%------------------------------------------------------------------------------
% File : Vampire---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 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 10:19:04 AM UTC 2026
% Result : Unsatisfiable 8.20s 2.08s
% Output : Refutation 8.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 22 unt; 0 def)
% Number of atoms : 37 ( 6 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 21 ( 11 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 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 : 40 ( 40 !; 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] :
( ~ quotient(X0,X1,zero)
| less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_quotient) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| less_equal(X2,X0) ),
file('/export/starexec/sandbox/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/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(X1,X0)
| ~ less_equal(X0,X1)
| 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(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(unit_resulting_resolution,[],[f1,f5]) ).
fof(f21,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(unit_resulting_resolution,[],[f3,f8]) ).
fof(f24,plain,
! [X0,X1] : quotient(divide(X0,X1),X0,zero),
inference(unit_resulting_resolution,[],[f1,f21]) ).
fof(f64,plain,
! [X0] : less_equal(divide(divide(X0,X0),zero),zero),
inference(unit_resulting_resolution,[],[f4,f11,f24,f8,f8,f8]) ).
fof(f115,plain,
! [X0] : zero = divide(divide(X0,X0),zero),
inference(unit_resulting_resolution,[],[f6,f5,f64]) ).
fof(f122,plain,
! [X0] : quotient(divide(X0,X0),zero,zero),
inference(superposition,[],[f8,f115]) ).
fof(f123,plain,
! [X0] : less_equal(divide(X0,X0),zero),
inference(unit_resulting_resolution,[],[f2,f122]) ).
fof(f292,plain,
! [X0] : zero = divide(X0,X0),
inference(unit_resulting_resolution,[],[f6,f5,f123]) ).
fof(f297,plain,
! [X0] : quotient(X0,X0,zero),
inference(superposition,[],[f8,f292]) ).
fof(f774,plain,
! [X0] : less_equal(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(unit_resulting_resolution,[],[f4,f11,f8,f8,f8,f297]) ).
fof(f1624,plain,
! [X0] : zero = divide(divide(X0,divide(X0,zero)),zero),
inference(unit_resulting_resolution,[],[f6,f5,f774]) ).
fof(f1643,plain,
! [X0] : quotient(divide(X0,divide(X0,zero)),zero,zero),
inference(superposition,[],[f8,f1624]) ).
fof(f1648,plain,
! [X0] : less_equal(divide(X0,divide(X0,zero)),zero),
inference(unit_resulting_resolution,[],[f2,f1643]) ).
fof(f2080,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(unit_resulting_resolution,[],[f6,f5,f1648]) ).
fof(f2100,plain,
! [X0] : quotient(X0,divide(X0,zero),zero),
inference(superposition,[],[f8,f2080]) ).
fof(f2102,plain,
! [X0] : less_equal(X0,divide(X0,zero)),
inference(unit_resulting_resolution,[],[f2,f2100]) ).
fof(f2856,plain,
! [X0] : divide(X0,zero) = X0,
inference(unit_resulting_resolution,[],[f6,f21,f2102]) ).
fof(f2886,plain,
! [X0] : quotient(X0,zero,X0),
inference(superposition,[],[f8,f2856]) ).
fof(f2895,plain,
$false,
inference(unit_resulting_resolution,[],[f2886,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n015.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 10:52:45 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 7.28/1.95 % (1477908)Input is clausal, will run a generic CNF schedule.
% 7.28/1.95 % (1477929)lrs+10_1_sil=8000:sp=occurrence:random_seed=1463849587:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 7.28/1.95 % (1477931)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2574414857:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 7.28/1.95 % (1477929)Instruction limit reached!
