%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN003-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 10:19:03 AM UTC 2026
% Result : Unsatisfiable 4.62s 1.72s
% Output : Refutation 4.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 28 ( 11 unt; 0 def)
% Number of atoms : 66 ( 16 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 77 ( 39 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 3 ( 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 : 73 ( 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal) ).
fof(f2,axiom,
! [X0,X1] :
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_quotient) ).
fof(f3,axiom,
! [X2,X0,X1] :
( less_equal(X2,X0)
| ~ quotient(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor_existence) ).
fof(f4,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( less_equal(X6,X7)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X3,X5)
| ~ quotient(X5,X4,X6)
| ~ quotient(X2,X3,X7)
| ~ quotient(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_property) ).
fof(f5,axiom,
! [X0] : less_equal(zero,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_smallest) ).
fof(f6,axiom,
! [X0,X1] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_and_equal) ).
fof(f8,axiom,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X0,X1,X3)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_defined) ).
fof(f11,axiom,
! [X0] : quotient(zero,X0,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
fof(f12,negated_conjecture,
~ quotient(x,x,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_x_divide_x_is_zero) ).
fof(f19,plain,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| divide(X0,X1) = X2 ),
inference(resolution,[],[f9,f8]) ).
fof(f38,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f40,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ quotient(X5,X2,X7)
| X0 = X1
| ~ quotient(X2,X3,X4)
| ~ quotient(X5,X3,X6)
| ~ quotient(X6,X4,X1)
| ~ quotient(X7,X3,X0)
| ~ less_equal(X0,X1) ),
inference(resolution,[],[f6,f4]) ).
fof(f49,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| zero = divide(X0,X1) ),
inference(resolution,[],[f19,f1]) ).
fof(f66,plain,
! [X0] :
( ~ quotient(X0,zero,zero)
| zero = X0 ),
inference(resolution,[],[f38,f2]) ).
fof(f76,plain,
! [X2,X0,X1] :
( ~ quotient(X1,X2,X0)
| zero = divide(X0,X1) ),
inference(resolution,[],[f49,f3]) ).
fof(f87,plain,
! [X0,X1] : zero = divide(divide(X0,X1),X0),
inference(resolution,[],[f76,f8]) ).
fof(f94,plain,
! [X0,X1] : quotient(divide(X0,X1),X0,zero),
inference(superposition,[],[f8,f87]) ).
fof(f98,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ less_equal(X0,X1)
| ~ quotient(X2,X3,X4)
| ~ quotient(X5,X3,X6)
| ~ quotient(X6,X4,X1)
| ~ quotient(divide(X5,X2),X3,X0)
| X0 = X1 ),
inference(resolution,[],[f40,f8]) ).
fof(f211,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X3,X1,X4)
| ~ quotient(X4,X2,X5)
| ~ quotient(divide(X3,X0),X1,zero)
| zero = X5 ),
inference(resolution,[],[f98,f5]) ).
fof(f555,plain,
! [X2,X3,X0,X1] :
( ~ quotient(X2,zero,X3)
| ~ quotient(X0,X1,X2)
| ~ quotient(divide(X0,zero),X1,zero)
| zero = X3 ),
inference(resolution,[],[f211,f11]) ).
fof(f973,plain,
! [X2,X0,X1] :
( ~ quotient(divide(X0,zero),X1,zero)
| ~ quotient(X0,X1,X2)
| zero = divide(X2,zero) ),
inference(resolution,[],[f555,f8]) ).
fof(f1725,plain,
! [X0,X1] :
( ~ quotient(X0,X0,X1)
| zero = divide(X1,zero) ),
inference(resolution,[],[f973,f94]) ).
fof(f1758,plain,
! [X0] : zero = divide(divide(X0,X0),zero),
inference(resolution,[],[f1725,f8]) ).
fof(f1782,plain,
! [X0] : quotient(divide(X0,X0),zero,zero),
inference(superposition,[],[f8,f1758]) ).
fof(f1809,plain,
! [X0] : zero = divide(X0,X0),
inference(resolution,[],[f1782,f66]) ).
fof(f1885,plain,
! [X0] : quotient(X0,X0,zero),
inference(superposition,[],[f8,f1809]) ).
fof(f2062,plain,
$false,
inference(resolution,[],[f1885,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 10:52:11 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.62/1.72 % (2656979)Input is clausal, will run a generic CNF schedule.
