%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KRS109+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 11:42:17 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.46s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 67 ( 9 unt; 0 def)
% Number of atoms : 232 ( 8 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 273 ( 108 ~; 100 |; 49 &)
% ( 10 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 124 ( 105 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [X0] :
( cUnsatisfiable(X0)
<=> ( cpxcomp(X0)
& ? [X1] :
( rf(X0,X1)
& ca_Ax2(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f27,axiom,
! [X0] :
( cp(X0)
<=> ~ ? [X1] : ra_Px1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f28,axiom,
! [X0] :
( cpxcomp(X0)
<=> ? [X1] : ra_Px1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f29,axiom,
! [X0] :
( ca_Ax2(X0)
<=> ( ! [X1] :
( rinvS(X0,X1)
=> cp(X1) )
& ! [X1] :
( rinvF(X0,X1)
=> ca_Vx3(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f30,axiom,
! [X0] :
( ca_Vx3(X0)
<=> ? [X1] :
( rs(X0,X1)
& cp(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f31,axiom,
! [X0,X1,X2] :
( ( rf(X0,X1)
& rf(X0,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
fof(f33,axiom,
! [X0,X1] :
( rinvF(X0,X1)
<=> rf(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
fof(f35,axiom,
! [X0,X1] :
( rinvS(X0,X1)
<=> rs(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
fof(f37,axiom,
cUnsatisfiable(i2003_11_14_17_21_08508),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
fof(f38,axiom,
! [X0,X1] :
( rs(X0,X1)
=> rf(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
fof(f40,plain,
! [X0] :
( ca_Ax2(X0)
<=> ( ! [X1] :
( rinvS(X0,X1)
=> cp(X1) )
& ! [X2] :
( rinvF(X0,X2)
=> ca_Vx3(X2) ) ) ),
inference(rectify,[],[f29]) ).
fof(f87,plain,
! [X0] :
( cp(X0)
<=> ! [X1] : ~ ra_Px1(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f88,plain,
! [X0] :
( ca_Ax2(X0)
<=> ( ! [X1] :
( cp(X1)
| ~ rinvS(X0,X1) )
& ! [X2] :
( ca_Vx3(X2)
| ~ rinvF(X0,X2) ) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f89,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf(X0,X1)
| ~ rf(X0,X2) ),
inference(ennf_transformation,[],[f31]) ).
fof(f90,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf(X0,X1)
| ~ rf(X0,X2) ),
inference(flattening,[],[f89]) ).
fof(f95,plain,
! [X0,X1] :
( rf(X0,X1)
| ~ rs(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f98,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ~ cpxcomp(X0)
| ! [X1] :
( ~ rf(X0,X1)
| ~ ca_Ax2(X1) ) )
& ( ( cpxcomp(X0)
& ? [X1] :
( rf(X0,X1)
& ca_Ax2(X1) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f99,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ~ cpxcomp(X0)
| ! [X1] :
( ~ rf(X0,X1)
| ~ ca_Ax2(X1) ) )
& ( ( cpxcomp(X0)
& ? [X1] :
( rf(X0,X1)
& ca_Ax2(X1) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ~ cpxcomp(X0)
| ! [X1] :
( ~ rf(X0,X1)
| ~ ca_Ax2(X1) ) )
& ( ( cpxcomp(X0)
& ? [X2] :
( rf(X0,X2)
& ca_Ax2(X2) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(rectify,[],[f99]) ).
fof(f101,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ~ cpxcomp(X0)
| ! [X1] :
( ~ rf(X0,X1)
| ~ ca_Ax2(X1) ) )
& ( ( cpxcomp(X0)
& rf(X0,sK0(X0))
& ca_Ax2(sK0(X0)) )
| ~ cUnsatisfiable(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0))],[f100]) ).
fof(f102,plain,
! [X0] :
( ( cp(X0)
| ? [X1] : ra_Px1(X0,X1) )
& ( ! [X1] : ~ ra_Px1(X0,X1)
| ~ cp(X0) ) ),
inference(nnf_transformation,[],[f87]) ).
