%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS116+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 : Thu Sep 24 12:59:43 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.84s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 19
% Syntax : Number of formulae : 118 ( 7 unt; 5 def)
% Number of atoms : 489 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 609 ( 238 ~; 222 |; 115 &)
% ( 24 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 24 ( 23 usr; 4 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 1 con; 0-1 aty)
% Number of variables : 274 ( 235 !; 39 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( cUnsatisfiable(X)
=> ca(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( cUnsatisfiable(X)
=> ? [Y] :
( ca_Ax2(Y)
& rs(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] :
( ca(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] :
( caxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( cc(X)
<=> ! [Y] :
( rinvR(X,Y)
=> ca_Vx7(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] :
( ca_Ax2(X)
<=> ( ! [Y] :
( rp(X,Y)
=> ca_Vx4(Y) )
& ? [Y] :
( cowlThing(Y)
& rp(X,Y) )
& ? [Y] :
( cowlThing(Y)
& rr(X,Y) )
& ! [Y] :
( rr(X,Y)
=> cc(Y) )
& ! [Y] :
( rp(X,Y)
=> ca_Vx5(Y) )
& ! [Y] :
( rp(X,Y)
=> ca_Vx3(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( ca_Vx3(X)
<=> ? [Y] :
( cowlThing(Y)
& rr(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] :
( ca_Vx5(X)
<=> ! [Y] :
( rr(X,Y)
=> cc(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] :
( ca_Vx6(X)
<=> ! [Y] :
( rinvS(X,Y)
=> caxcomp(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X] :
( ca_Vx7(X)
<=> ! [Y] :
( rinvP(X,Y)
=> ca_Vx6(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y] :
( rinvP(X,Y)
<=> rp(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
cUnsatisfiable(i2003_11_14_17_21_33997),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [X] :
( ca(X)
| ~ cUnsatisfiable(X) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f27,plain,
! [X0] :
( ca(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X] :
( ? [Y] :
( ca_Ax2(Y)
& rs(X,Y) )
| ~ cUnsatisfiable(X) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f29,plain,
! [X] :
( ( ca_Ax2(sK0_skl(X))
& rs(X,sK0_skl(X)) )
| ~ cUnsatisfiable(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y,sK0_skl(X))],[f28]) ).
fof(f30,plain,
! [X0] :
( rs(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [X0] :
( ca_Ax2(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f32,plain,
! [X] :
( ca(X)
<=> ! [Y] : ~ ra_Px1(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f33,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| ca(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ ca(X) ) ),
inference(NNF_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
( ! [X] :
( ? [Y] : ra_Px1(X,Y)
| ca(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ ca(X) ) ),
inference(miniscoping,[status(thm)],[f33]) ).
fof(f35,plain,
( ! [X] :
( ra_Px1(X,sK1_skl(X))
| ca(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ ca(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y,sK1_skl(X))],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ~ ra_Px1(X0,X1)
| ~ ca(X0) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f38,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| caxcomp(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ caxcomp(X) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f39,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| caxcomp(X) )
& ! [X] :
( ? [Y0] : ra_Px1(X,Y0)
| ~ caxcomp(X) ) ),
inference(miniscoping,[status(thm)],[f38]) ).
fof(f40,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| caxcomp(X) )
& ! [X] :
( ra_Px1(X,sK2_skl(X))
| ~ caxcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y0,sK2_skl(X))],[f39]) ).
fof(f41,plain,
! [X0] :
( ra_Px1(X0,sK2_skl(X0))
| ~ caxcomp(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,plain,
! [X] :
( cc(X)
<=> ! [Y] :
( ca_Vx7(Y)
| ~ rinvR(X,Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f44,plain,
! [X] :
( ( ? [Y] :
( ~ ca_Vx7(Y)
& rinvR(X,Y) )
| cc(X) )
& ( ! [Y] :
( ca_Vx7(Y)
| ~ rinvR(X,Y) )
| ~ cc(X) ) ),
inference(NNF_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
( ! [X] :
( ? [Y] :
( ~ ca_Vx7(Y)
& rinvR(X,Y) )
| cc(X) )
& ! [X] :
( ! [Y] :
( ca_Vx7(Y)
| ~ rinvR(X,Y) )
| ~ cc(X) ) ),
inference(miniscoping,[status(thm)],[f44]) ).
