%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS070+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 11:41:35 AM UTC 2026
% Result : Unsatisfiable 2.65s 1.34s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 5 unt; 0 def)
% Number of atoms : 166 ( 9 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 210 ( 84 ~; 75 |; 45 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 86 ( 69 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f30,axiom,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] :
( rrx4(X0,X1)
& cc2(X1) )
& ~ ? [X1] :
( rrx3(X0,X1)
& cc2(X1)
& cc1(X1) )
& ? [X1] :
( rrx3(X0,X1)
& cc1(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f31,axiom,
! [X0,X1,X2] :
( ( rrx(X0,X1)
& rrx(X0,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f36,axiom,
cUnsatisfiable(i2003_11_14_17_18_32242),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
fof(f37,axiom,
! [X0,X1] :
( rrx3(X0,X1)
=> rrx(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
fof(f44,axiom,
! [X0,X1] :
( rrx4(X0,X1)
=> rrx(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_16) ).
fof(f45,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] :
( rrx4(X0,X1)
& cc2(X1) )
& ~ ? [X2] :
( rrx3(X0,X2)
& cc2(X2)
& cc1(X2) )
& ? [X3] :
( rrx3(X0,X3)
& cc1(X3) ) ) ),
inference(rectify,[],[f30]) ).
fof(f100,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] :
( rrx4(X0,X1)
& cc2(X1) )
& ! [X2] :
( ~ rrx3(X0,X2)
| ~ cc2(X2)
| ~ cc1(X2) )
& ? [X3] :
( rrx3(X0,X3)
& cc1(X3) ) ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f101,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rrx(X0,X1)
| ~ rrx(X0,X2) ),
inference(ennf_transformation,[],[f31]) ).
fof(f102,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rrx(X0,X1)
| ~ rrx(X0,X2) ),
inference(flattening,[],[f101]) ).
fof(f111,plain,
! [X0,X1] :
( rrx(X0,X1)
| ~ rrx3(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f118,plain,
! [X0,X1] :
( rrx(X0,X1)
| ~ rrx4(X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f120,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rrx4(X0,X1)
| ~ cc2(X1) )
| ? [X2] :
( rrx3(X0,X2)
& cc2(X2)
& cc1(X2) )
| ! [X3] :
( ~ rrx3(X0,X3)
| ~ cc1(X3) ) )
& ( ( ? [X1] :
( rrx4(X0,X1)
& cc2(X1) )
& ! [X2] :
( ~ rrx3(X0,X2)
| ~ cc2(X2)
| ~ cc1(X2) )
& ? [X3] :
( rrx3(X0,X3)
& cc1(X3) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(nnf_transformation,[],[f100]) ).
fof(f121,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rrx4(X0,X1)
| ~ cc2(X1) )
| ? [X2] :
( rrx3(X0,X2)
& cc2(X2)
& cc1(X2) )
| ! [X3] :
( ~ rrx3(X0,X3)
| ~ cc1(X3) ) )
& ( ( ? [X1] :
( rrx4(X0,X1)
& cc2(X1) )
& ! [X2] :
( ~ rrx3(X0,X2)
| ~ cc2(X2)
| ~ cc1(X2) )
& ? [X3] :
( rrx3(X0,X3)
& cc1(X3) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(flattening,[],[f120]) ).
fof(f122,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rrx4(X0,X1)
| ~ cc2(X1) )
| ? [X2] :
( rrx3(X0,X2)
& cc2(X2)
& cc1(X2) )
| ! [X3] :
( ~ rrx3(X0,X3)
| ~ cc1(X3) ) )
& ( ( ? [X4] :
( rrx4(X0,X4)
& cc2(X4) )
& ! [X5] :
( ~ rrx3(X0,X5)
| ~ cc2(X5)
| ~ cc1(X5) )
& ? [X6] :
( rrx3(X0,X6)
& cc1(X6) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(rectify,[],[f121]) ).