fof(f103,plain,
! [X0] :
( ( cp(X0)
| ? [X1] : ra_Px1(X0,X1) )
& ( ! [X2] : ~ ra_Px1(X0,X2)
| ~ cp(X0) ) ),
inference(rectify,[],[f102]) ).
fof(f104,plain,
! [X0] :
( ( cp(X0)
| ra_Px1(X0,sK1(X0)) )
& ( ! [X2] : ~ ra_Px1(X0,X2)
| ~ cp(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f103]) ).
fof(f105,plain,
! [X0] :
( ( cpxcomp(X0)
| ! [X1] : ~ ra_Px1(X0,X1) )
& ( ? [X1] : ra_Px1(X0,X1)
| ~ cpxcomp(X0) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f106,plain,
! [X0] :
( ( cpxcomp(X0)
| ! [X1] : ~ ra_Px1(X0,X1) )
& ( ? [X2] : ra_Px1(X0,X2)
| ~ cpxcomp(X0) ) ),
inference(rectify,[],[f105]) ).
fof(f107,plain,
! [X0] :
( ( cpxcomp(X0)
| ! [X1] : ~ ra_Px1(X0,X1) )
& ( ra_Px1(X0,sK2(X0))
| ~ cpxcomp(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0))],[f106]) ).
fof(f108,plain,
! [X0] :
( ( ca_Ax2(X0)
| ? [X1] :
( ~ cp(X1)
& rinvS(X0,X1) )
| ? [X2] :
( ~ ca_Vx3(X2)
& rinvF(X0,X2) ) )
& ( ( ! [X1] :
( cp(X1)
| ~ rinvS(X0,X1) )
& ! [X2] :
( ca_Vx3(X2)
| ~ rinvF(X0,X2) ) )
| ~ ca_Ax2(X0) ) ),
inference(nnf_transformation,[],[f88]) ).
fof(f109,plain,
! [X0] :
( ( ca_Ax2(X0)
| ? [X1] :
( ~ cp(X1)
& rinvS(X0,X1) )
| ? [X2] :
( ~ ca_Vx3(X2)
& rinvF(X0,X2) ) )
& ( ( ! [X1] :
( cp(X1)
| ~ rinvS(X0,X1) )
& ! [X2] :
( ca_Vx3(X2)
| ~ rinvF(X0,X2) ) )
| ~ ca_Ax2(X0) ) ),
inference(flattening,[],[f108]) ).
fof(f110,plain,
! [X0] :
( ( ca_Ax2(X0)
| ? [X1] :
( ~ cp(X1)
& rinvS(X0,X1) )
| ? [X2] :
( ~ ca_Vx3(X2)
& rinvF(X0,X2) ) )
& ( ( ! [X3] :
( cp(X3)
| ~ rinvS(X0,X3) )
& ! [X4] :
( ca_Vx3(X4)
| ~ rinvF(X0,X4) ) )
| ~ ca_Ax2(X0) ) ),
inference(rectify,[],[f109]) ).
fof(f111,plain,
! [X0] :
( ( ca_Ax2(X0)
| ( ~ cp(sK3(X0))
& rinvS(X0,sK3(X0)) )
| ( ~ ca_Vx3(sK4(X0))
& rinvF(X0,sK4(X0)) ) )
& ( ( ! [X3] :
( cp(X3)
| ~ rinvS(X0,X3) )
& ! [X4] :
( ca_Vx3(X4)
| ~ rinvF(X0,X4) ) )
| ~ ca_Ax2(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X1,sK3(X0)),skolemize(X2,sK4(X0))],[f110]) ).
