%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN006-6 : 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 : n006.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 5.45s 1.95s
% Output : Refutation 5.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 24 unt; 0 def)
% Number of atoms : 49 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ less_equal(X0,X1)
| divide(X0,X1) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal1) ).
fof(f2,axiom,
! [X0,X1] :
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
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(X0,X1)
| ~ less_equal(X1,X0)
| 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,axiom,
less_equal(divide(a,b),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_divide_b_LE_d) ).
fof(f15,negated_conjecture,
~ less_equal(divide(a,d),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_divide_d_LE_b) ).
fof(f21,plain,
zero = divide(divide(a,b),d),
inference(resolution,[],[f1,f14]) ).
fof(f22,plain,
! [X0,X1] : zero = divide(divide(X0,X1),X0),
inference(resolution,[],[f1,f3]) ).
fof(f23,plain,
zero != divide(divide(a,d),b),
inference(resolution,[],[f2,f15]) ).
fof(f25,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f27,plain,
! [X0,X1] :
( zero != divide(X1,X0)
| X0 = X1
| ~ less_equal(X0,X1) ),
inference(resolution,[],[f6,f2]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ less_equal(divide(divide(X0,X1),X2),divide(divide(X0,X2),divide(X1,X2)))
| divide(divide(X0,X1),X2) = divide(divide(X0,X2),divide(X1,X2)) ),
inference(resolution,[],[f4,f6]) ).
fof(f48,plain,
! [X0,X1] : less_equal(divide(divide(X0,X1),zero),divide(divide(X0,zero),X1)),
inference(superposition,[],[f4,f11]) ).
fof(f67,plain,
! [X0] :
( zero != divide(X0,zero)
| zero = X0 ),
inference(resolution,[],[f25,f2]) ).
fof(f86,plain,
! [X2,X0,X1] : less_equal(divide(divide(X0,X1),zero),divide(divide(X0,divide(X1,X2)),X1)),
inference(superposition,[],[f4,f22]) ).
fof(f185,plain,
! [X0] : less_equal(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(superposition,[],[f48,f13]) ).
fof(f213,plain,
! [X0] : zero = divide(divide(X0,divide(X0,zero)),zero),
inference(resolution,[],[f185,f25]) ).
fof(f302,plain,
( ~ less_equal(zero,divide(divide(a,d),divide(b,d)))
| zero = divide(divide(a,d),divide(b,d)) ),
inference(superposition,[],[f41,f21]) ).
fof(f338,plain,
zero = divide(divide(a,d),divide(b,d)),
inference(forward_subsumption_resolution,[],[f302,f5]) ).
fof(f559,plain,
! [X0] :
( zero != zero
| zero = divide(X0,divide(X0,zero)) ),
inference(superposition,[],[f67,f213]) ).
fof(f581,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(trivial_inequality_removal,[],[f559]) ).
fof(f617,plain,
! [X0] :
( zero != zero
| divide(X0,zero) = X0
| ~ less_equal(divide(X0,zero),X0) ),
inference(superposition,[],[f27,f581]) ).
fof(f648,plain,
! [X0] :
( divide(X0,zero) = X0
| ~ less_equal(divide(X0,zero),X0) ),
inference(trivial_inequality_removal,[],[f617]) ).
fof(f658,plain,
! [X0] : divide(X0,zero) = X0,
inference(forward_subsumption_resolution,[],[f648,f3]) ).
fof(f947,plain,
! [X2,X0,X1] : less_equal(divide(X0,X1),divide(divide(X0,divide(X1,X2)),X1)),
inference(forward_demodulation,[],[f86,f658]) ).
fof(f984,plain,
less_equal(divide(divide(a,d),b),divide(zero,b)),
inference(superposition,[],[f947,f338]) ).
fof(f995,plain,
less_equal(divide(divide(a,d),b),zero),
inference(forward_demodulation,[],[f984,f11]) ).
fof(f1026,plain,
zero = divide(divide(a,d),b),
inference(resolution,[],[f995,f25]) ).
fof(f1031,plain,
$false,
inference(forward_subsumption_resolution,[],[f1026,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : HEN006-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.44 % Computer : n006.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sun Sep 27 10:50:32 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.49 Running first-order theorem proving
% 0.23/0.49 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
% 5.45/1.95 % (2799955)Input is clausal, will run a generic CNF schedule.
