%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN004-6 : 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 10:19:05 AM UTC 2026
% Result : Unsatisfiable 2.86s 1.38s
% Output : Refutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 17 unt; 0 def)
% Number of atoms : 42 ( 28 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 13 |; 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 : 36 ( 36 !; 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] :
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
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(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_and_equal) ).
fof(f10,axiom,
! [X0] : divide(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
fof(f11,plain,
! [X0] : zero = divide(zero,X0),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
divide(a,zero) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_x_divide_zero_is_x) ).
fof(f13,plain,
a != divide(a,zero),
inference(reorient_equations,[],[f12]) ).
fof(f18,plain,
! [X0,X1] : zero = divide(divide(X0,X1),X0),
inference(resolution,[],[f1,f3]) ).
fof(f24,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f27,plain,
! [X0,X1] :
( ~ less_equal(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[],[f6,f3]) ).
fof(f30,plain,
! [X0] :
( zero != divide(X0,zero)
| zero = X0 ),
inference(resolution,[],[f24,f2]) ).
fof(f38,plain,
! [X0,X1] : less_equal(divide(divide(X0,X1),zero),divide(divide(X0,zero),X1)),
inference(superposition,[],[f4,f11]) ).
fof(f71,plain,
! [X0,X1] :
( zero != divide(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[],[f27,f2]) ).
fof(f90,plain,
! [X0,X1] :
( ~ less_equal(divide(divide(X0,zero),X1),divide(divide(X0,X1),zero))
| divide(divide(X0,zero),X1) = divide(divide(X0,X1),zero) ),
inference(resolution,[],[f38,f6]) ).
fof(f98,plain,
! [X0] : less_equal(divide(divide(X0,X0),zero),zero),
inference(superposition,[],[f38,f18]) ).
fof(f107,plain,
! [X0] : zero = divide(divide(X0,X0),zero),
inference(resolution,[],[f98,f24]) ).
fof(f263,plain,
! [X0] :
( zero != zero
| zero = divide(X0,X0) ),
inference(superposition,[],[f30,f107]) ).
fof(f282,plain,
! [X0] : zero = divide(X0,X0),
inference(trivial_inequality_removal,[],[f263]) ).
fof(f1843,plain,
! [X0] :
( ~ less_equal(zero,divide(divide(X0,divide(X0,zero)),zero))
| zero = divide(divide(X0,divide(X0,zero)),zero) ),
inference(superposition,[],[f90,f282]) ).
fof(f1872,plain,
! [X0] : zero = divide(divide(X0,divide(X0,zero)),zero),
inference(forward_subsumption_resolution,[],[f1843,f5]) ).
fof(f1946,plain,
! [X0] :
( zero != zero
| zero = divide(X0,divide(X0,zero)) ),
inference(superposition,[],[f30,f1872]) ).
fof(f1987,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(trivial_inequality_removal,[],[f1946]) ).
fof(f2047,plain,
! [X0] :
( zero != zero
| divide(X0,zero) = X0 ),
inference(superposition,[],[f71,f1987]) ).
fof(f2121,plain,
! [X0] : divide(X0,zero) = X0,
inference(trivial_inequality_removal,[],[f2047]) ).
fof(f2253,plain,
a != a,
inference(superposition,[],[f13,f2121]) ).
fof(f2254,plain,
$false,
inference(trivial_inequality_removal,[],[f2253]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN004-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n005.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 10:49:37 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 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
% 2.86/1.38 % (3810486)Input is clausal, will run a generic CNF schedule.
% 2.86/1.38 % (3810564)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2684147036:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.86/1.38 % (3810564)First to succeed.
% 2.86/1.38 % (3810564)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3810486"
% 2.86/1.38 % (3810560)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3386889754:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.86/1.38 % (3810566)dis-21_1_sil=8000:lcm=predicate:random_seed=770828660: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)
% 2.86/1.38 % (3810562)lrs+10_1_sil=8000:sp=occurrence:random_seed=160428670:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.86/1.38 % (3810557)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=1651656539:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.86/1.38 % (3810563)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1221046635:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.86/1.38 % (3810559)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1622009417:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.86/1.38 % (3810566)Refutation not found, incomplete strategy
% 2.86/1.38 % (3810566)------------------------------
% 2.86/1.38 % (3810566)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.38 % (3810566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.38 % (3810566)CaDiCaL version: 2.1.3
% 2.86/1.38 % (3810566)Termination reason: Refutation not found, incomplete strategy
% 2.86/1.38 % (3810566)Time elapsed: 0.002 s
% 2.86/1.38 % (3810566)Peak memory usage: 88 MB
% 2.86/1.38 % (3810562)Instruction limit reached!
% 2.86/1.38 % (3810562)------------------------------
% 2.86/1.38 % (3810562)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.38 % (3810562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.38 % (3810562)CaDiCaL version: 2.1.3
% 2.86/1.38 % (3810562)Termination reason: Instruction limit
% 2.86/1.38 % (3810562)Termination phase: Saturation
% 2.86/1.38 % (3810562)Time elapsed: 0.062 s
% 2.86/1.38 % (3810562)Peak memory usage: 89 MB
% 2.86/1.38 % (3810562)Instructions burned: 108 (million)
% 2.86/1.38 % (3810563)Instruction limit reached!
% 2.86/1.38 % (3810563)------------------------------
% 2.86/1.38 % (3810563)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.38 % (3810563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.38 % (3810563)CaDiCaL version: 2.1.3
% 2.86/1.38 % (3810563)Termination reason: Instruction limit
% 2.86/1.38 % (3810563)Termination phase: Saturation
% 2.86/1.38 % (3810563)Time elapsed: 0.069 s
% 2.86/1.38 % (3810563)Peak memory usage: 88 MB
% 2.86/1.38 % (3810563)Instructions burned: 114 (million)
% 2.86/1.38 % (3810564)Refutation found. Thanks to Tanya!
% 2.86/1.38 % SZS status Unsatisfiable for theBenchmark
% 2.86/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.86/1.38 % (3810564)------------------------------
% 2.86/1.38 % (3810564)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.38 % (3810564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.38 % (3810564)CaDiCaL version: 2.1.3
% 2.86/1.38 % (3810564)Termination reason: Refutation
% 2.86/1.38 % (3810564)Time elapsed: 0.022 s
% 2.86/1.38 % (3810564)Peak memory usage: 89 MB
% 2.86/1.38 % (3810564)Instructions burned: 67 (million)
% 2.86/1.38 % (3810564)------------------------------
% 2.86/1.38 % (3810564)------------------------------
% 2.86/1.38 % (3810486)Success in time 0.325 s
% 2.86/1.38 % Vampire exiting
%------------------------------------------------------------------------------