fof(f112,plain,
! [X0] :
( ( ca_Vx3(X0)
| ! [X1] :
( ~ rs(X0,X1)
| ~ cp(X1) ) )
& ( ? [X1] :
( rs(X0,X1)
& cp(X1) )
| ~ ca_Vx3(X0) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f113,plain,
! [X0] :
( ( ca_Vx3(X0)
| ! [X1] :
( ~ rs(X0,X1)
| ~ cp(X1) ) )
& ( ? [X2] :
( rs(X0,X2)
& cp(X2) )
| ~ ca_Vx3(X0) ) ),
inference(rectify,[],[f112]) ).
fof(f114,plain,
! [X0] :
( ( ca_Vx3(X0)
| ! [X1] :
( ~ rs(X0,X1)
| ~ cp(X1) ) )
& ( ( rs(X0,sK5(X0))
& cp(sK5(X0)) )
| ~ ca_Vx3(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0))],[f113]) ).
fof(f115,plain,
! [X0,X1] :
( ( rinvF(X0,X1)
| ~ rf(X1,X0) )
& ( rf(X1,X0)
| ~ rinvF(X0,X1) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f117,plain,
! [X0,X1] :
( ( rinvS(X0,X1)
| ~ rs(X1,X0) )
& ( rs(X1,X0)
| ~ rinvS(X0,X1) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f145,plain,
! [X0] :
( ca_Ax2(sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f146,plain,
! [X0] :
( rf(X0,sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f147,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| cpxcomp(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f149,plain,
! [X2,X0] :
( ~ ra_Px1(X0,X2)
| ~ cp(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f151,plain,
! [X0] :
( ra_Px1(X0,sK2(X0))
| ~ cpxcomp(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f153,plain,
! [X0,X4] :
( ~ rinvF(X0,X4)
| ca_Vx3(X4)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f154,plain,
! [X3,X0] :
( ~ rinvS(X0,X3)
| cp(X3)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f160,plain,
! [X0] :
( rs(X0,sK5(X0))
| ~ ca_Vx3(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f162,plain,
! [X2,X0,X1] :
( ~ rf(X0,X2)
| ~ rf(X0,X1)
| X1 = X2 ),
inference(cnf_transformation,[],[f90]) ).
fof(f165,plain,
! [X0,X1] :
( ~ rf(X1,X0)
| rinvF(X0,X1) ),
inference(cnf_transformation,[],[f115]) ).
fof(f169,plain,
! [X0,X1] :
( ~ rs(X1,X0)
| rinvS(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f171,plain,
cUnsatisfiable(i2003_11_14_17_21_08508),
inference(cnf_transformation,[],[f37]) ).
fof(f172,plain,
! [X0,X1] :
( ~ rs(X0,X1)
| rf(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f198,plain,
cpxcomp(i2003_11_14_17_21_08508),
inference(resolution,[],[f147,f171]) ).
fof(f202,plain,
! [X0] :
( ~ cpxcomp(X0)
| ~ cp(X0) ),
inference(resolution,[],[f151,f149]) ).
fof(f203,plain,
~ cp(i2003_11_14_17_21_08508),
inference(resolution,[],[f202,f198]) ).
fof(f205,plain,
! [X0] :
( rinvF(sK0(X0),X0)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f165,f146]) ).
fof(f206,plain,
! [X0] :
( rinvS(sK5(X0),X0)
| ~ ca_Vx3(X0) ),
inference(resolution,[],[f169,f160]) ).
fof(f207,plain,
! [X0] :
( rf(X0,sK5(X0))
| ~ ca_Vx3(X0) ),
inference(resolution,[],[f172,f160]) ).
fof(f210,plain,
! [X0] :
( ca_Vx3(X0)
| ~ ca_Ax2(sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f153,f205]) ).
fof(f211,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| ca_Vx3(X0) ),
inference(forward_subsumption_resolution,[],[f210,f145]) ).
fof(f212,plain,
ca_Vx3(i2003_11_14_17_21_08508),
inference(resolution,[],[f211,f171]) ).
fof(f214,plain,
! [X0] :
( ~ ca_Ax2(sK5(X0))
| cp(X0)
| ~ ca_Vx3(X0) ),
inference(resolution,[],[f206,f154]) ).