fof(f123,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rrx4(X0,X1)
| ~ cc2(X1) )
| ( rrx3(X0,sK0(X0))
& cc2(sK0(X0))
& cc1(sK0(X0)) )
| ! [X3] :
( ~ rrx3(X0,X3)
| ~ cc1(X3) ) )
& ( ( rrx4(X0,sK1(X0))
& cc2(sK1(X0))
& ! [X5] :
( ~ rrx3(X0,X5)
| ~ cc2(X5)
| ~ cc1(X5) )
& rrx3(X0,sK2(X0))
& cc1(sK2(X0)) )
| ~ cUnsatisfiable(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0)),skolemize(X4,sK1(X0)),skolemize(X6,sK2(X0))],[f122]) ).
fof(f155,plain,
! [X0] :
( cc1(sK2(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f156,plain,
! [X0] :
( rrx3(X0,sK2(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f157,plain,
! [X0,X5] :
( ~ cc2(X5)
| ~ rrx3(X0,X5)
| ~ cc1(X5)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f158,plain,
! [X0] :
( cc2(sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f159,plain,
! [X0] :
( rrx4(X0,sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f163,plain,
! [X2,X0,X1] :
( ~ rrx(X0,X1)
| X1 = X2
| ~ rrx(X0,X2) ),
inference(cnf_transformation,[],[f102]) ).
fof(f168,plain,
cUnsatisfiable(i2003_11_14_17_18_32242),
inference(cnf_transformation,[],[f36]) ).
fof(f169,plain,
! [X0,X1] :
( rrx(X0,X1)
| ~ rrx3(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f176,plain,
! [X0,X1] :
( rrx(X0,X1)
| ~ rrx4(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f204,plain,
! [X0,X1] :
( ~ cc1(sK1(X1))
| ~ rrx3(X0,sK1(X1))
| ~ cUnsatisfiable(X0)
| ~ cUnsatisfiable(X1) ),
inference(resolution,[],[f157,f158]) ).
fof(f205,plain,
! [X2,X0,X1] :
( ~ rrx4(X2,X0)
| ~ rrx(X2,X1)
| X0 = X1 ),
inference(resolution,[],[f163,f176]) ).
fof(f214,plain,
! [X0,X1] :
( ~ rrx(X0,X1)
| sK1(X0) = X1
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f205,f159]) ).
fof(f221,plain,
! [X0,X1] :
( ~ rrx3(X0,X1)
| ~ cUnsatisfiable(X0)
| sK1(X0) = X1 ),
inference(resolution,[],[f214,f169]) ).
fof(f224,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| sK1(X0) = sK2(X0)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f221,f156]) ).
fof(f225,plain,
! [X0] :
( sK1(X0) = sK2(X0)
| ~ cUnsatisfiable(X0) ),
inference(duplicate_literal_removal,[],[f224]) ).
fof(f226,plain,
! [X0] :
( rrx3(X0,sK1(X0))
| ~ cUnsatisfiable(X0)
| ~ cUnsatisfiable(X0) ),
inference(superposition,[],[f156,f225]) ).
fof(f227,plain,
! [X0] :
( cc1(sK1(X0))
| ~ cUnsatisfiable(X0)
| ~ cUnsatisfiable(X0) ),
inference(superposition,[],[f155,f225]) ).
fof(f228,plain,
! [X0] :
( cc1(sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(duplicate_literal_removal,[],[f227]) ).
fof(f229,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| rrx3(X0,sK1(X0)) ),
inference(duplicate_literal_removal,[],[f226]) ).
fof(f232,plain,
! [X0,X1] :
( ~ cUnsatisfiable(X0)
| ~ rrx3(X1,sK1(X0))
| ~ cUnsatisfiable(X1)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f228,f204]) ).
fof(f233,plain,
! [X0,X1] :
( ~ rrx3(X1,sK1(X0))
| ~ cUnsatisfiable(X0)
| ~ cUnsatisfiable(X1) ),
inference(duplicate_literal_removal,[],[f232]) ).
