%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN007-3 : 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 : n010.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 10:19:07 AM UTC 2026
% Result : Unsatisfiable 0.27s 2.90s
% Output : Refutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 25 unt; 0 def)
% Number of atoms : 54 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 16 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 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 : 59 ( 59 !; 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] :
( divide(X0,X1) != zero
| less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal2) ).
fof(f3,axiom,
! [X0,X1] : less_equal(divide(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
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(f8,axiom,
less_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_LE_b) ).
fof(f9,negated_conjecture,
~ less_equal(divide(c,b),divide(c,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_divide_b_LE_c_divide_a) ).
fof(f25,plain,
! [X0,X1] :
( ~ less_equal(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[],[f6,f3]) ).
fof(f26,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f38,plain,
! [X0] : zero = divide(zero,X0),
inference(resolution,[],[f26,f3]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ less_equal(X2,X1)
| less_equal(divide(divide(X0,X1),zero),divide(divide(X0,X2),X1)) ),
inference(superposition,[],[f4,f1]) ).
fof(f49,plain,
! [X0,X1] : less_equal(divide(divide(X0,X1),zero),divide(divide(X0,zero),X1)),
inference(superposition,[],[f4,f38]) ).
fof(f53,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(f95,plain,
! [X2,X0,X1] : less_equal(divide(divide(X0,X1),zero),divide(divide(X0,divide(X1,X2)),X1)),
inference(resolution,[],[f48,f3]) ).
fof(f99,plain,
! [X0] : less_equal(divide(divide(X0,b),zero),divide(divide(X0,a),b)),
inference(resolution,[],[f48,f8]) ).
fof(f342,plain,
! [X0,X1] : less_equal(divide(divide(X0,X0),divide(X1,X0)),zero),
inference(resolution,[],[f53,f3]) ).
fof(f388,plain,
! [X0] : less_equal(divide(divide(X0,X0),zero),zero),
inference(superposition,[],[f342,f38]) ).
fof(f404,plain,
! [X0] : zero = divide(divide(X0,X0),zero),
inference(resolution,[],[f388,f26]) ).
fof(f433,plain,
! [X0] :
( zero != zero
| less_equal(divide(X0,X0),zero) ),
inference(superposition,[],[f2,f404]) ).
fof(f443,plain,
! [X0] : less_equal(divide(X0,X0),zero),
inference(trivial_inequality_removal,[],[f433]) ).
fof(f452,plain,
! [X0] : zero = divide(X0,X0),
inference(resolution,[],[f443,f26]) ).
fof(f486,plain,
! [X0] : less_equal(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(superposition,[],[f49,f452]) ).
fof(f687,plain,
! [X0] : zero = divide(divide(X0,divide(X0,zero)),zero),
inference(resolution,[],[f486,f26]) ).
fof(f721,plain,
! [X0] :
( zero != zero
| less_equal(divide(X0,divide(X0,zero)),zero) ),
inference(superposition,[],[f2,f687]) ).
fof(f731,plain,
! [X0] : less_equal(divide(X0,divide(X0,zero)),zero),
inference(trivial_inequality_removal,[],[f721]) ).
fof(f856,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(resolution,[],[f731,f26]) ).
fof(f885,plain,
! [X0] :
( zero != zero
| less_equal(X0,divide(X0,zero)) ),
inference(superposition,[],[f2,f856]) ).
fof(f909,plain,
! [X0] : less_equal(X0,divide(X0,zero)),
inference(trivial_inequality_removal,[],[f885]) ).
fof(f929,plain,
! [X0] : divide(X0,zero) = X0,
inference(resolution,[],[f909,f25]) ).
fof(f963,plain,
! [X2,X0,X1] : less_equal(divide(X0,X1),divide(divide(X0,divide(X1,X2)),X1)),
inference(backward_demodulation,[],[f95,f929]) ).
fof(f978,plain,
! [X0] : less_equal(divide(X0,b),divide(divide(X0,a),b)),
inference(backward_demodulation,[],[f99,f929]) ).
fof(f1371,plain,
! [X2,X0,X1] :
( less_equal(divide(X0,X1),divide(zero,X1))
| ~ less_equal(X0,divide(X1,X2)) ),
inference(superposition,[],[f963,f1]) ).
fof(f1389,plain,
! [X2,X0,X1] :
( less_equal(divide(X0,X1),zero)
| ~ less_equal(X0,divide(X1,X2)) ),
inference(forward_demodulation,[],[f1371,f38]) ).
