%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN006-4 : 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 : 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 10:19:06 AM UTC 2026
% Result : Unsatisfiable 3.67s 1.43s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 18 ( 11 unt; 0 def)
% Number of atoms : 27 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 10 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ less_equal(X0,X1)
| divide(X0,X1) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal1) ).
fof(f2,axiom,
! [X0,X1] :
( divide(X0,X1) != zero
| less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal2) ).
fof(f3,axiom,
! [X0,X1] : less_equal(divide(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
fof(f4,axiom,
! [X2,X0,X1] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
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(f16,axiom,
! [X2,X0,X1] :
( ~ less_equal(X1,X2)
| ~ less_equal(X0,X1)
| less_equal(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
fof(f17,axiom,
less_equal(divide(a,b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_divide_b_LE_d) ).
fof(f18,negated_conjecture,
~ less_equal(divide(a,d),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_divide_d_LE_b) ).
fof(f25,plain,
zero = divide(divide(a,b),d),
inference(resolution,[],[f1,f17]) ).
fof(f49,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ less_equal(X0,divide(X1,X2))
| less_equal(X0,X1) ),
inference(resolution,[],[f16,f3]) ).
fof(f104,plain,
less_equal(divide(divide(a,d),divide(b,d)),zero),
inference(superposition,[],[f4,f25]) ).
fof(f370,plain,
zero = divide(divide(a,d),divide(b,d)),
inference(resolution,[],[f104,f49]) ).
fof(f890,plain,
( zero != zero
| less_equal(divide(a,d),divide(b,d)) ),
inference(superposition,[],[f2,f370]) ).
fof(f914,plain,
less_equal(divide(a,d),divide(b,d)),
inference(trivial_inequality_removal,[],[f890]) ).
fof(f979,plain,
less_equal(divide(a,d),b),
inference(resolution,[],[f914,f63]) ).
fof(f992,plain,
$false,
inference(forward_subsumption_resolution,[],[f979,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN006-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 % Computer : n005.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sun Sep 27 10:50:38 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.44 Running first-order theorem proving
% 0.15/0.44 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
% 3.67/1.43 % (3811413)Input is clausal, will run a generic CNF schedule.
% 3.67/1.43 % (3811541)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=314834221:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.67/1.43 % (3811535)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=663897298:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.67/1.43 % (3811533)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=591776088:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.67/1.43 % (3811536)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4042604742:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.67/1.43 % (3811538)lrs+10_1_sil=8000:sp=occurrence:random_seed=1368951394:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.67/1.43 % (3811545)dis-21_1_sil=8000:lcm=predicate:random_seed=353923995: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)
% 3.67/1.43 % (3811541)Instruction limit reached!
% 3.67/1.43 % (3811541)------------------------------
% 3.67/1.43 % (3811541)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.43 % (3811541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.43 % (3811541)CaDiCaL version: 2.1.3
% 3.67/1.43 % (3811541)Termination reason: Instruction limit
% 3.67/1.43 % (3811541)Termination phase: Saturation
% 3.67/1.43 % (3811541)Time elapsed: 0.034 s
% 3.67/1.43 % (3811541)Peak memory usage: 88 MB
% 3.67/1.43 % (3811541)Instructions burned: 116 (million)
% 3.67/1.43 % (3811543)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2908454319:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.67/1.43 % (3811538)First to succeed.
% 3.67/1.43 % (3811538)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3811413"
% 3.67/1.43 % (3811543)Also succeeded, but the first one will report.
% 3.67/1.43 % (3811545)Instruction limit reached!
% 3.67/1.43 % (3811545)------------------------------
% 3.67/1.43 % (3811545)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.43 % (3811545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.43 % (3811545)CaDiCaL version: 2.1.3
% 3.67/1.43 % (3811545)Termination reason: Instruction limit
% 3.67/1.43 % (3811545)Termination phase: Saturation
% 3.67/1.43 % (3811545)Time elapsed: 0.071 s
% 3.67/1.43 % (3811545)Peak memory usage: 88 MB
% 3.67/1.43 % (3811545)Instructions burned: 118 (million)
% 3.67/1.43 % (3811585)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=116852769:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.67/1.43 % (3811585)Instruction limit reached!
% 3.67/1.43 % (3811585)------------------------------
% 3.67/1.43 % (3811585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.43 % (3811585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.43 % (3811585)CaDiCaL version: 2.1.3
% 3.67/1.43 % (3811585)Termination reason: Instruction limit
% 3.67/1.43 % (3811585)Termination phase: Saturation
% 3.67/1.43 % (3811585)Time elapsed: 0.047 s
% 3.67/1.43 % (3811585)Peak memory usage: 89 MB
% 3.67/1.43 % (3811585)Instructions burned: 143 (million)
% 3.67/1.43 % (3811587)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3251990123: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)
% 3.67/1.43 % (3811587)Also succeeded, but the first one will report.
% 3.67/1.43 % (3811538)Refutation found. Thanks to Tanya!
% 3.67/1.43 % SZS status Unsatisfiable for theBenchmark
% 3.67/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.43 % (3811538)------------------------------
% 3.67/1.43 % (3811538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.43 % (3811538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.43 % (3811538)CaDiCaL version: 2.1.3
% 3.67/1.43 % (3811538)Termination reason: Refutation
% 3.67/1.43 % (3811538)Time elapsed: 0.019 s
% 3.67/1.43 % (3811538)Peak memory usage: 88 MB
% 3.67/1.43 % (3811538)Instructions burned: 27 (million)
% 3.67/1.43 % (3811538)------------------------------
% 3.67/1.43 % (3811538)------------------------------
% 3.67/1.43 % (3811413)Success in time 0.446 s
% 3.67/1.43 % Vampire exiting
%------------------------------------------------------------------------------