%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN005-4 : 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 : n006.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 10:19:05 AM UTC 2026
% Result : Unsatisfiable 3.95s 1.75s
% Output : Refutation 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 26 ( 16 unt; 0 def)
% Number of atoms : 37 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( divide(X0,X1) = zero
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal1) ).
fof(f2,axiom,
! [X0,X1] :
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal2) ).
fof(f4,axiom,
! [X2,X0,X1] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
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(f10,axiom,
! [X0] : divide(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
fof(f11,plain,
! [X0] : zero = divide(zero,X0),
inference(reorient_equations,[],[f10]) ).
fof(f14,axiom,
! [X0] : divide(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_zero_is_x) ).
fof(f15,axiom,
less_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_LE_b) ).
fof(f16,axiom,
less_equal(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_LE_c) ).
fof(f17,negated_conjecture,
~ less_equal(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_LE_c) ).
fof(f21,plain,
zero != divide(a,c),
inference(resolution,[],[f2,f17]) ).
fof(f27,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f55,plain,
! [X2,X0,X1] :
( less_equal(divide(divide(X0,X1),zero),divide(divide(X0,X2),X1))
| ~ less_equal(X2,X1) ),
inference(superposition,[],[f4,f1]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ less_equal(divide(X0,X2),X1)
| less_equal(divide(divide(X0,X1),divide(X2,X1)),zero) ),
inference(superposition,[],[f4,f1]) ).
fof(f131,plain,
! [X2,X0,X1] :
( ~ less_equal(X2,X1)
| less_equal(divide(X0,X1),divide(divide(X0,X2),X1)) ),
inference(forward_demodulation,[],[f55,f14]) ).
fof(f139,plain,
! [X0] : less_equal(divide(X0,c),divide(divide(X0,b),c)),
inference(resolution,[],[f131,f16]) ).
fof(f150,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| less_equal(divide(divide(X0,X1),divide(zero,X1)),zero) ),
inference(superposition,[],[f62,f14]) ).
fof(f155,plain,
! [X0,X1] :
( less_equal(divide(divide(X0,X1),zero),zero)
| ~ less_equal(X0,X1) ),
inference(forward_demodulation,[],[f150,f11]) ).
fof(f160,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| less_equal(divide(X0,X1),zero) ),
inference(forward_demodulation,[],[f155,f14]) ).
fof(f247,plain,
less_equal(divide(a,b),zero),
inference(resolution,[],[f160,f15]) ).
fof(f252,plain,
zero = divide(a,b),
inference(resolution,[],[f247,f27]) ).
fof(f388,plain,
less_equal(divide(a,c),divide(zero,c)),
inference(superposition,[],[f139,f252]) ).
fof(f390,plain,
less_equal(divide(a,c),zero),
inference(forward_demodulation,[],[f388,f11]) ).
fof(f455,plain,
zero = divide(a,c),
inference(resolution,[],[f390,f27]) ).
fof(f465,plain,
$false,
inference(forward_subsumption_resolution,[],[f455,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : HEN005-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.47 % Computer : n006.cluster.edu
% 0.20/0.47 % Model : x86_64 x86_64
% 0.20/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.47 % Memory : 8046.5625MB
% 0.20/0.47 % OS : Linux 6.8.0-71-generic
% 0.20/0.47 % CPULimit : 300
% 0.20/0.47 % WCLimit : 300
% 0.20/0.47 % DateTime : Sun Sep 27 10:49:31 UTC 2026
% 0.20/0.48 % CPUTime :
% 0.20/0.48 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.54 Running first-order theorem proving
% 0.25/0.54 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
% 3.95/1.75 % (2799091)Input is clausal, will run a generic CNF schedule.