fof(f1745,plain,
! [X2,X0,X1] :
( ~ less_equal(X0,divide(X1,X2))
| divide(X0,X1) = zero ),
inference(resolution,[],[f1389,f26]) ).
fof(f1774,plain,
! [X0] : zero = divide(divide(X0,b),divide(X0,a)),
inference(resolution,[],[f1745,f978]) ).
fof(f1852,plain,
! [X0] :
( zero != zero
| less_equal(divide(X0,b),divide(X0,a)) ),
inference(superposition,[],[f2,f1774]) ).
fof(f1874,plain,
! [X0] : less_equal(divide(X0,b),divide(X0,a)),
inference(trivial_inequality_removal,[],[f1852]) ).
fof(f1898,plain,
$false,
inference(resolution,[],[f1874,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN007-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n010.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 27 10:51:07 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.52 Running first-order theorem proving
% 0.23/0.52 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
% 8.55/2.52 % (786855)Input is clausal, will run a generic CNF schedule.
% 8.55/2.52 % (786864)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=32411204:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 8.55/2.52 % (786864)Refutation not found, incomplete strategy
% 8.55/2.52 % (786864)------------------------------
% 8.55/2.52 % (786864)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.55/2.52 % (786864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.55/2.52 % (786864)CaDiCaL version: 2.1.3
% 8.55/2.52 % (786864)Termination reason: Refutation not found, incomplete strategy
% 8.55/2.52 % (786864)Time elapsed: 0.001 s
% 8.55/2.52 % (786864)Peak memory usage: 87 MB
% 8.55/2.52 % (786861)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1100460696:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 8.55/2.52 % (786860)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=2149987723:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 8.55/2.52 % (786862)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2966008787:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 8.55/2.52 % (786863)lrs+10_1_sil=8000:sp=occurrence:random_seed=2869003566:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 8.55/2.52 % (786866)dis-21_1_sil=8000:lcm=predicate:random_seed=234381669: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)
% 8.55/2.52 % (786865)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2243541728:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 8.55/2.52 % (786866)Refutation not found, incomplete strategy
% 8.55/2.52 % (786866)------------------------------
% 8.55/2.52 % (786866)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.55/2.52 % (786866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.55/2.52 % (786866)CaDiCaL version: 2.1.3
% 8.55/2.52 % (786866)Termination reason: Refutation not found, incomplete strategy
% 8.55/2.52 % (786866)Time elapsed: 0.002 s
% 8.55/2.52 % (786866)Peak memory usage: 88 MB
% 8.55/2.52 % (786863)Instruction limit reached!
% 8.55/2.52 % (786863)------------------------------
% 8.55/2.52 % (786863)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.55/2.52 % (786863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.55/2.52 % (786863)CaDiCaL version: 2.1.3
% 8.55/2.52 % (786863)Termination reason: Instruction limit
% 8.55/2.52 % (786863)Termination phase: Saturation
% 8.55/2.52 % (786863)Time elapsed: 0.098 s
% 8.55/2.52 % (786863)Peak memory usage: 89 MB
% 8.55/2.52 % (786863)Instructions burned: 108 (million)
% 8.55/2.52 % (786864)------------------------------
% 8.55/2.52 % (786864)------------------------------
% 8.55/2.52 % (786865)Instruction limit reached!
% 8.55/2.52 % (786865)------------------------------
% 8.55/2.52 % (786865)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.55/2.52 % (786865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.55/2.52 % (786865)CaDiCaL version: 2.1.3
% 8.55/2.52 % (786865)Termination reason: Instruction limit
% 8.55/2.52 % (786865)Termination phase: Saturation
% 8.55/2.52 % (786865)Time elapsed: 0.176 s
% 8.55/2.52 % (786865)Peak memory usage: 90 MB
% 8.55/2.52 % (786865)Instructions burned: 182 (million)
% 8.55/2.52 % (786874)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=3972167227:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 8.55/2.52 % (786874)Refutation not found, incomplete strategy
% 8.55/2.52 % (786874)------------------------------
% 8.55/2.52 % (786874)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.55/2.52 % (786874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.55/2.52 % (786874)CaDiCaL version: 2.1.3
% 8.55/2.52 % (786874)Termination reason: Refutation not found, incomplete strategy
% 8.55/2.52 % (786874)Time elapsed: 0.002 s
% 8.55/2.52 % (786874)Peak memory usage: 88 MB
% 8.55/2.52 % (786876)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1824128145:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 0.27/2.90 % (786876)Refutation not found, incomplete strategy
% 0.27/2.90 % (786876)------------------------------
% 0.27/2.90 % (786876)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/2.90 % (786876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/2.90 % (786876)CaDiCaL version: 2.1.3
% 0.27/2.90 % (786876)Termination reason: Refutation not found, incomplete strategy
% 0.27/2.90 % (786876)Time elapsed: 0.001 s
% 0.27/2.90 % (786876)Peak memory usage: 88 MB
% 0.27/2.90 % (786866)------------------------------
% 0.27/2.90 % (786866)------------------------------
% 0.27/2.90 % (786875)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=774394860:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2995 on theBenchmark for (2995ds/189Mi)
% 0.27/2.90 % (786876)------------------------------
% 0.27/2.90 % (786876)------------------------------
% 0.27/2.90 % (786875)Instruction limit reached!