% 7.28/1.95 % (1477929)------------------------------
% 7.28/1.95 % (1477929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/1.95 % (1477929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.95 % (1477929)CaDiCaL version: 2.1.3
% 7.28/1.95 % (1477929)Termination reason: Instruction limit
% 7.28/1.95 % (1477929)Termination phase: Saturation
% 7.28/1.95 % (1477929)Time elapsed: 0.038 s
% 7.28/1.95 % (1477929)Peak memory usage: 88 MB
% 7.28/1.95 % (1477929)Instructions burned: 109 (million)
% 7.28/1.95 % (1477928)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3438393013:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 7.28/1.95 % (1477930)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3264301326:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 7.28/1.95 % (1477927)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2863854369:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 7.28/1.95 % (1477926)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=2020923194:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 7.28/1.95 % (1477930)Refutation not found, incomplete strategy
% 7.28/1.95 % (1477930)------------------------------
% 7.28/1.95 % (1477930)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/1.95 % (1477930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.95 % (1477930)CaDiCaL version: 2.1.3
% 7.28/1.95 % (1477930)Termination reason: Refutation not found, incomplete strategy
% 7.28/1.95 % (1477930)Time elapsed: 0.004 s
% 7.28/1.95 % (1477930)Peak memory usage: 87 MB
% 7.28/1.95 % (1477930)Instructions burned: 2 (million)
% 7.28/1.95 % (1477932)dis-21_1_sil=8000:lcm=predicate:random_seed=2316198027: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)
% 7.28/1.95 % (1477932)Refutation not found, incomplete strategy
% 7.28/1.95 % (1477932)------------------------------
% 7.28/1.95 % (1477932)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/1.95 % (1477932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.95 % (1477932)CaDiCaL version: 2.1.3
% 7.28/1.95 % (1477932)Termination reason: Refutation not found, incomplete strategy
% 7.28/1.95 % (1477932)Time elapsed: 0.002 s
% 7.28/1.95 % (1477932)Peak memory usage: 88 MB
% 7.28/1.95 % (1477931)Instruction limit reached!
% 7.28/1.95 % (1477931)------------------------------
% 7.28/1.95 % (1477931)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/1.95 % (1477931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.95 % (1477931)CaDiCaL version: 2.1.3
% 7.28/1.95 % (1477931)Termination reason: Instruction limit
% 7.28/1.95 % (1477931)Termination phase: Saturation
% 7.28/1.95 % (1477931)Time elapsed: 0.163 s
% 7.28/1.95 % (1477931)Peak memory usage: 89 MB
% 7.28/1.95 % (1477931)Instructions burned: 180 (million)
% 7.28/1.95 % (1477945)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=3123869001:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 7.28/1.95 % (1477945)Refutation not found, incomplete strategy
% 7.28/1.95 % (1477945)------------------------------
% 7.28/1.95 % (1477945)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/1.95 % (1477945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/1.95 % (1477945)CaDiCaL version: 2.1.3
% 7.28/1.95 % (1477945)Termination reason: Refutation not found, incomplete strategy
% 7.28/1.95 % (1477945)Time elapsed: 0.001 s
% 7.28/1.95 % (1477945)Peak memory usage: 87 MB
% 7.28/1.95 % (1477930)------------------------------
% 7.28/1.95 % (1477930)------------------------------
% 7.28/1.95 % (1477945)------------------------------
% 8.20/2.08 % (1477945)------------------------------
% 8.20/2.08 % (1477950)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1992954595: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)
% 8.20/2.08 % (1477932)------------------------------
% 8.20/2.08 % (1477932)------------------------------
% 8.20/2.08 % (1477950)Refutation not found, incomplete strategy
% 8.20/2.08 % (1477950)------------------------------
% 8.20/2.08 % (1477950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.20/2.08 % (1477950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/2.08 % (1477950)CaDiCaL version: 2.1.3
% 8.20/2.08 % (1477950)Termination reason: Refutation not found, incomplete strategy
% 8.20/2.08 % (1477950)Time elapsed: 0.002 s
% 8.20/2.08 % (1477950)Peak memory usage: 87 MB
% 8.20/2.08 % (1477961)lrs+10_64_to=lpo:sil=8000:random_seed=322458841:i=126:bd=preordered_2994 on theBenchmark for (2994ds/126Mi)
% 8.20/2.08 % (1477960)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1326311394:st=4:i=219:sd=3:ss=axioms_2994 on theBenchmark for (2994ds/219Mi)
% 8.20/2.08 % (1477960)Refutation not found, incomplete strategy
% 8.20/2.08 % (1477960)------------------------------
% 8.20/2.08 % (1477960)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.20/2.08 % (1477960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/2.08 % (1477960)CaDiCaL version: 2.1.3
% 8.20/2.08 % (1477960)Termination reason: Refutation not found, incomplete strategy
% 8.20/2.08 % (1477960)Time elapsed: 0.001 s
% 8.20/2.08 % (1477960)Peak memory usage: 87 MB
% 8.20/2.08 % (1477962)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2173499399:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 8.20/2.08 % (1477961)Instruction limit reached!
% 8.20/2.08 % (1477961)------------------------------
% 8.20/2.08 % (1477961)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.20/2.08 % (1477961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/2.08 % (1477961)CaDiCaL version: 2.1.3
% 8.20/2.08 % (1477961)Termination reason: Instruction limit
% 8.20/2.08 % (1477961)Termination phase: Saturation
% 8.20/2.08 % (1477961)Time elapsed: 0.075 s
% 8.20/2.08 % (1477961)Peak memory usage: 87 MB
% 8.20/2.08 % (1477961)Instructions burned: 127 (million)
% 8.20/2.08 % (1477962)Instruction limit reached!
