%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : HEN009-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 10:19:18 AM UTC 2026
% Result : Unsatisfiable 2.09s 0.85s
% Output : Refutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 22 unt; 3 def)
% Number of atoms : 42 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 24 ( 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( ~ less_equal(X1,X0)
| ~ less_equal(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',less_equal_and_equal) ).
fof(f7,axiom,
! [X0] : less_equal(X0,identity),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',identity_is_largest) ).
fof(f16,axiom,
! [X2,X0,X1] :
( ~ less_equal(X1,X2)
| ~ less_equal(X0,X1)
| less_equal(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ~ less_equal(divide(X0,X1),X2)
| less_equal(divide(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide1) ).
fof(f19,axiom,
! [X2,X0,X1] :
( less_equal(divide(X0,X2),divide(X1,X2))
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide3) ).
fof(f20,negated_conjecture,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f21,definition,
sF0 = divide(identity,a),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f22,plain,
divide(identity,a) = sF0,
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
sF1 = divide(identity,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f24,plain,
divide(identity,sF0) = sF1,
inference(reorient_equations,[],[f23]) ).
fof(f25,definition,
sF2 = divide(identity,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f26,plain,
divide(identity,sF1) = sF2,
inference(reorient_equations,[],[f25]) ).
fof(f27,plain,
sF0 != sF2,
inference(definition_folding,[],[f20,f26,f24,f22,f22]) ).
fof(f131,plain,
! [X0] :
( less_equal(divide(X0,a),sF0)
| ~ less_equal(X0,identity) ),
inference(superposition,[],[f19,f22]) ).
fof(f132,plain,
! [X0] :
( less_equal(divide(X0,sF0),sF1)
| ~ less_equal(X0,identity) ),
inference(superposition,[],[f19,f24]) ).
fof(f133,plain,
! [X0] :
( less_equal(divide(X0,sF1),sF2)
| ~ less_equal(X0,identity) ),
inference(superposition,[],[f19,f26]) ).
fof(f135,plain,
! [X0] : less_equal(divide(X0,sF1),sF2),
inference(forward_subsumption_resolution,[],[f133,f7]) ).
fof(f136,plain,
! [X0] : less_equal(divide(X0,sF0),sF1),
inference(forward_subsumption_resolution,[],[f132,f7]) ).
fof(f137,plain,
! [X0] : less_equal(divide(X0,a),sF0),
inference(forward_subsumption_resolution,[],[f131,f7]) ).
fof(f139,plain,
! [X0] : less_equal(divide(X0,sF2),sF1),
inference(resolution,[],[f135,f17]) ).
fof(f194,plain,
! [X0] : less_equal(divide(X0,sF1),sF0),
inference(resolution,[],[f136,f17]) ).
fof(f202,plain,
! [X0] : less_equal(divide(X0,sF0),a),
inference(resolution,[],[f137,f17]) ).
fof(f226,plain,
less_equal(sF2,sF0),
inference(superposition,[],[f194,f26]) ).
fof(f232,plain,
( ~ less_equal(sF0,sF2)
| sF0 = sF2 ),
inference(resolution,[],[f226,f6]) ).
fof(f234,plain,
~ less_equal(sF0,sF2),
inference(forward_subsumption_resolution,[],[f232,f27]) ).
fof(f275,plain,
less_equal(sF1,a),
inference(superposition,[],[f202,f24]) ).
fof(f294,plain,
! [X0] :
( ~ less_equal(X0,sF1)
| less_equal(X0,a) ),
inference(resolution,[],[f275,f16]) ).
fof(f999,plain,
! [X0] : less_equal(divide(X0,sF2),a),
inference(resolution,[],[f294,f139]) ).
fof(f1030,plain,
! [X0] : less_equal(divide(X0,a),sF2),
inference(resolution,[],[f999,f17]) ).
fof(f1076,plain,
less_equal(sF0,sF2),
inference(superposition,[],[f1030,f22]) ).
fof(f1078,plain,
$false,
inference(forward_subsumption_resolution,[],[f1076,f234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n005.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 10:51:02 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.09/0.85 % (3812940)Will run a generic schedule for satisfiability detection.
