%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : HEN004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 10:19:13 AM UTC 2026
% Result : Unsatisfiable 1.06s 0.60s
% Output : Refutation 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 22 unt; 0 def)
% Number of atoms : 64 ( 13 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 55 ( 28 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 75 ( 75 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ less_equal(X0,X1)
| quotient(X0,X1,zero) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).
fof(f2,axiom,
! [X0,X1] :
( ~ quotient(X0,X1,zero)
| less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| less_equal(X2,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
fof(f4,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ quotient(X2,X3,X7)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X3,X5)
| ~ quotient(X5,X4,X6)
| ~ quotient(X0,X1,X2)
| less_equal(X6,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
fof(f5,axiom,
! [X0] : less_equal(zero,X0),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
fof(f6,axiom,
! [X0,X1] :
( ~ less_equal(X1,X0)
| ~ less_equal(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
fof(f8,axiom,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',closure) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',well_defined) ).
fof(f10,negated_conjecture,
~ quotient(x,zero,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_x_divde_zero_is_x) ).
fof(f11,plain,
! [X0] : quotient(zero,X0,zero),
inference(resolution,[],[f1,f5]) ).
fof(f14,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[],[f3,f8]) ).
fof(f18,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f20,plain,
! [X0,X1] :
( ~ less_equal(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[],[f14,f6]) ).
fof(f21,plain,
! [X0,X1] : quotient(divide(X0,X1),X0,zero),
inference(resolution,[],[f14,f1]) ).
fof(f22,plain,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| divide(X0,X1) = X2 ),
inference(resolution,[],[f9,f8]) ).
fof(f27,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ quotient(X3,X0,X6)
| ~ quotient(X3,X1,X4)
| ~ quotient(X4,X2,X5)
| ~ quotient(X0,X1,X2)
| less_equal(X5,divide(X6,X1)) ),
inference(resolution,[],[f4,f8]) ).
fof(f41,plain,
! [X0,X1] : zero = divide(divide(X0,X1),X0),
inference(resolution,[],[f22,f21]) ).
fof(f45,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ quotient(X5,X1,X3)
| ~ quotient(X2,X3,X4)
| ~ quotient(X0,X1,X2)
| less_equal(X4,divide(divide(X0,X5),X1)) ),
inference(resolution,[],[f27,f8]) ).
fof(f104,plain,
! [X2,X3,X0,X1] :
( ~ quotient(X2,X3,X0)
| ~ quotient(X0,zero,X1)
| less_equal(X1,divide(divide(X2,zero),X3)) ),
inference(resolution,[],[f45,f11]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ quotient(divide(X0,X1),zero,X2)
| less_equal(X2,divide(divide(X0,zero),X1)) ),
inference(resolution,[],[f104,f8]) ).
fof(f226,plain,
! [X0,X1] : less_equal(divide(divide(X0,X1),zero),divide(divide(X0,zero),X1)),
inference(resolution,[],[f139,f8]) ).
fof(f237,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,[],[f226,f6]) ).
fof(f246,plain,
! [X0] : less_equal(divide(divide(X0,X0),zero),zero),
inference(superposition,[],[f226,f41]) ).
fof(f266,plain,
! [X0] : zero = divide(divide(X0,X0),zero),
inference(resolution,[],[f246,f18]) ).
fof(f285,plain,
! [X0] : quotient(divide(X0,X0),zero,zero),
inference(superposition,[],[f8,f266]) ).
fof(f327,plain,
! [X0] : less_equal(divide(X0,X0),zero),
inference(resolution,[],[f285,f2]) ).
fof(f362,plain,
! [X0] : zero = divide(X0,X0),
inference(resolution,[],[f327,f18]) ).
fof(f1252,plain,
! [X0] :
( ~ less_equal(zero,divide(divide(X0,divide(X0,zero)),zero))
| zero = divide(divide(X0,divide(X0,zero)),zero) ),
inference(superposition,[],[f237,f362]) ).
fof(f1264,plain,
! [X0] : zero = divide(divide(X0,divide(X0,zero)),zero),
inference(forward_subsumption_resolution,[],[f1252,f5]) ).
fof(f1385,plain,
! [X0] : quotient(divide(X0,divide(X0,zero)),zero,zero),
inference(superposition,[],[f8,f1264]) ).
fof(f1532,plain,
! [X0] : less_equal(divide(X0,divide(X0,zero)),zero),
inference(resolution,[],[f1385,f2]) ).
fof(f1688,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(resolution,[],[f1532,f18]) ).
fof(f1856,plain,
! [X0] : quotient(X0,divide(X0,zero),zero),
inference(superposition,[],[f8,f1688]) ).
fof(f1978,plain,
! [X0] : less_equal(X0,divide(X0,zero)),
inference(resolution,[],[f1856,f2]) ).
fof(f2161,plain,
! [X0] : divide(X0,zero) = X0,
inference(resolution,[],[f1978,f20]) ).
fof(f2371,plain,
! [X0] : quotient(X0,zero,X0),
inference(superposition,[],[f8,f2161]) ).
fof(f2484,plain,
$false,
inference(resolution,[],[f2371,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n026.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 10:52:31 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 Running first-order model finding
% 0.11/0.39 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
% 1.06/0.60 % (2657873)Will run a generic schedule for satisfiability detection.