% 0.27/2.90 % (786875)------------------------------
% 0.27/2.90 % (786875)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/2.90 % (786875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/2.90 % (786875)CaDiCaL version: 2.1.3
% 0.27/2.90 % (786875)Termination reason: Instruction limit
% 0.27/2.90 % (786875)Termination phase: Saturation
% 0.27/2.90 % (786875)Time elapsed: 0.204 s
% 0.27/2.90 % (786875)Peak memory usage: 90 MB
% 0.27/2.90 % (786875)Instructions burned: 189 (million)
% 0.27/2.90 % (786880)lrs+10_64_to=lpo:sil=8000:random_seed=2679892471:i=126:bd=preordered_2993 on theBenchmark for (2993ds/126Mi)
% 0.27/2.90 % (786874)------------------------------
% 0.27/2.90 % (786874)------------------------------
% 0.27/2.90 % (786880)Instruction limit reached!
% 0.27/2.90 % (786880)------------------------------
% 0.27/2.90 % (786880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/2.90 % (786880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/2.90 % (786880)CaDiCaL version: 2.1.3
% 0.27/2.90 % (786880)Termination reason: Instruction limit
% 0.27/2.90 % (786880)Termination phase: Saturation
% 0.27/2.90 % (786880)Time elapsed: 0.124 s
% 0.27/2.90 % (786880)Peak memory usage: 88 MB
% 0.27/2.90 % (786880)Instructions burned: 126 (million)
% 0.27/2.90 % (786881)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1026582743:avsq=on:i=194:fgj=on:bd=preordered_2992 on theBenchmark for (2992ds/194Mi)
% 0.27/2.90 % (786881)First to succeed.
% 0.27/2.90 % (786881)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-786855"
% 0.27/2.90 % (786882)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=963143436:i=157:gtg=all_2991 on theBenchmark for (2991ds/157Mi)
% 0.27/2.90 % (786884)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=1411339645:i=3394:sd=4:ss=included:sgt=64_2990 on theBenchmark for (2990ds/3394Mi)
% 0.27/2.90 % (786886)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=1942507693:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2990 on theBenchmark for (2990ds/106Mi)
% 0.27/2.90 % (786882)Instruction limit reached!
% 0.27/2.90 % (786882)------------------------------
% 0.27/2.90 % (786882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/2.90 % (786882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/2.90 % (786882)CaDiCaL version: 2.1.3
% 0.27/2.90 % (786882)Termination reason: Instruction limit
% 0.27/2.90 % (786882)Termination phase: Saturation
% 0.27/2.90 % (786882)Time elapsed: 0.158 s
% 0.27/2.90 % (786882)Peak memory usage: 90 MB
% 0.27/2.90 % (786882)Instructions burned: 158 (million)
% 0.27/2.90 % (786881)Refutation found. Thanks to Tanya!
% 0.27/2.90 % SZS status Unsatisfiable for theBenchmark
% 0.27/2.90 % SZS output start Proof for theBenchmark
% See solution above
% 0.27/2.90 % (786881)------------------------------
% 0.27/2.90 % (786881)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/2.90 % (786881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/2.90 % (786881)CaDiCaL version: 2.1.3
% 0.27/2.90 % (786881)Termination reason: Refutation
% 0.27/2.90 % (786881)Time elapsed: 0.031 s
% 0.27/2.90 % (786881)Peak memory usage: 88 MB
% 0.27/2.90 % (786881)Instructions burned: 53 (million)
% 0.27/2.90 % (786881)------------------------------
% 0.27/2.90 % (786881)------------------------------
% 0.27/2.90 % (786855)Success in time 1.262 s
% 0.27/2.90 % Vampire exiting
%------------------------------------------------------------------------------