% 3.95/1.75 % (2799109)lrs+10_1_sil=8000:sp=occurrence:random_seed=2595904315:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.95/1.75 % (2799109)Refutation not found, incomplete strategy
% 3.95/1.75 % (2799109)------------------------------
% 3.95/1.75 % (2799109)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.75 % (2799109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.75 % (2799109)CaDiCaL version: 2.1.3
% 3.95/1.75 % (2799109)Termination reason: Refutation not found, incomplete strategy
% 3.95/1.75 % (2799109)Time elapsed: 0.0000 s
% 3.95/1.75 % (2799109)Peak memory usage: 87 MB
% 3.95/1.75 % (2799108)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3990817021:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.95/1.75 % (2799112)dis-21_1_sil=8000:lcm=predicate:random_seed=2854395726: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)
% 3.95/1.75 % (2799110)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=717473659:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.95/1.75 % (2799111)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3778588552:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.95/1.75 % (2799107)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1892587922:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.95/1.75 % (2799106)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=3748191940:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.95/1.75 % (2799112)Refutation not found, incomplete strategy
% 3.95/1.75 % (2799112)------------------------------
% 3.95/1.75 % (2799112)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.75 % (2799112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.75 % (2799112)CaDiCaL version: 2.1.3
% 3.95/1.75 % (2799112)Termination reason: Refutation not found, incomplete strategy
% 3.95/1.75 % (2799112)Time elapsed: 0.001 s
% 3.95/1.75 % (2799112)Peak memory usage: 88 MB
% 3.95/1.75 % (2799111)First to succeed.
% 3.95/1.75 % (2799111)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2799091"
% 3.95/1.75 % (2799110)Instruction limit reached!
% 3.95/1.75 % (2799110)------------------------------
% 3.95/1.75 % (2799110)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.75 % (2799110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.75 % (2799110)CaDiCaL version: 2.1.3
% 3.95/1.75 % (2799110)Termination reason: Instruction limit
% 3.95/1.75 % (2799110)Termination phase: Saturation
% 3.95/1.75 % (2799110)Time elapsed: 0.071 s
% 3.95/1.75 % (2799110)Peak memory usage: 88 MB
% 3.95/1.75 % (2799110)Instructions burned: 115 (million)
% 3.95/1.75 % (2799109)------------------------------
% 3.95/1.75 % (2799109)------------------------------
% 3.95/1.75 % (2799196)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=3113170535:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.95/1.75 % (2799209)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=347157185: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)
% 3.95/1.75 % (2799196)Refutation not found, incomplete strategy
% 3.95/1.75 % (2799196)------------------------------
% 3.95/1.75 % (2799196)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.75 % (2799196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.75 % (2799196)CaDiCaL version: 2.1.3
% 3.95/1.75 % (2799196)Termination reason: Refutation not found, incomplete strategy
% 3.95/1.75 % (2799196)Time elapsed: 0.002 s
% 3.95/1.75 % (2799196)Peak memory usage: 87 MB
% 3.95/1.75 % (2799209)Also succeeded, but the first one will report.
% 3.95/1.75 % (2799112)------------------------------
% 3.95/1.75 % (2799112)------------------------------
% 3.95/1.75 % (2799111)Refutation found. Thanks to Tanya!
% 3.95/1.75 % SZS status Unsatisfiable for theBenchmark
% 3.95/1.75 % SZS output start Proof for theBenchmark
% See solution above
% 3.95/1.75 % (2799111)------------------------------
% 3.95/1.75 % (2799111)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.75 % (2799111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.75 % (2799111)CaDiCaL version: 2.1.3
% 3.95/1.75 % (2799111)Termination reason: Refutation
% 3.95/1.75 % (2799111)Time elapsed: 0.009 s
% 3.95/1.75 % (2799111)Peak memory usage: 88 MB
% 3.95/1.75 % (2799111)Instructions burned: 11 (million)
% 3.95/1.75 % (2799111)------------------------------
% 3.95/1.75 % (2799111)------------------------------
% 3.95/1.75 % (2799091)Success in time 0.432 s
% 3.95/1.75 % Vampire exiting
%------------------------------------------------------------------------------