% 2.09/0.85 % (3812948)% WARNING: option uhcvi not known.
% 2.09/0.85 % (3812948)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2406015938:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.09/0.85 % (3812947)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2918673848_2999 on theBenchmark for (2999ds/0Mi)
% 2.09/0.85 % (3812952)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=643145132:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.09/0.85 % (3812949)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3362041046:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.09/0.85 % (3812953)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1792535017:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.09/0.85 % (3812951)dis+10_1_sil=32000:sp=arity:random_seed=2852319173:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.09/0.85 % (3812954)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3960529442:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.09/0.85 % TRYING [1]
% 2.09/0.85 % TRYING [2]
% 2.09/0.85 % TRYING [3]
% 2.09/0.85 % TRYING [4]
% 2.09/0.85 % TRYING [5]
% 2.09/0.85 % TRYING [6]
% 2.09/0.85 % (3812951)Instruction limit reached!
% 2.09/0.85 % (3812951)------------------------------
% 2.09/0.85 % (3812951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.85 % (3812951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.85 % (3812951)CaDiCaL version: 2.1.3
% 2.09/0.85 % (3812951)Termination reason: Instruction limit
% 2.09/0.85 % (3812951)Termination phase: Saturation
% 2.09/0.85 % (3812951)Time elapsed: 0.061 s
% 2.09/0.85 % (3812951)Peak memory usage: 12 MB
% 2.09/0.85 % (3812951)Instructions burned: 104 (million)
% 2.09/0.85 % (3812952)Instruction limit reached!
% 2.09/0.85 % (3812952)------------------------------
% 2.09/0.85 % (3812952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.85 % (3812952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.85 % (3812952)CaDiCaL version: 2.1.3
% 2.09/0.85 % (3812952)Termination reason: Instruction limit
% 2.09/0.85 % (3812952)Termination phase: Saturation
% 2.09/0.85 % (3812952)Time elapsed: 0.069 s
% 2.09/0.85 % (3812952)Peak memory usage: 12 MB
% 2.09/0.85 % (3812952)Instructions burned: 117 (million)
% 2.09/0.85 % TRYING [7]
% 2.09/0.85 % (3812953)Instruction limit reached!
% 2.09/0.85 % (3812953)------------------------------
% 2.09/0.85 % (3812953)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.85 % (3812953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.85 % (3812953)CaDiCaL version: 2.1.3
% 2.09/0.85 % (3812953)Termination reason: Instruction limit
% 2.09/0.85 % (3812953)Termination phase: Saturation
% 2.09/0.85 % (3812953)Time elapsed: 0.078 s
% 2.09/0.85 % (3812953)Peak memory usage: 12 MB
% 2.09/0.85 % (3812953)Instructions burned: 132 (million)
% 2.09/0.85 % (3812989)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1085433793:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.09/0.85 % TRYING [1]
% 2.09/0.85 % TRYING [2]
% 2.09/0.85 % TRYING [3]
% 2.09/0.85 % TRYING [4]
% 2.09/0.85 % (3812993)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2743123872:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.09/0.85 % TRYING [5]
% 2.09/0.85 % (3812998)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3937722330:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.09/0.85 % (3812954)Instruction limit reached!
% 2.09/0.85 % (3812954)------------------------------
% 2.09/0.85 % (3812954)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.85 % (3812954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.85 % (3812954)CaDiCaL version: 2.1.3
% 2.09/0.85 % (3812954)Termination reason: Instruction limit
% 2.09/0.85 % (3812954)Termination phase: Saturation
% 2.09/0.85 % (3812954)Time elapsed: 0.105 s
% 2.09/0.85 % (3812954)Peak memory usage: 13 MB
% 2.09/0.85 % (3812954)Instructions burned: 160 (million)
% 2.09/0.85 % TRYING [6]
% 2.09/0.85 % (3813018)ott-21_1_sil=16000:fs=off:random_seed=3378956139:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.09/0.85 % TRYING [8]
% 2.09/0.85 % TRYING [7]
% 2.09/0.85 % (3812993)Instruction limit reached!
