%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n015.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 10:19:09 AM UTC 2026
% Result : Unsatisfiable 7.03s 1.99s
% Output : Refutation 7.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 36 ( 24 unt; 0 def)
% Number of atoms : 49 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 13 |; 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 : 27 ( 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( divide(X0,X1) = zero
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal1) ).
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(f7,axiom,
! [X0] : less_equal(X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_is_largest) ).
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(f25,plain,
! [X0] : less_equal(divide(b,divide(X0,a)),divide(divide(identity,X0),a)),
inference(superposition,[],[f4,f17]) ).
fof(f30,plain,
! [X0] :
( less_equal(divide(X0,a),b)
| ~ less_equal(X0,identity) ),
inference(superposition,[],[f15,f17]) ).
fof(f31,plain,
! [X0] : less_equal(divide(X0,a),b),
inference(forward_subsumption_resolution,[],[f30,f7]) ).
fof(f54,plain,
! [X0] :
( less_equal(divide(X0,b),c)
| ~ less_equal(X0,identity) ),
inference(superposition,[],[f15,f18]) ).
fof(f55,plain,
! [X0] : less_equal(divide(X0,b),c),
inference(forward_subsumption_resolution,[],[f54,f7]) ).
fof(f96,plain,
! [X0] : less_equal(divide(X0,b),a),
inference(resolution,[],[f31,f14]) ).
fof(f97,plain,
! [X0] :
( ~ less_equal(b,divide(X0,a))
| b = divide(X0,a) ),
inference(resolution,[],[f31,f6]) ).
fof(f103,plain,
! [X0] : less_equal(divide(X0,c),b),
inference(resolution,[],[f55,f14]) ).
fof(f128,plain,
less_equal(c,a),
inference(superposition,[],[f96,f18]) ).
fof(f151,plain,
less_equal(d,b),
inference(superposition,[],[f103,f19]) ).
fof(f155,plain,
( ~ less_equal(b,d)
| b = d ),
inference(resolution,[],[f151,f6]) ).
fof(f156,plain,
~ less_equal(b,d),
inference(forward_subsumption_resolution,[],[f155,f20]) ).
fof(f581,plain,
less_equal(divide(b,divide(c,a)),divide(d,a)),
inference(superposition,[],[f25,f19]) ).
fof(f1033,plain,
( less_equal(divide(b,zero),divide(d,a))
| ~ less_equal(c,a) ),
inference(superposition,[],[f581,f1]) ).
fof(f1037,plain,
less_equal(divide(b,zero),divide(d,a)),
inference(forward_subsumption_resolution,[],[f1033,f128]) ).
fof(f1213,plain,
less_equal(divide(b,divide(d,a)),zero),
inference(resolution,[],[f1037,f14]) ).
fof(f1432,plain,
( ~ less_equal(zero,divide(b,divide(d,a)))
| zero = divide(b,divide(d,a)) ),
inference(resolution,[],[f1213,f6]) ).
fof(f1436,plain,
zero = divide(b,divide(d,a)),
inference(forward_subsumption_resolution,[],[f1432,f5]) ).
fof(f1461,plain,
( zero != zero
| less_equal(b,divide(d,a)) ),
inference(superposition,[],[f2,f1436]) ).
fof(f1469,plain,
less_equal(b,divide(d,a)),
inference(trivial_inequality_removal,[],[f1461]) ).
fof(f1473,plain,
b = divide(d,a),
inference(resolution,[],[f1469,f97]) ).
fof(f1512,plain,
less_equal(b,d),
inference(superposition,[],[f3,f1473]) ).
fof(f1520,plain,
$false,
inference(forward_subsumption_resolution,[],[f1512,f156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % 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 10:54:15 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 7.03/1.99 % (1480432)Input is clausal, will run a generic CNF schedule.
% 7.03/1.99 % (1480452)dis-21_1_sil=8000:lcm=predicate:random_seed=2903812466: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)
% 7.03/1.99 % (1480446)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3292263939:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 7.03/1.99 % (1480448)lrs+10_1_sil=8000:sp=occurrence:random_seed=337113463:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 7.03/1.99 % (1480449)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3849615667:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 7.03/1.99 % (1480451)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2541385108:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 7.03/1.99 % (1480445)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=2684788041:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 7.03/1.99 % (1480447)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3958008694:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 7.03/1.99 % (1480452)Instruction limit reached!
% 7.03/1.99 % (1480452)------------------------------
% 7.03/1.99 % (1480452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.03/1.99 % (1480452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.03/1.99 % (1480452)CaDiCaL version: 2.1.3
% 7.03/1.99 % (1480452)Termination reason: Instruction limit
% 7.03/1.99 % (1480452)Termination phase: Saturation
% 7.03/1.99 % (1480452)Time elapsed: 0.094 s
% 7.03/1.99 % (1480452)Peak memory usage: 88 MB
% 7.03/1.99 % (1480452)Instructions burned: 118 (million)
% 7.03/1.99 % (1480448)Instruction limit reached!