% 8.20/2.08 % (1477962)------------------------------
% 8.20/2.08 % (1477962)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.20/2.08 % (1477962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/2.08 % (1477962)CaDiCaL version: 2.1.3
% 8.20/2.08 % (1477962)Termination reason: Instruction limit
% 8.20/2.08 % (1477962)Termination phase: Saturation
% 8.20/2.08 % (1477962)Time elapsed: 0.083 s
% 8.20/2.08 % (1477962)Peak memory usage: 88 MB
% 8.20/2.08 % (1477962)Instructions burned: 198 (million)
% 8.20/2.08 % (1477950)------------------------------
% 8.20/2.08 % (1477950)------------------------------
% 8.20/2.08 % (1477966)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=1301424032:i=157:gtg=all_2992 on theBenchmark for (2992ds/157Mi)
% 8.20/2.08 % (1477968)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=742546399:i=3394:sd=4:ss=included:sgt=64_2992 on theBenchmark for (2992ds/3394Mi)
% 8.20/2.08 % (1477969)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=4071919970:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2991 on theBenchmark for (2991ds/106Mi)
% 8.20/2.08 % (1477960)------------------------------
% 8.20/2.08 % (1477960)------------------------------
% 8.20/2.08 % (1477927)First to succeed.
% 8.20/2.08 % (1477927)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1477908"
% 8.20/2.08 % (1477966)Instruction limit reached!
% 8.20/2.08 % (1477966)------------------------------
% 8.20/2.08 % (1477966)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.20/2.08 % (1477966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/2.08 % (1477966)CaDiCaL version: 2.1.3
% 8.20/2.08 % (1477966)Termination reason: Instruction limit
% 8.20/2.08 % (1477966)Termination phase: Saturation
% 8.20/2.08 % (1477966)Time elapsed: 0.098 s
% 8.20/2.08 % (1477966)Peak memory usage: 89 MB
% 8.20/2.08 % (1477966)Instructions burned: 158 (million)
% 8.20/2.08 % (1477926)Also succeeded, but the first one will report.
% 8.20/2.08 % (1477969)Instruction limit reached!
% 8.20/2.08 % (1477969)------------------------------
% 8.20/2.08 % (1477969)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.20/2.08 % (1477969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/2.08 % (1477969)CaDiCaL version: 2.1.3
% 8.20/2.08 % (1477969)Termination reason: Instruction limit
% 8.20/2.08 % (1477969)Termination phase: Saturation
% 8.20/2.08 % (1477969)Time elapsed: 0.064 s
% 8.20/2.08 % (1477969)Peak memory usage: 88 MB
% 8.20/2.08 % (1477969)Instructions burned: 107 (million)
% 8.20/2.08 % (1477928)Also succeeded, but the first one will report.
% 8.20/2.08 % (1477973)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=1031065901:i=107_2990 on theBenchmark for (2990ds/107Mi)
% 8.20/2.08 % (1477973)Refutation not found, incomplete strategy
% 8.20/2.08 % (1477973)------------------------------
% 8.20/2.08 % (1477973)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.20/2.08 % (1477973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/2.08 % (1477973)CaDiCaL version: 2.1.3
% 8.20/2.08 % (1477973)Termination reason: Refutation not found, incomplete strategy
% 8.20/2.08 % (1477973)Time elapsed: 0.001 s
% 8.20/2.08 % (1477973)Peak memory usage: 87 MB
% 8.20/2.08 % (1477927)Refutation found. Thanks to Tanya!
% 8.20/2.08 % SZS status Unsatisfiable for theBenchmark
% 8.20/2.08 % SZS output start Proof for theBenchmark
% See solution above
% 8.20/2.08 % (1477927)------------------------------
% 8.20/2.08 % (1477927)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.20/2.08 % (1477927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/2.08 % (1477927)CaDiCaL version: 2.1.3
% 8.20/2.08 % (1477927)Termination reason: Refutation
% 8.20/2.08 % (1477927)Time elapsed: 0.773 s
% 8.20/2.08 % (1477927)Peak memory usage: 129 MB
% 8.20/2.08 % (1477927)Instructions burned: 1092 (million)
% 8.20/2.08 % (1477927)------------------------------
% 8.20/2.08 % (1477927)------------------------------
% 8.20/2.08 % (1477908)Success in time 1.093 s
% 8.20/2.08 % Vampire exiting
%------------------------------------------------------------------------------