% 1.06/0.60 % (2657878)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3239316735_2999 on theBenchmark for (2999ds/0Mi)
% 1.06/0.60 % TRYING [1]
% 1.06/0.60 % TRYING [2]
% 1.06/0.60 % TRYING [3]
% 1.06/0.60 % TRYING [4]
% 1.06/0.60 % TRYING [5]
% 1.06/0.60 % (2657880)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3618039605:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.06/0.60 % (2657881)dis+10_1_sil=32000:sp=arity:random_seed=1372429163:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.06/0.60 % (2657882)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2942125730:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.06/0.60 % (2657879)% WARNING: option uhcvi not known.
% 1.06/0.60 % TRYING [6]
% 1.06/0.60 % (2657879)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1426826916:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.06/0.60 % (2657884)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1933825551:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.06/0.60 % (2657883)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2806327188:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.06/0.60 % TRYING [7]
% 1.06/0.60 % (2657882)Instruction limit reached!
% 1.06/0.60 % (2657882)------------------------------
% 1.06/0.60 % (2657882)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.60 % (2657882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.60 % (2657882)CaDiCaL version: 2.1.3
% 1.06/0.60 % (2657882)Termination reason: Instruction limit
% 1.06/0.60 % (2657882)Termination phase: Saturation
% 1.06/0.60 % (2657882)Time elapsed: 0.062 s
% 1.06/0.60 % (2657882)Peak memory usage: 11 MB
% 1.06/0.60 % (2657882)Instructions burned: 116 (million)
% 1.06/0.60 % TRYING [8]
% 1.06/0.60 % (2657881)Instruction limit reached!
% 1.06/0.60 % (2657881)------------------------------
% 1.06/0.60 % (2657881)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.60 % (2657881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.60 % (2657881)CaDiCaL version: 2.1.3
% 1.06/0.60 % (2657881)Termination reason: Instruction limit
% 1.06/0.60 % (2657881)Termination phase: Saturation
% 1.06/0.60 % (2657881)Time elapsed: 0.066 s
% 1.06/0.60 % (2657881)Peak memory usage: 11 MB
% 1.06/0.60 % (2657881)Instructions burned: 103 (million)
% 1.06/0.60 % (2657892)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=561823554:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 1.06/0.60 % TRYING [1]
% 1.06/0.60 % TRYING [2]
% 1.06/0.60 % TRYING [3]
% 1.06/0.60 % (2657893)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1009334172:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.06/0.60 % TRYING [4]
% 1.06/0.60 % TRYING [5]
% 1.06/0.60 % TRYING [6]
% 1.06/0.60 % (2657884)Instruction limit reached!
% 1.06/0.60 % (2657884)------------------------------
% 1.06/0.60 % (2657884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.60 % (2657884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.60 % (2657884)CaDiCaL version: 2.1.3
% 1.06/0.60 % (2657884)Termination reason: Instruction limit
% 1.06/0.60 % (2657884)Termination phase: Saturation
% 1.06/0.60 % (2657884)Time elapsed: 0.100 s
% 1.06/0.60 % (2657884)Peak memory usage: 12 MB
% 1.06/0.60 % (2657884)Instructions burned: 159 (million)
% 1.06/0.60 % TRYING [9]
% 1.06/0.60 % (2657896)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=968422524:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.06/0.60 % (2657883)Instruction limit reached!
% 1.06/0.60 % (2657883)------------------------------
% 1.06/0.60 % (2657883)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.60 % (2657883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.60 % (2657883)CaDiCaL version: 2.1.3
% 1.06/0.60 % (2657883)Termination reason: Instruction limit
% 1.06/0.60 % (2657883)Termination phase: Saturation
% 1.06/0.60 % (2657883)Time elapsed: 0.121 s
% 1.06/0.60 % (2657883)Peak memory usage: 12 MB
% 1.06/0.60 % (2657883)Instructions burned: 132 (million)
% 1.06/0.60 % (2657893) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2657873-2657893"...
% 1.06/0.60 % (2657893)...printing done.
% 1.06/0.60 % (2657893)Refutation found. Thanks to Tanya!
% 1.06/0.60 % SZS status Unsatisfiable for theBenchmark
% 1.06/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 1.06/0.60 % (2657893)------------------------------
% 1.06/0.60 % (2657893)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.60 % (2657893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.60 % (2657893)CaDiCaL version: 2.1.3
% 1.06/0.60 % (2657893)Termination reason: Refutation
% 1.06/0.60 % (2657893)Time elapsed: 0.065 s
% 1.06/0.60 % (2657893)Peak memory usage: 12 MB
% 1.06/0.60 % (2657893)Instructions burned: 98 (million)
% 1.06/0.60 % (2657873)Success in time 0.195 s
% 1.06/0.60 % Vampire exiting
%------------------------------------------------------------------------------