%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN010-2 : 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 : n001.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 5.39s 1.65s
% Output : Refutation 5.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 12
% Syntax : Number of formulae : 19 ( 14 unt; 0 def)
% Number of atoms : 33 ( 4 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 31 ( 17 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| less_equal(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divisor_existence) ).
fof(f4,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ quotient(X5,X4,X6)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X3,X5)
| ~ quotient(X0,X1,X2)
| ~ quotient(X2,X3,X7)
| less_equal(X6,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_property) ).
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(f8,axiom,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure) ).
fof(f12,axiom,
! [X0] : quotient(X0,X0,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
fof(f13,axiom,
! [X0] : quotient(X0,zero,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
fof(f15,axiom,
! [X2,X3,X0,X1,X4] :
( ~ quotient(X0,X3,X4)
| ~ less_equal(X2,X3)
| ~ quotient(X0,X1,X2)
| less_equal(X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQyLEz_implies_xQzLEy) ).
fof(f18,axiom,
! [X2,X3,X0,X1] :
( ~ quotient(identity,X2,X3)
| ~ quotient(identity,X1,X2)
| ~ quotient(identity,X0,X1)
| X1 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_inversion_equals_three) ).
fof(f19,axiom,
quotient(identity,a,idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_a) ).
fof(f20,axiom,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_idQa) ).
fof(f21,axiom,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).
fof(f22,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_idQa_equals_idQa_Q__idQ_idQa) ).
fof(f186,plain,
idQa = divide(identity,idQ_idQa),
inference(unit_resulting_resolution,[],[f18,f19,f8,f20]) ).
fof(f348,plain,
less_equal(idQa_Q__idQ_idQa,idQa),
inference(unit_resulting_resolution,[],[f3,f21]) ).
fof(f399,plain,
less_equal(divide(divide(identity,idQ_idQa),idQa_Q__idQ_idQa),zero),
inference(unit_resulting_resolution,[],[f4,f8,f12,f20,f8,f21]) ).
fof(f457,plain,
less_equal(divide(idQa,idQa_Q__idQ_idQa),zero),
inference(forward_demodulation,[],[f399,f186]) ).
fof(f552,plain,
~ less_equal(idQa,idQa_Q__idQ_idQa),
inference(unit_resulting_resolution,[],[f6,f22,f348]) ).
fof(f624,plain,
~ less_equal(divide(idQa,idQa_Q__idQ_idQa),zero),
inference(unit_resulting_resolution,[],[f15,f13,f8,f552]) ).
fof(f649,plain,
$false,
inference(forward_subsumption_resolution,[],[f624,f457]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN010-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:56:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 5.39/1.65 % (3382381)Input is clausal, will run a generic CNF schedule.
% 5.39/1.65 % (3382392)dis-21_1_sil=8000:lcm=predicate:random_seed=95789390: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)
% 5.39/1.65 % (3382392)Instruction limit reached!
% 5.39/1.65 % (3382392)------------------------------
% 5.39/1.65 % (3382392)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.39/1.65 % (3382392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.39/1.65 % (3382392)CaDiCaL version: 2.1.3
% 5.39/1.65 % (3382392)Termination reason: Instruction limit
% 5.39/1.65 % (3382392)Termination phase: Saturation
% 5.39/1.65 % (3382392)Time elapsed: 0.033 s
% 5.39/1.65 % (3382392)Peak memory usage: 88 MB
% 5.39/1.65 % (3382392)Instructions burned: 117 (million)
% 5.39/1.65 % (3382389)lrs+10_1_sil=8000:sp=occurrence:random_seed=1857564649:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.39/1.65 % (3382387)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=323004535:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.39/1.65 % (3382386)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=617804413:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.39/1.65 % (3382390)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=26916090:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.39/1.65 % (3382388)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=54756459:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.39/1.65 % (3382391)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2161971061:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.39/1.65 % (3382389)Refutation not found, incomplete strategy
% 5.39/1.65 % (3382389)------------------------------
% 5.39/1.65 % (3382389)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.39/1.65 % (3382389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.39/1.65 % (3382389)CaDiCaL version: 2.1.3
% 5.39/1.65 % (3382389)Termination reason: Refutation not found, incomplete strategy
% 5.39/1.65 % (3382389)Time elapsed: 0.022 s
% 5.39/1.65 % (3382389)Peak memory usage: 88 MB
% 5.39/1.65 % (3382389)Instructions burned: 31 (million)
% 5.39/1.65 % (3382390)Instruction limit reached!
