less_equal(zQy,divide(zQx,y)),
inference(forward_subsumption_resolution,[],[f330,f15]) ).
fof(f350,plain,
less_equal(zQy,zQx),
inference(resolution,[],[f347,f43]) ).
fof(f363,plain,
$false,
inference(forward_subsumption_resolution,[],[f350,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN007-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:54:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 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
% 5.56/1.71 % (1479596)Input is clausal, will run a generic CNF schedule.
% 5.56/1.71 % (1479619)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=2898331347:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.56/1.71 % (1479624)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1357691817:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.56/1.71 % (1479620)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3303827870:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.56/1.71 % (1479623)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2798224026:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.56/1.71 % (1479622)lrs+10_1_sil=8000:sp=occurrence:random_seed=1860401044:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.56/1.71 % (1479621)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3415282979:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.56/1.71 % (1479622)Refutation not found, incomplete strategy
% 5.56/1.71 % (1479622)------------------------------
% 5.56/1.71 % (1479622)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.71 % (1479622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.71 % (1479622)CaDiCaL version: 2.1.3
% 5.56/1.71 % (1479622)Termination reason: Refutation not found, incomplete strategy
% 5.56/1.71 % (1479622)Time elapsed: 0.002 s
% 5.56/1.71 % (1479622)Peak memory usage: 88 MB
% 5.56/1.71 % (1479622)Instructions burned: 1 (million)
% 5.56/1.71 % (1479625)dis-21_1_sil=8000:lcm=predicate:random_seed=1992698980: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)
% 5.56/1.71 % (1479623)Instruction limit reached!
% 5.56/1.71 % (1479623)------------------------------
% 5.56/1.71 % (1479623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.71 % (1479623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.71 % (1479623)CaDiCaL version: 2.1.3
% 5.56/1.71 % (1479623)Termination reason: Instruction limit
% 5.56/1.71 % (1479623)Termination phase: Saturation
% 5.56/1.71 % (1479623)Time elapsed: 0.054 s
% 5.56/1.71 % (1479623)Peak memory usage: 87 MB
% 5.56/1.71 % (1479623)Instructions burned: 115 (million)
% 5.56/1.71 % (1479624)Instruction limit reached!
% 5.56/1.71 % (1479624)------------------------------
% 5.56/1.71 % (1479624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.71 % (1479624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.71 % (1479624)CaDiCaL version: 2.1.3
% 5.56/1.71 % (1479624)Termination reason: Instruction limit
% 5.56/1.71 % (1479624)Termination phase: Saturation
% 5.56/1.71 % (1479624)Time elapsed: 0.106 s
% 5.56/1.71 % (1479624)Peak memory usage: 89 MB
% 5.56/1.71 % (1479624)Instructions burned: 184 (million)
% 5.56/1.71 % (1479625)Instruction limit reached!
% 5.56/1.71 % (1479625)------------------------------
% 5.56/1.71 % (1479625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.71 % (1479625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.71 % (1479625)CaDiCaL version: 2.1.3
% 5.56/1.71 % (1479625)Termination reason: Instruction limit
% 5.56/1.71 % (1479625)Termination phase: Saturation
% 5.56/1.71 % (1479625)Time elapsed: 0.096 s
% 5.56/1.71 % (1479625)Peak memory usage: 88 MB
% 5.56/1.71 % (1479625)Instructions burned: 118 (million)
% 5.56/1.71 % (1479635)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=3781574902:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.56/1.71 % (1479622)------------------------------
% 5.56/1.71 % (1479622)------------------------------
% 5.56/1.71 % (1479636)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=380109141: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)
% 5.56/1.71 % (1479637)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=399635950:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 5.56/1.71 % (1479635)Instruction limit reached!
% 5.56/1.71 % (1479635)------------------------------
% 5.56/1.71 % (1479635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.71 % (1479635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.71 % (1479635)CaDiCaL version: 2.1.3
% 5.56/1.71 % (1479635)Termination reason: Instruction limit
% 5.56/1.71 % (1479635)Termination phase: Saturation
% 5.56/1.71 % (1479635)Time elapsed: 0.090 s
% 5.56/1.71 % (1479635)Peak memory usage: 89 MB
% 5.56/1.71 % (1479635)Instructions burned: 144 (million)
% 5.56/1.71 % (1479619)First to succeed.
% 5.56/1.71 % (1479619)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1479596"
% 5.56/1.71 % (1479636)Instruction limit reached!
% 5.56/1.71 % (1479636)------------------------------
% 5.56/1.71 % (1479636)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.71 % (1479636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.71 % (1479636)CaDiCaL version: 2.1.3
% 5.56/1.71 % (1479636)Termination reason: Instruction limit
% 5.56/1.71 % (1479636)Termination phase: Saturation
% 5.56/1.71 % (1479636)Time elapsed: 0.107 s
% 5.56/1.71 % (1479636)Peak memory usage: 88 MB
% 5.56/1.71 % (1479636)Instructions burned: 190 (million)
% 5.56/1.71 % (1479637)Instruction limit reached!
% 5.56/1.71 % (1479637)------------------------------
% 5.56/1.71 % (1479637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.71 % (1479637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.71 % (1479637)CaDiCaL version: 2.1.3
% 5.56/1.71 % (1479637)Termination reason: Instruction limit
% 5.56/1.71 % (1479637)Termination phase: Saturation
% 5.56/1.71 % (1479637)Time elapsed: 0.087 s
% 5.56/1.71 % (1479637)Peak memory usage: 88 MB
% 5.56/1.71 % (1479637)Instructions burned: 221 (million)
% 5.56/1.71 % (1479641)lrs+10_64_to=lpo:sil=8000:random_seed=4141669581:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 5.56/1.71 % (1479643)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=634224380:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 5.56/1.71 % (1479641)Instruction limit reached!
% 5.56/1.71 % (1479641)------------------------------
% 5.56/1.71 % (1479641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.71 % (1479641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.71 % (1479641)CaDiCaL version: 2.1.3
% 5.56/1.71 % (1479641)Termination reason: Instruction limit
% 5.56/1.71 % (1479641)Termination phase: Saturation
% 5.56/1.71 % (1479641)Time elapsed: 0.071 s
% 5.56/1.71 % (1479641)Peak memory usage: 88 MB
% 5.56/1.71 % (1479641)Instructions burned: 126 (million)
% 5.56/1.71 % (1479619)Refutation found. Thanks to Tanya!
% 5.56/1.71 % SZS status Unsatisfiable for theBenchmark
% 5.56/1.71 % SZS output start Proof for theBenchmark
% See solution above
% 5.56/1.71 % (1479619)------------------------------
% 5.56/1.71 % (1479619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.71 % (1479619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.71 % (1479619)CaDiCaL version: 2.1.3
% 5.56/1.71 % (1479619)Termination reason: Refutation
% 5.56/1.71 % (1479619)Time elapsed: 0.360 s
% 5.56/1.71 % (1479619)Peak memory usage: 128 MB
% 5.56/1.71 % (1479619)Instructions burned: 970 (million)
% 5.56/1.71 % (1479619)------------------------------
% 5.56/1.71 % (1479619)------------------------------
% 5.56/1.71 % (1479596)Success in time 0.705 s
% 5.56/1.71 % Vampire exiting
%------------------------------------------------------------------------------