fof(f227,plain,
! [X0,X1] :
( ~ rf(X0,X1)
| sK0(X0) = X1
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f162,f146]) ).
fof(f242,plain,
! [X0] :
( sK0(X0) = sK5(X0)
| ~ cUnsatisfiable(X0)
| ~ ca_Vx3(X0) ),
inference(resolution,[],[f227,f207]) ).
fof(f245,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| sK0(X0) = sK5(X0) ),
inference(forward_subsumption_resolution,[],[f242,f211]) ).
fof(f249,plain,
sK0(i2003_11_14_17_21_08508) = sK5(i2003_11_14_17_21_08508),
inference(resolution,[],[f245,f171]) ).
fof(f261,plain,
( ~ ca_Ax2(sK0(i2003_11_14_17_21_08508))
| cp(i2003_11_14_17_21_08508)
| ~ ca_Vx3(i2003_11_14_17_21_08508) ),
inference(superposition,[],[f214,f249]) ).
fof(f266,plain,
( ~ ca_Ax2(sK0(i2003_11_14_17_21_08508))
| ~ ca_Vx3(i2003_11_14_17_21_08508) ),
inference(forward_subsumption_resolution,[],[f261,f203]) ).
fof(f272,plain,
~ ca_Ax2(sK0(i2003_11_14_17_21_08508)),
inference(forward_subsumption_resolution,[],[f266,f212]) ).
fof(f278,plain,
~ cUnsatisfiable(i2003_11_14_17_21_08508),
inference(resolution,[],[f272,f145]) ).
fof(f279,plain,
$false,
inference(forward_subsumption_resolution,[],[f278,f171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS109+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n019.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
% 0.11/0.37 % DateTime : Sun Sep 27 13:24:48 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.41 Running first-order model finding
% 0.14/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.46 % (3098219)Will run a generic schedule for satisfiability detection.
% 0.14/0.46 % (3098224)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2625944362_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.46 % TRYING [1]
% 0.14/0.46 % TRYING [2]
% 0.14/0.46 % TRYING [3]
% 0.14/0.46 % TRYING [4]
% 0.14/0.46 % TRYING [5]
% 0.14/0.46 % (3098225)% WARNING: option uhcvi not known.
% 0.14/0.46 % TRYING [6]
% 0.14/0.46 % TRYING [7]
% 0.14/0.46 % TRYING [8]
% 0.14/0.46 % (3098230)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1947133621:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.14/0.46 % (3098226)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2111349596:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.46 % (3098227)dis+10_1_sil=32000:sp=arity:random_seed=3513101617:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.46 % (3098228)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2428137319:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.46 % (3098229)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2722210671:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.14/0.46 % TRYING [9]
% 0.14/0.46 % (3098225)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=709623575:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.46 % (3098227) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3098219-3098227"...
% 0.14/0.46 % (3098228) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3098219-3098228"...
% 0.14/0.46 % (3098230) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3098219-3098230"...
% 0.14/0.46 % (3098229) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3098219-3098229"...
% 0.14/0.46 % TRYING [10]
% 0.14/0.46 % (3098227)...printing done.
% 0.14/0.46 % (3098228)...printing done.
% 0.14/0.46 % (3098227)Refutation found. Thanks to Tanya!
% 0.14/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.46 % (3098227)------------------------------
% 0.14/0.46 % (3098227)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.46 % (3098227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.46 % (3098227)CaDiCaL version: 2.1.3
% 0.14/0.46 % (3098227)Termination reason: Refutation
% 0.14/0.46 % (3098227)Time elapsed: 0.005 s
% 0.14/0.46 % (3098227)Peak memory usage: 12 MB
% 0.14/0.46 % (3098227)Instructions burned: 6 (million)
% 0.14/0.46 % (3098219)Success in time 0.04 s
% 0.14/0.46 % Vampire exiting
%------------------------------------------------------------------------------