%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN004-4 : 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 : 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 10:19:04 AM UTC 2026
% Result : Unsatisfiable 3.63s 1.48s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 18 unt; 0 def)
% Number of atoms : 31 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( divide(X0,X1) != zero
| less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal2) ).
fof(f3,axiom,
! [X0,X1] : less_equal(divide(X0,X1),X0),
file('/export/starexec/sandbox2/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/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(f10,axiom,
! [X0] : divide(zero,X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
fof(f11,plain,
! [X0] : zero = divide(zero,X0),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X0] : divide(X0,X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
fof(f13,plain,
! [X0] : zero = divide(X0,X0),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
divide(a,zero) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_x_divide_zero_is_x) ).
fof(f15,plain,
a != divide(a,zero),
inference(reorient_equations,[],[f14]) ).
fof(f36,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f39,plain,
! [X0,X1] :
( ~ less_equal(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[],[f6,f3]) ).
fof(f51,plain,
! [X0,X1] : less_equal(divide(divide(X0,X1),zero),divide(divide(X0,zero),X1)),
inference(superposition,[],[f4,f11]) ).
fof(f161,plain,
! [X0] : less_equal(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(superposition,[],[f51,f13]) ).
fof(f187,plain,
! [X0] : zero = divide(divide(X0,divide(X0,zero)),zero),
inference(resolution,[],[f161,f36]) ).
fof(f358,plain,
! [X0] :
( zero != zero
| less_equal(divide(X0,divide(X0,zero)),zero) ),
inference(superposition,[],[f2,f187]) ).
fof(f377,plain,
! [X0] : less_equal(divide(X0,divide(X0,zero)),zero),
inference(trivial_inequality_removal,[],[f358]) ).
fof(f430,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(resolution,[],[f377,f36]) ).
fof(f535,plain,
! [X0] :
( zero != zero
| less_equal(X0,divide(X0,zero)) ),
inference(superposition,[],[f2,f430]) ).
fof(f569,plain,
! [X0] : less_equal(X0,divide(X0,zero)),
inference(trivial_inequality_removal,[],[f535]) ).
fof(f675,plain,
! [X0] : divide(X0,zero) = X0,
inference(resolution,[],[f569,f39]) ).
fof(f811,plain,
a != a,
inference(superposition,[],[f15,f675]) ).
fof(f812,plain,
$false,
inference(trivial_inequality_removal,[],[f811]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN004-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 10:45:10 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 3.63/1.48 % (2365052)Input is clausal, will run a generic CNF schedule.
% 3.63/1.48 % (2365061)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2089799612:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.63/1.48 % (2365058)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1409927926:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.63/1.48 % (2365057)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=1886050313:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.63/1.48 % (2365059)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4246324488:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.63/1.48 % (2365060)lrs+10_1_sil=8000:sp=occurrence:random_seed=1278885951:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.63/1.48 % (2365061)Instruction limit reached!
% 3.63/1.48 % (2365061)------------------------------
% 3.63/1.48 % (2365061)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.48 % (2365061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.48 % (2365061)CaDiCaL version: 2.1.3
% 3.63/1.48 % (2365061)Termination reason: Instruction limit
% 3.63/1.48 % (2365061)Termination phase: Saturation
% 3.63/1.48 % (2365061)Time elapsed: 0.039 s
% 3.63/1.48 % (2365061)Peak memory usage: 88 MB
% 3.63/1.48 % (2365061)Instructions burned: 116 (million)
% 3.63/1.48 % (2365060)First to succeed.
% 3.63/1.48 % (2365060)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2365052"
% 3.63/1.48 % (2365062)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2824771047:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.63/1.48 % (2365063)dis-21_1_sil=8000:lcm=predicate:random_seed=3106816700: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)
% 3.63/1.48 % (2365063)Refutation not found, incomplete strategy
% 3.63/1.48 % (2365063)------------------------------
% 3.63/1.48 % (2365063)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.48 % (2365063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.48 % (2365063)CaDiCaL version: 2.1.3
% 3.63/1.48 % (2365063)Termination reason: Refutation not found, incomplete strategy
% 3.63/1.48 % (2365063)Time elapsed: 0.002 s
% 3.63/1.48 % (2365063)Peak memory usage: 88 MB
% 3.63/1.48 % (2365063)Instructions burned: 1 (million)
% 3.63/1.48 % (2365062)Also succeeded, but the first one will report.
% 3.63/1.48 % (2365069)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=3944444649:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.63/1.48 % (2365069)Refutation not found, incomplete strategy
% 3.63/1.48 % (2365069)------------------------------
% 3.63/1.48 % (2365069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.48 % (2365069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.48 % (2365069)CaDiCaL version: 2.1.3
% 3.63/1.48 % (2365069)Termination reason: Refutation not found, incomplete strategy
% 3.63/1.48 % (2365069)Time elapsed: 0.001 s
% 3.63/1.48 % (2365069)Peak memory usage: 88 MB
% 3.63/1.48 % (2365060)Refutation found. Thanks to Tanya!
% 3.63/1.48 % SZS status Unsatisfiable for theBenchmark
% 3.63/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.48 % (2365060)------------------------------
% 3.63/1.48 % (2365060)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.48 % (2365060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.48 % (2365060)CaDiCaL version: 2.1.3
% 3.63/1.48 % (2365060)Termination reason: Refutation
% 3.63/1.48 % (2365060)Time elapsed: 0.015 s
% 3.63/1.48 % (2365060)Peak memory usage: 88 MB
% 3.63/1.48 % (2365060)Instructions burned: 21 (million)
% 3.63/1.48 % (2365060)------------------------------
% 3.63/1.48 % (2365060)------------------------------
% 3.63/1.48 % (2365052)Success in time 0.435 s
% 3.63/1.48 % Vampire exiting
%------------------------------------------------------------------------------