% 4.62/1.72 % (2657019)lrs+10_1_sil=8000:sp=occurrence:random_seed=3063684630:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.62/1.72 % (2657019)Refutation not found, incomplete strategy
% 4.62/1.72 % (2657019)------------------------------
% 4.62/1.72 % (2657019)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.62/1.72 % (2657019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.62/1.72 % (2657019)CaDiCaL version: 2.1.3
% 4.62/1.72 % (2657019)Termination reason: Refutation not found, incomplete strategy
% 4.62/1.72 % (2657019)Time elapsed: 0.001 s
% 4.62/1.72 % (2657019)Peak memory usage: 88 MB
% 4.62/1.72 % (2657019)Instructions burned: 1 (million)
% 4.62/1.72 % (2657017)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3244490335:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.62/1.72 % (2657018)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4094507034:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.62/1.72 % (2657016)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=1699905684:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.62/1.72 % (2657020)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2861466646:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.62/1.72 % (2657020)Refutation not found, incomplete strategy
% 4.62/1.72 % (2657020)------------------------------
% 4.62/1.72 % (2657020)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.62/1.72 % (2657020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.62/1.72 % (2657020)CaDiCaL version: 2.1.3
% 4.62/1.72 % (2657020)Termination reason: Refutation not found, incomplete strategy
% 4.62/1.72 % (2657020)Time elapsed: 0.003 s
% 4.62/1.72 % (2657020)Peak memory usage: 87 MB
% 4.62/1.72 % (2657020)Instructions burned: 3 (million)
% 4.62/1.72 % (2657022)dis-21_1_sil=8000:lcm=predicate:random_seed=2301098811: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)
% 4.62/1.72 % (2657021)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2300918534:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.62/1.72 % (2657022)Instruction limit reached!
% 4.62/1.72 % (2657022)------------------------------
% 4.62/1.72 % (2657022)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.62/1.72 % (2657022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.62/1.72 % (2657022)CaDiCaL version: 2.1.3
% 4.62/1.72 % (2657022)Termination reason: Instruction limit
% 4.62/1.72 % (2657022)Termination phase: Saturation
% 4.62/1.72 % (2657022)Time elapsed: 0.057 s
% 4.62/1.72 % (2657022)Peak memory usage: 88 MB
% 4.62/1.72 % (2657022)Instructions burned: 118 (million)
% 4.62/1.72 % (2657021)First to succeed.
% 4.62/1.72 % (2657021)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2656979"
% 4.62/1.72 % (2657019)------------------------------
% 4.62/1.72 % (2657019)------------------------------
% 4.62/1.72 % (2657030)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=2921327653:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.62/1.72 % (2657031)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3682905396: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)
% 4.62/1.72 % (2657031)Refutation not found, incomplete strategy
% 4.62/1.72 % (2657031)------------------------------
% 4.62/1.72 % (2657031)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.62/1.72 % (2657031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.62/1.72 % (2657031)CaDiCaL version: 2.1.3
% 4.62/1.72 % (2657031)Termination reason: Refutation not found, incomplete strategy
% 4.62/1.72 % (2657031)Time elapsed: 0.001 s
% 4.62/1.72 % (2657031)Peak memory usage: 88 MB
% 4.62/1.72 % (2657030)Refutation not found, incomplete strategy
% 4.62/1.72 % (2657030)------------------------------
% 4.62/1.72 % (2657030)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.62/1.72 % (2657030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.62/1.72 % (2657030)CaDiCaL version: 2.1.3
% 4.62/1.72 % (2657030)Termination reason: Refutation not found, incomplete strategy
% 4.62/1.72 % (2657030)Time elapsed: 0.001 s
% 4.62/1.72 % (2657030)Peak memory usage: 88 MB
% 4.62/1.72 % (2657020)------------------------------
% 4.62/1.72 % (2657020)------------------------------
% 4.62/1.72 % (2657031)------------------------------
% 4.62/1.72 % (2657031)------------------------------
% 4.62/1.72 % (2657021)Refutation found. Thanks to Tanya!
% 4.62/1.72 % SZS status Unsatisfiable for theBenchmark
% 4.62/1.72 % SZS output start Proof for theBenchmark
% See solution above
% 4.62/1.72 % (2657021)------------------------------
% 4.62/1.72 % (2657021)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.62/1.72 % (2657021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.62/1.72 % (2657021)CaDiCaL version: 2.1.3
% 4.62/1.72 % (2657021)Termination reason: Refutation
% 4.62/1.72 % (2657021)Time elapsed: 0.081 s
% 4.62/1.72 % (2657021)Peak memory usage: 89 MB
% 4.62/1.72 % (2657021)Instructions burned: 123 (million)
% 4.62/1.72 % (2657021)------------------------------
% 4.62/1.72 % (2657021)------------------------------
% 4.62/1.72 % (2656979)Success in time 0.557 s
% 4.62/1.72 % Vampire exiting
%------------------------------------------------------------------------------