% 5.39/1.65 % (3382390)------------------------------
% 5.39/1.65 % (3382390)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.39/1.65 % (3382390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.39/1.65 % (3382390)CaDiCaL version: 2.1.3
% 5.39/1.65 % (3382390)Termination reason: Instruction limit
% 5.39/1.65 % (3382390)Termination phase: Saturation
% 5.39/1.65 % (3382390)Time elapsed: 0.063 s
% 5.39/1.65 % (3382390)Peak memory usage: 88 MB
% 5.39/1.65 % (3382390)Instructions burned: 115 (million)
% 5.39/1.65 % (3382391)Instruction limit reached!
% 5.39/1.65 % (3382391)------------------------------
% 5.39/1.65 % (3382391)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.39/1.65 % (3382391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.39/1.65 % (3382391)CaDiCaL version: 2.1.3
% 5.39/1.65 % (3382391)Termination reason: Instruction limit
% 5.39/1.65 % (3382391)Termination phase: Saturation
% 5.39/1.65 % (3382391)Time elapsed: 0.098 s
% 5.39/1.65 % (3382391)Peak memory usage: 88 MB
% 5.39/1.65 % (3382391)Instructions burned: 182 (million)
% 5.39/1.65 % (3382394)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=609013615:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 5.39/1.65 % (3382394)Refutation not found, incomplete strategy
% 5.39/1.65 % (3382394)------------------------------
% 5.39/1.65 % (3382394)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.39/1.65 % (3382394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.39/1.65 % (3382394)CaDiCaL version: 2.1.3
% 5.39/1.65 % (3382394)Termination reason: Refutation not found, incomplete strategy
% 5.39/1.65 % (3382394)Time elapsed: 0.008 s
% 5.39/1.65 % (3382394)Peak memory usage: 88 MB
% 5.39/1.65 % (3382394)Instructions burned: 18 (million)
% 5.39/1.65 % (3382401)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=558456991:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 5.39/1.65 % (3382401)First to succeed.
% 5.39/1.65 % (3382401)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3382381"
% 5.39/1.65 % (3382402)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3888120055:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.39/1.65 % (3382389)------------------------------
% 5.39/1.65 % (3382389)------------------------------
% 5.39/1.65 % (3382394)------------------------------
% 5.39/1.65 % (3382394)------------------------------
% 5.39/1.65 % (3382402)Instruction limit reached!
% 5.39/1.65 % (3382402)------------------------------
% 5.39/1.65 % (3382402)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.39/1.65 % (3382402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.39/1.65 % (3382402)CaDiCaL version: 2.1.3
% 5.39/1.65 % (3382402)Termination reason: Instruction limit
% 5.39/1.65 % (3382402)Termination phase: Saturation
% 5.39/1.65 % (3382402)Time elapsed: 0.094 s
% 5.39/1.65 % (3382402)Peak memory usage: 88 MB
% 5.39/1.65 % (3382402)Instructions burned: 220 (million)
% 5.39/1.65 % (3382406)lrs+10_64_to=lpo:sil=8000:random_seed=708674830:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 5.39/1.65 % (3382407)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2054799596:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 5.39/1.65 % (3382406)Instruction limit reached!
% 5.39/1.65 % (3382406)------------------------------
% 5.39/1.65 % (3382406)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.39/1.65 % (3382406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.39/1.65 % (3382406)CaDiCaL version: 2.1.3
% 5.39/1.65 % (3382406)Termination reason: Instruction limit
% 5.39/1.65 % (3382406)Termination phase: Saturation
% 5.39/1.65 % (3382406)Time elapsed: 0.043 s
% 5.39/1.65 % (3382406)Peak memory usage: 88 MB
% 5.39/1.65 % (3382406)Instructions burned: 129 (million)
% 5.39/1.65 % (3382408)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2714317800:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 5.39/1.65 % (3382401)Refutation found. Thanks to Tanya!
% 5.39/1.65 % SZS status Unsatisfiable for theBenchmark
% 5.39/1.65 % SZS output start Proof for theBenchmark
% See solution above
% 5.39/1.65 % (3382401)------------------------------
% 5.39/1.65 % (3382401)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.39/1.65 % (3382401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.39/1.65 % (3382401)CaDiCaL version: 2.1.3
% 5.39/1.65 % (3382401)Termination reason: Refutation
% 5.39/1.65 % (3382401)Time elapsed: 0.020 s
% 5.39/1.65 % (3382401)Peak memory usage: 88 MB
% 5.39/1.65 % (3382401)Instructions burned: 35 (million)
% 5.39/1.65 % (3382401)------------------------------
% 5.39/1.65 % (3382401)------------------------------
% 5.39/1.65 % (3382381)Success in time 0.697 s
% 5.39/1.65 % Vampire exiting
%------------------------------------------------------------------------------