fof(f234,plain,
rrx3(i2003_11_14_17_18_32242,sK1(i2003_11_14_17_18_32242)),
inference(resolution,[],[f229,f168]) ).
fof(f241,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ cUnsatisfiable(i2003_11_14_17_18_32242) ),
inference(resolution,[],[f233,f234]) ).
fof(f242,plain,
~ cUnsatisfiable(i2003_11_14_17_18_32242),
inference(duplicate_literal_removal,[],[f241]) ).
fof(f243,plain,
$false,
inference(forward_subsumption_resolution,[],[f242,f168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS070+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 13:21:53 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.65/1.34 % (2353112)Detected formulas, will run a generic FOF schedule.
% 2.65/1.34 % (2353122)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1017301520:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.65/1.34 % (2353122)First to succeed.
% 2.65/1.34 % (2353122)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2353112"
% 2.65/1.34 % (2353120)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2637649104:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.65/1.34 % (2353118)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=4140882711:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.65/1.34 % (2353117)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=1036182211:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.65/1.34 % (2353119)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=1937504281:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.65/1.34 % (2353121)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1451512962:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.65/1.34 % (2353121)Refutation not found, incomplete strategy
% 2.65/1.34 % (2353121)------------------------------
% 2.65/1.34 % (2353121)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.34 % (2353121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.34 % (2353120)Refutation not found, incomplete strategy
% 2.65/1.34 % (2353120)------------------------------
% 2.65/1.34 % (2353120)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.34 % (2353121)CaDiCaL version: 2.1.3
% 2.65/1.34 % (2353121)Termination reason: Refutation not found, incomplete strategy
% 2.65/1.34 % (2353121)Time elapsed: 0.0000 s
% 2.65/1.34 % (2353120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.34 % (2353121)Peak memory usage: 86 MB
% 2.65/1.34 % (2353120)CaDiCaL version: 2.1.3
% 2.65/1.34 % (2353120)Termination reason: Refutation not found, incomplete strategy
% 2.65/1.34 % (2353120)Time elapsed: 0.0000 s
% 2.65/1.34 % (2353120)Peak memory usage: 86 MB
% 2.65/1.34 % (2353123)dis-21_1_sil=8000:lcm=predicate:random_seed=2395378027: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)
% 2.65/1.34 % (2353123)Instruction limit reached!
% 2.65/1.34 % (2353123)------------------------------
% 2.65/1.34 % (2353123)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.34 % (2353123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.34 % (2353123)CaDiCaL version: 2.1.3
% 2.65/1.34 % (2353123)Termination reason: Instruction limit
% 2.65/1.34 % (2353123)Termination phase: Saturation
% 2.65/1.34 % (2353123)Time elapsed: 0.056 s
% 2.65/1.34 % (2353123)Peak memory usage: 88 MB
% 2.65/1.34 % (2353123)Instructions burned: 130 (million)
% 2.65/1.34 % (2353122)Refutation found. Thanks to Tanya!
% 2.65/1.34 % SZS status Unsatisfiable for theBenchmark
% 2.65/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.35 % (2353122)------------------------------
% 2.65/1.35 % (2353122)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.35 % (2353122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.35 % (2353122)CaDiCaL version: 2.1.3
% 2.65/1.35 % (2353122)Termination reason: Refutation
% 2.65/1.35 % (2353122)Time elapsed: 0.003 s
% 2.65/1.35 % (2353122)Peak memory usage: 89 MB
% 2.65/1.35 % (2353122)Instructions burned: 5 (million)
% 2.65/1.35 % (2353122)------------------------------
% 2.65/1.35 % (2353122)------------------------------
% 2.65/1.35 % (2353112)Success in time 0.291 s
% 2.65/1.35 % Vampire exiting
%------------------------------------------------------------------------------