% 2.09/0.85 % (3812993)------------------------------
% 2.09/0.85 % (3812993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.85 % (3812993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.85 % (3812993)CaDiCaL version: 2.1.3
% 2.09/0.85 % (3812993)Termination reason: Instruction limit
% 2.09/0.85 % (3812993)Termination phase: Saturation
% 2.09/0.85 % (3812993)Time elapsed: 0.085 s
% 2.09/0.85 % (3812993)Peak memory usage: 13 MB
% 2.09/0.85 % (3812993)Instructions burned: 131 (million)
% 2.09/0.85 % (3813041)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=325760521:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 2.09/0.85 % (3813018)Instruction limit reached!
% 2.09/0.85 % (3813018)------------------------------
% 2.09/0.85 % (3813018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.85 % (3813018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.85 % (3813018)CaDiCaL version: 2.1.3
% 2.09/0.85 % (3813018)Termination reason: Instruction limit
% 2.09/0.85 % (3813018)Termination phase: Saturation
% 2.09/0.85 % (3813018)Time elapsed: 0.085 s
% 2.09/0.85 % (3813018)Peak memory usage: 11 MB
% 2.09/0.85 % (3813018)Instructions burned: 182 (million)
% 2.09/0.85 % (3813051)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1708657777:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 2.09/0.85 % TRYING [1]
% 2.09/0.85 % TRYING [2]
% 2.09/0.85 % TRYING [3]
% 2.09/0.85 % TRYING [4]
% 2.09/0.85 % TRYING [5]
% 2.09/0.85 % TRYING [8]
% 2.09/0.85 % TRYING [6]
% 2.09/0.85 % TRYING [9]
% 2.09/0.85 % (3812989)Instruction limit reached!
% 2.09/0.85 % (3812989)------------------------------
% 2.09/0.85 % (3812989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.85 % (3812989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.85 % (3812989)CaDiCaL version: 2.1.3
% 2.09/0.85 % (3812989)Termination reason: Instruction limit
% 2.09/0.85 % (3812989)Termination phase: Finite model building constraint generation
% 2.09/0.85 % (3812989)Time elapsed: 0.258 s
% 2.09/0.85 % (3812989)Peak memory usage: 29 MB
% 2.09/0.85 % (3812989)Instructions burned: 715 (million)
% 2.09/0.85 % (3813072)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=769484510:i=1179_2996 on theBenchmark for (2996ds/1179Mi)
% 2.09/0.85 % TRYING [7]
% 2.09/0.85 % (3813072) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3812940-3813072"...
% 2.09/0.85 % (3813072)...printing done.
% 2.09/0.85 % (3813072)Refutation found. Thanks to Tanya!
% 2.09/0.85 % SZS status Unsatisfiable for theBenchmark
% 2.09/0.85 % SZS output start Proof for theBenchmark
% See solution above
% 2.09/0.85 % (3813072)------------------------------
% 2.09/0.86 % (3813072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.86 % (3813072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.86 % (3813072)CaDiCaL version: 2.1.3
% 2.09/0.86 % (3813072)Termination reason: Refutation
% 2.09/0.86 % (3813072)Time elapsed: 0.019 s
% 2.09/0.86 % (3813072)Peak memory usage: 11 MB
% 2.09/0.86 % (3813072)Instructions burned: 28 (million)
% 2.09/0.86 % (3812940)Success in time 0.43 s
% 2.09/0.86 % Vampire exiting
%------------------------------------------------------------------------------