% 7.03/1.99 % (1480448)------------------------------
% 7.03/1.99 % (1480448)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.03/1.99 % (1480448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.03/1.99 % (1480448)CaDiCaL version: 2.1.3
% 7.03/1.99 % (1480448)Termination reason: Instruction limit
% 7.03/1.99 % (1480448)Termination phase: Saturation
% 7.03/1.99 % (1480448)Time elapsed: 0.113 s
% 7.03/1.99 % (1480448)Peak memory usage: 89 MB
% 7.03/1.99 % (1480448)Instructions burned: 107 (million)
% 7.03/1.99 % (1480449)Instruction limit reached!
% 7.03/1.99 % (1480449)------------------------------
% 7.03/1.99 % (1480449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.03/1.99 % (1480449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.03/1.99 % (1480449)CaDiCaL version: 2.1.3
% 7.03/1.99 % (1480449)Termination reason: Instruction limit
% 7.03/1.99 % (1480449)Termination phase: Saturation
% 7.03/1.99 % (1480449)Time elapsed: 0.114 s
% 7.03/1.99 % (1480449)Peak memory usage: 88 MB
% 7.03/1.99 % (1480449)Instructions burned: 115 (million)
% 7.03/1.99 % (1480451)Instruction limit reached!
% 7.03/1.99 % (1480451)------------------------------
% 7.03/1.99 % (1480451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.03/1.99 % (1480451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.03/1.99 % (1480451)CaDiCaL version: 2.1.3
% 7.03/1.99 % (1480451)Termination reason: Instruction limit
% 7.03/1.99 % (1480451)Termination phase: Saturation
% 7.03/1.99 % (1480451)Time elapsed: 0.176 s
% 7.03/1.99 % (1480451)Peak memory usage: 89 MB
% 7.03/1.99 % (1480451)Instructions burned: 180 (million)
% 7.03/1.99 % (1480467)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=194765204:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 7.03/1.99 % (1480467)First to succeed.
% 7.03/1.99 % (1480467)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1480432"
% 7.03/1.99 % (1480469)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1133445583:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 7.03/1.99 % (1480470)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1173512753:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 7.03/1.99 % (1480470)Refutation not found, incomplete strategy
% 7.03/1.99 % (1480470)------------------------------
% 7.03/1.99 % (1480470)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.03/1.99 % (1480470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.03/1.99 % (1480470)CaDiCaL version: 2.1.3
% 7.03/1.99 % (1480470)Termination reason: Refutation not found, incomplete strategy
% 7.03/1.99 % (1480470)Time elapsed: 0.006 s
% 7.03/1.99 % (1480470)Peak memory usage: 88 MB
% 7.03/1.99 % (1480470)Instructions burned: 3 (million)
% 7.03/1.99 % (1480472)lrs+10_64_to=lpo:sil=8000:random_seed=59953645:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 7.03/1.99 % (1480469)Instruction limit reached!
% 7.03/1.99 % (1480469)------------------------------
% 7.03/1.99 % (1480469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.03/1.99 % (1480469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.03/1.99 % (1480469)CaDiCaL version: 2.1.3
% 7.03/1.99 % (1480469)Termination reason: Instruction limit
% 7.03/1.99 % (1480469)Termination phase: Saturation
% 7.03/1.99 % (1480469)Time elapsed: 0.193 s
% 7.03/1.99 % (1480469)Peak memory usage: 89 MB
% 7.03/1.99 % (1480469)Instructions burned: 189 (million)
% 7.03/1.99 % (1480472)Instruction limit reached!
% 7.03/1.99 % (1480472)------------------------------
% 7.03/1.99 % (1480472)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.03/1.99 % (1480472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.03/1.99 % (1480472)CaDiCaL version: 2.1.3
% 7.03/1.99 % (1480472)Termination reason: Instruction limit
% 7.03/1.99 % (1480472)Termination phase: Saturation
% 7.03/1.99 % (1480472)Time elapsed: 0.115 s
% 7.03/1.99 % (1480472)Peak memory usage: 88 MB
% 7.03/1.99 % (1480472)Instructions burned: 126 (million)
% 7.03/1.99 % (1480446)Also succeeded, but the first one will report.
% 7.03/1.99 % (1480467)Refutation found. Thanks to Tanya!
% 7.03/1.99 % SZS status Unsatisfiable for theBenchmark
% 7.03/1.99 % SZS output start Proof for theBenchmark
% See solution above
% 7.03/1.99 % (1480467)------------------------------
% 7.03/1.99 % (1480467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.03/1.99 % (1480467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.03/1.99 % (1480467)CaDiCaL version: 2.1.3
% 7.03/1.99 % (1480467)Termination reason: Refutation
% 7.03/1.99 % (1480467)Time elapsed: 0.035 s
% 7.03/1.99 % (1480467)Peak memory usage: 88 MB
% 7.03/1.99 % (1480467)Instructions burned: 35 (million)
% 7.03/1.99 % (1480467)------------------------------
% 7.03/1.99 % (1480467)------------------------------
% 7.03/1.99 % (1480432)Success in time 0.907 s
% 7.03/1.99 % Vampire exiting
%------------------------------------------------------------------------------