%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV606+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:58:25 PM UTC 2026
% Result : Theorem 3.65s 1.60s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 7 unt; 0 def)
% Number of atoms : 66 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 73 ( 26 ~; 18 |; 15 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 12 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1138,axiom,
! [X0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X0)
=> ! [X1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X1)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X1))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X0,X0),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Coq.ZArith.BinInt.Z.square_le_simpl_nonneg') ).
fof(f1728,conjecture,
! [X0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X0)
=> ! [X1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X1)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X1))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X0,X0)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X1,X0)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
fof(f1729,negated_conjecture,
~ ! [X0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X0)
=> ! [X1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X1)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X1))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X0,X0)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X1,X0)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1728]) ).
fof(f1730,plain,
? [X0] :
( ? [X1] :
( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X1,X0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X0,X0)))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X1))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X0))
& cCoq_2eNumbers_2eBinNums_2eZ___24t(X1) )
& cCoq_2eNumbers_2eBinNums_2eZ___24t(X0) ),
inference(ennf_transformation,[],[f1729]) ).
fof(f1731,plain,
? [X0] :
( ? [X1] :
( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X1,X0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X0,X0)))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X1))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X0))
& cCoq_2eNumbers_2eBinNums_2eZ___24t(X1) )
& cCoq_2eNumbers_2eBinNums_2eZ___24t(X0) ),
inference(flattening,[],[f1730]) ).
fof(f1767,plain,
! [X0] :
( ! [X1] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X0,X1))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X0,X0),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1)))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X1))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X1) )
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X0) ),
inference(ennf_transformation,[],[f1138]) ).
fof(f1768,plain,
! [X0] :
( ! [X1] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X0,X1))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X0,X0),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1)))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X1))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X1) )
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X0) ),
inference(flattening,[],[f1767]) ).
fof(f1893,plain,
( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(sK1,sK0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(sK1,sK1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(sK0,sK0)))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,sK1))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,sK0))
& cCoq_2eNumbers_2eBinNums_2eZ___24t(sK1)
& cCoq_2eNumbers_2eBinNums_2eZ___24t(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f1731]) ).
fof(f1914,plain,
cCoq_2eNumbers_2eBinNums_2eZ___24t(sK0),
inference(cnf_transformation,[],[f1893]) ).
fof(f1915,plain,
cCoq_2eNumbers_2eBinNums_2eZ___24t(sK1),
inference(cnf_transformation,[],[f1893]) ).
fof(f1916,plain,
p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,sK0)),
inference(cnf_transformation,[],[f1893]) ).
fof(f1918,plain,
p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(sK1,sK1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(sK0,sK0))),
inference(cnf_transformation,[],[f1893]) ).
fof(f1919,plain,
~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(sK1,sK0)),
inference(cnf_transformation,[],[f1893]) ).
fof(f1939,plain,
! [X0,X1] :
( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X0,X0),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1)))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X0,X1))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X1))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X1)
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X0) ),
inference(cnf_transformation,[],[f1768]) ).
fof(f2140,plain,
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(sK1,sK0))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,sK0))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(sK0)
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(sK1) ),
inference(resolution,[],[f1918,f1939]) ).
fof(f2197,plain,
( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,sK0))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(sK0)
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(sK1) ),
inference(forward_subsumption_resolution,[],[f2140,f1919]) ).
fof(f2246,plain,
( ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(sK0)
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(sK1) ),
inference(forward_subsumption_resolution,[],[f2197,f1916]) ).
fof(f2247,plain,
~ cCoq_2eNumbers_2eBinNums_2eZ___24t(sK1),
inference(forward_subsumption_resolution,[],[f2246,f1914]) ).
fof(f2248,plain,
$false,
inference(forward_subsumption_resolution,[],[f2247,f1915]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV606+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n001.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 06:47:33 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.65/1.60 % (165136)Detected formulas, will run a generic FOF schedule.
% 3.65/1.60 % (165143)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4039850692:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.65/1.60 % (165142)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1582354863:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.65/1.60 % (165144)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1401029203:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.65/1.60 % (165145)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3517508743:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.65/1.60 % (165147)dis-21_1_sil=8000:lcm=predicate:random_seed=3735847483:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.65/1.60 % (165141)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=84039364:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.65/1.60 % (165146)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=782810345:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.65/1.60 % (165144)First to succeed.
% 3.65/1.60 % (165144)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-165136"
% 3.65/1.60 % (165146)Instruction limit reached!
% 3.65/1.60 % (165146)------------------------------
% 3.65/1.60 % (165146)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.60 % (165146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.60 % (165146)CaDiCaL version: 2.1.3
% 3.65/1.60 % (165146)Termination reason: Instruction limit
% 3.65/1.60 % (165146)Termination phase: Property scanning
% 3.65/1.60 % (165146)Time elapsed: 0.070 s
% 3.65/1.60 % (165146)Peak memory usage: 91 MB
% 3.65/1.60 % (165146)Instructions burned: 140 (million)
% 3.65/1.60 % (165145)Instruction limit reached!
% 3.65/1.60 % (165145)------------------------------
% 3.65/1.60 % (165145)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.60 % (165145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.60 % (165145)CaDiCaL version: 2.1.3
% 3.65/1.60 % (165145)Termination reason: Instruction limit
% 3.65/1.60 % (165145)Termination phase: Saturation
% 3.65/1.60 % (165145)Time elapsed: 0.070 s
% 3.65/1.60 % (165145)Peak memory usage: 90 MB
% 3.65/1.60 % (165145)Instructions burned: 120 (million)
% 3.65/1.60 % (165147)Instruction limit reached!
% 3.65/1.60 % (165147)------------------------------
% 3.65/1.60 % (165147)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.60 % (165147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.60 % (165147)CaDiCaL version: 2.1.3
% 3.65/1.60 % (165147)Termination reason: Instruction limit
% 3.65/1.60 % (165147)Termination phase: Property scanning
% 3.65/1.60 % (165147)Time elapsed: 0.070 s
% 3.65/1.60 % (165147)Peak memory usage: 92 MB
% 3.65/1.60 % (165147)Instructions burned: 131 (million)
% 3.65/1.60 % (165156)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3110141577:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 3.65/1.60 % (165157)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2007494135:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 3.65/1.60 % (165155)lrs+10_1_sil=8000:sp=occurrence:random_seed=955440283:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 3.65/1.60 % (165157)Also succeeded, but the first one will report.
% 3.65/1.60 % (165155)Also succeeded, but the first one will report.
% 3.65/1.60 % (165156)Also succeeded, but the first one will report.
% 3.65/1.60 % (165144)Refutation found. Thanks to Tanya!
% 3.65/1.60 % SZS status Theorem for theBenchmark
% 3.65/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 3.65/1.60 % (165144)------------------------------
% 3.65/1.60 % (165144)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.60 % (165144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.60 % (165144)CaDiCaL version: 2.1.3
% 3.65/1.60 % (165144)Termination reason: Refutation
% 3.65/1.60 % (165144)Time elapsed: 0.016 s
% 3.65/1.60 % (165144)Peak memory usage: 91 MB
% 3.65/1.60 % (165144)Instructions burned: 25 (million)
% 3.65/1.60 % (165144)------------------------------
% 3.65/1.60 % (165144)------------------------------
% 3.65/1.60 % (165136)Success in time 0.512 s
% 3.65/1.60 % Vampire exiting
%------------------------------------------------------------------------------