%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : HEN009-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 10:19:18 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.41s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 41 ( 25 unt; 0 def)
% Number of atoms : 58 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 19 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 37 ( 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ less_equal(X0,X1)
| divide(X0,X1) = zero ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).
fof(f2,axiom,
! [X0,X1] :
( divide(X0,X1) != zero
| less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_less_equal2) ).
fof(f3,axiom,
! [X0,X1] : less_equal(divide(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_smaller_than_numerator) ).
fof(f5,axiom,
! [X0] : less_equal(zero,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
fof(f6,axiom,
! [X0,X1] :
( ~ less_equal(X1,X0)
| ~ less_equal(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',less_equal_and_equal) ).
fof(f7,axiom,
! [X0] : less_equal(X0,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',identity_is_largest) ).
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,axiom,
! [X2,X0,X1] :
( ~ less_equal(divide(X0,X1),X2)
| less_equal(divide(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide1) ).
fof(f15,axiom,
! [X2,X0,X1] :
( less_equal(divide(X0,X2),divide(X1,X2))
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide3) ).
fof(f17,axiom,
divide(identity,a) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id_divide_a_is_b) ).
fof(f18,axiom,
divide(identity,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id_divide_b_is_c) ).
fof(f19,axiom,
divide(identity,c) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id_divide_c_is_d) ).
fof(f20,negated_conjecture,
b != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_equals_d) ).
fof(f93,plain,
! [X0] :
( zero != zero
| less_equal(X0,X0) ),
inference(superposition,[],[f2,f13]) ).
fof(f101,plain,
! [X0] : less_equal(X0,X0),
inference(trivial_inequality_removal,[],[f93]) ).
fof(f162,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f600,plain,
! [X0,X1] : less_equal(divide(X0,divide(X0,X1)),X1),
inference(resolution,[],[f14,f101]) ).
fof(f606,plain,
! [X0] :
( less_equal(divide(identity,X0),a)
| ~ less_equal(b,X0) ),
inference(superposition,[],[f14,f17]) ).
fof(f789,plain,
( less_equal(c,a)
| ~ less_equal(b,b) ),
inference(superposition,[],[f606,f18]) ).
fof(f794,plain,
less_equal(c,a),
inference(forward_subsumption_resolution,[],[f789,f101]) ).
fof(f804,plain,
zero = divide(c,a),
inference(resolution,[],[f794,f1]) ).
fof(f869,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(resolution,[],[f600,f162]) ).
fof(f875,plain,
less_equal(divide(identity,c),b),
inference(superposition,[],[f600,f18]) ).
fof(f879,plain,
less_equal(d,b),
inference(forward_demodulation,[],[f875,f19]) ).
fof(f882,plain,
( ~ less_equal(b,d)
| b = d ),
inference(resolution,[],[f879,f6]) ).
fof(f884,plain,
~ less_equal(b,d),
inference(forward_subsumption_resolution,[],[f882,f20]) ).
fof(f937,plain,
! [X0] :
( zero != zero
| less_equal(X0,divide(X0,zero)) ),
inference(superposition,[],[f2,f869]) ).
fof(f944,plain,
! [X0] : less_equal(X0,divide(X0,zero)),
inference(trivial_inequality_removal,[],[f937]) ).
fof(f947,plain,
! [X0] :
( ~ less_equal(divide(X0,zero),X0)
| divide(X0,zero) = X0 ),
inference(resolution,[],[f944,f6]) ).
fof(f954,plain,
! [X0] : divide(X0,zero) = X0,
inference(forward_subsumption_resolution,[],[f947,f3]) ).
fof(f1348,plain,
! [X0] :
( less_equal(divide(X0,c),d)
| ~ less_equal(X0,identity) ),
inference(superposition,[],[f15,f19]) ).
fof(f1351,plain,
! [X0] :
( less_equal(divide(X0,a),zero)
| ~ less_equal(X0,c) ),
inference(superposition,[],[f15,f804]) ).
fof(f1356,plain,
! [X0] : less_equal(divide(X0,c),d),
inference(forward_subsumption_resolution,[],[f1348,f7]) ).
fof(f2719,plain,
! [X0] : less_equal(divide(X0,d),c),
inference(resolution,[],[f1356,f14]) ).
fof(f3639,plain,
! [X0] :
( ~ less_equal(X0,c)
| less_equal(divide(X0,zero),a) ),
inference(resolution,[],[f1351,f14]) ).
fof(f3655,plain,
! [X0] :
( ~ less_equal(X0,c)
| less_equal(X0,a) ),
inference(forward_demodulation,[],[f3639,f954]) ).
fof(f3773,plain,
! [X0] : less_equal(divide(X0,d),a),
inference(resolution,[],[f3655,f2719]) ).
fof(f3805,plain,
! [X0] : less_equal(divide(X0,a),d),
inference(resolution,[],[f3773,f14]) ).
fof(f3872,plain,
less_equal(b,d),
inference(superposition,[],[f3805,f17]) ).
fof(f3876,plain,
$false,
inference(forward_subsumption_resolution,[],[f3872,f884]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : HEN009-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 10:50:35 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.04/0.33 Running first-order model finding
% 0.04/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.41 % (2203305)Will run a generic schedule for satisfiability detection.
% 0.08/0.41 % (2203312)% WARNING: option uhcvi not known.
% 0.08/0.41 % (2203316)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4079060058:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.08/0.41 % (2203312)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2205147699:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.08/0.41 % (2203311)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=214307727_3000 on theBenchmark for (3000ds/0Mi)
% 0.08/0.41 % (2203315)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=306469503:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.08/0.41 % (2203313)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3416962175:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.08/0.41 % (2203314)dis+10_1_sil=32000:sp=arity:random_seed=3924164561:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.08/0.41 % (2203317)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2173327305:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.08/0.41 % TRYING [1]
% 0.08/0.41 % TRYING [2]
% 0.08/0.41 % TRYING [3]
% 0.08/0.41 % TRYING [4]
% 0.08/0.41 % TRYING [5]
% 0.08/0.41 % TRYING [6]
% 0.08/0.41 % (2203314) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2203305-2203314"...
% 0.08/0.41 % (2203313) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2203305-2203313"...
% 0.08/0.41 % (2203313)...printing done.
% 0.08/0.41 % (2203314)...printing done.
% 0.08/0.41 % (2203313)Refutation found. Thanks to Tanya!
% 0.08/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.41 % (2203313)------------------------------
% 0.08/0.41 % (2203313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.41 % (2203313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.41 % (2203313)CaDiCaL version: 2.1.3
% 0.08/0.41 % (2203313)Termination reason: Refutation
% 0.08/0.41 % (2203313)Time elapsed: 0.043 s
% 0.08/0.41 % (2203313)Peak memory usage: 12 MB
% 0.08/0.41 % (2203313)Instructions burned: 75 (million)
% 0.08/0.41 % (2203305)Success in time 0.066 s
% 0.08/0.41 % Vampire exiting
%------------------------------------------------------------------------------