% 5.45/1.95 % (2799966)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=1609169816:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.45/1.95 % (2799970)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1151837297:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.45/1.95 % (2799967)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2090303453:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.45/1.95 % (2799969)lrs+10_1_sil=8000:sp=occurrence:random_seed=1895476050:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.45/1.95 % (2799971)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3329144929:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.45/1.95 % (2799968)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1939313795:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.45/1.95 % (2799972)dis-21_1_sil=8000:lcm=predicate:random_seed=339415296: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)
% 5.45/1.95 % (2799969)Refutation not found, incomplete strategy
% 5.45/1.95 % (2799969)------------------------------
% 5.45/1.95 % (2799969)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.45/1.95 % (2799969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.45/1.95 % (2799969)CaDiCaL version: 2.1.3
% 5.45/1.95 % (2799969)Termination reason: Refutation not found, incomplete strategy
% 5.45/1.95 % (2799969)Time elapsed: 0.001 s
% 5.45/1.95 % (2799969)Peak memory usage: 87 MB
% 5.45/1.95 % (2799972)Refutation not found, incomplete strategy
% 5.45/1.95 % (2799972)------------------------------
% 5.45/1.95 % (2799972)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.45/1.95 % (2799972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.45/1.95 % (2799972)CaDiCaL version: 2.1.3
% 5.45/1.95 % (2799972)Termination reason: Refutation not found, incomplete strategy
% 5.45/1.95 % (2799972)Time elapsed: 0.002 s
% 5.45/1.95 % (2799972)Peak memory usage: 88 MB
% 5.45/1.95 % (2799970)Instruction limit reached!
% 5.45/1.95 % (2799970)------------------------------
% 5.45/1.95 % (2799970)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.45/1.95 % (2799970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.45/1.95 % (2799970)CaDiCaL version: 2.1.3
% 5.45/1.95 % (2799970)Termination reason: Instruction limit
% 5.45/1.95 % (2799970)Termination phase: Saturation
% 5.45/1.95 % (2799970)Time elapsed: 0.083 s
% 5.45/1.95 % (2799970)Peak memory usage: 88 MB
% 5.45/1.95 % (2799970)Instructions burned: 114 (million)
% 5.45/1.95 % (2799971)First to succeed.
% 5.45/1.95 % (2799971)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2799955"
% 5.45/1.95 % (2799981)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=2227470239:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.45/1.95 % (2799981)Refutation not found, incomplete strategy
% 5.45/1.95 % (2799981)------------------------------
% 5.45/1.95 % (2799981)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.45/1.95 % (2799981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.45/1.95 % (2799981)CaDiCaL version: 2.1.3
% 5.45/1.95 % (2799981)Termination reason: Refutation not found, incomplete strategy
% 5.45/1.95 % (2799981)Time elapsed: 0.003 s
% 5.45/1.95 % (2799981)Peak memory usage: 88 MB
% 5.45/1.95 % (2799981)Instructions burned: 1 (million)
% 5.45/1.95 % (2799969)------------------------------
% 5.45/1.95 % (2799969)------------------------------
% 5.45/1.95 % (2799972)------------------------------
% 5.45/1.95 % (2799972)------------------------------
% 5.45/1.95 % (2799971)Refutation found. Thanks to Tanya!
% 5.45/1.95 % SZS status Unsatisfiable for theBenchmark
% 5.45/1.95 % SZS output start Proof for theBenchmark
% See solution above
% 5.45/1.95 % (2799971)------------------------------
% 5.45/1.95 % (2799971)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.45/1.95 % (2799971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.45/1.95 % (2799971)CaDiCaL version: 2.1.3
% 5.45/1.95 % (2799971)Termination reason: Refutation
% 5.45/1.95 % (2799971)Time elapsed: 0.030 s
% 5.45/1.95 % (2799971)Peak memory usage: 89 MB
% 5.45/1.95 % (2799971)Instructions burned: 29 (million)
% 5.45/1.95 % (2799971)------------------------------
% 5.45/1.95 % (2799971)------------------------------
% 5.45/1.95 % (2799955)Success in time 0.646 s
% 5.45/1.95 % Vampire exiting
%------------------------------------------------------------------------------