fof(f46,plain,
( ! [X] :
( ( ~ ca_Vx7(sK3_skl(X))
& rinvR(X,sK3_skl(X)) )
| cc(X) )
& ! [X] :
( ! [Y] :
( ca_Vx7(Y)
| ~ rinvR(X,Y) )
| ~ cc(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(Y,sK3_skl(X))],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ca_Vx7(X1)
| ~ rinvR(X0,X1)
| ~ cc(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f50,plain,
! [X] :
( ca_Ax2(X)
<=> ( ! [Y] :
( ca_Vx4(Y)
| ~ rp(X,Y) )
& ? [Y] :
( cowlThing(Y)
& rp(X,Y) )
& ? [Y] :
( cowlThing(Y)
& rr(X,Y) )
& ! [Y] :
( cc(Y)
| ~ rr(X,Y) )
& ! [Y] :
( ca_Vx5(Y)
| ~ rp(X,Y) )
& ! [Y] :
( ca_Vx3(Y)
| ~ rp(X,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f51,definition,
! [X] :
( sP0_prd(X)
<=> ( ? [Y] :
( cowlThing(Y)
& rp(X,Y) )
& ? [Y] :
( cowlThing(Y)
& rr(X,Y) )
& ! [Y] :
( cc(Y)
| ~ rr(X,Y) )
& ! [Y] :
( ca_Vx5(Y)
| ~ rp(X,Y) )
& ! [Y] :
( ca_Vx3(Y)
| ~ rp(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f52,plain,
! [X] :
( ca_Ax2(X)
<=> ( ! [Y] :
( ca_Vx4(Y)
| ~ rp(X,Y) )
& sP0_prd(X) ) ),
inference(formula_renaming,[status(thm)],[f50,f51]) ).
fof(f53,plain,
! [X] :
( ( ? [Y] :
( ~ ca_Vx4(Y)
& rp(X,Y) )
| ~ sP0_prd(X)
| ca_Ax2(X) )
& ( ( ! [Y] :
( ca_Vx4(Y)
| ~ rp(X,Y) )
& sP0_prd(X) )
| ~ ca_Ax2(X) ) ),
inference(NNF_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
( ! [X] :
( ? [Y] :
( ~ ca_Vx4(Y)
& rp(X,Y) )
| ~ sP0_prd(X)
| ca_Ax2(X) )
& ! [X] :
( ( ! [Y] :
( ca_Vx4(Y)
| ~ rp(X,Y) )
& sP0_prd(X) )
| ~ ca_Ax2(X) ) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f55,plain,
( ! [X] :
( ( ~ ca_Vx4(sK4_skl(X))
& rp(X,sK4_skl(X)) )
| ~ sP0_prd(X)
| ca_Ax2(X) )
& ! [X] :
( ( ! [Y] :
( ca_Vx4(Y)
| ~ rp(X,Y) )
& sP0_prd(X) )
| ~ ca_Ax2(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(Y,sK4_skl(X))],[f54]) ).
fof(f56,plain,
! [X0] :
( sP0_prd(X0)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f60,plain,
! [X] :
( ( ! [Y] :
( ~ cowlThing(Y)
| ~ rr(X,Y) )
| ca_Vx3(X) )
& ( ? [Y] :
( cowlThing(Y)
& rr(X,Y) )
| ~ ca_Vx3(X) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f61,plain,
( ! [X] :
( ! [Y] :
( ~ cowlThing(Y)
| ~ rr(X,Y) )
| ca_Vx3(X) )
& ! [X] :
( ? [Y] :
( cowlThing(Y)
& rr(X,Y) )
| ~ ca_Vx3(X) ) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,plain,
( ! [X] :
( ! [Y] :
( ~ cowlThing(Y)
| ~ rr(X,Y) )
| ca_Vx3(X) )
& ! [X] :
( ( cowlThing(sK5_skl(X))
& rr(X,sK5_skl(X)) )
| ~ ca_Vx3(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(Y,sK5_skl(X))],[f61]) ).
fof(f63,plain,
! [X0] :
( rr(X0,sK5_skl(X0))
| ~ ca_Vx3(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f72,plain,
! [X] :
( ca_Vx5(X)
<=> ! [Y] :
( cc(Y)
| ~ rr(X,Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f73,plain,
! [X] :
( ( ? [Y] :
( ~ cc(Y)
& rr(X,Y) )
| ca_Vx5(X) )
& ( ! [Y] :
( cc(Y)
| ~ rr(X,Y) )
| ~ ca_Vx5(X) ) ),
inference(NNF_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
( ! [X] :
( ? [Y] :
( ~ cc(Y)
& rr(X,Y) )
| ca_Vx5(X) )
& ! [X] :
( ! [Y] :
( cc(Y)
| ~ rr(X,Y) )
| ~ ca_Vx5(X) ) ),
inference(miniscoping,[status(thm)],[f73]) ).
fof(f75,plain,
( ! [X] :
( ( ~ cc(sK7_skl(X))
& rr(X,sK7_skl(X)) )
| ca_Vx5(X) )
& ! [X] :
( ! [Y] :
( cc(Y)
| ~ rr(X,Y) )
| ~ ca_Vx5(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(Y,sK7_skl(X))],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( cc(X1)
| ~ rr(X0,X1)
| ~ ca_Vx5(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f79,plain,
! [X] :
( ca_Vx6(X)
<=> ! [Y] :
( caxcomp(Y)
| ~ rinvS(X,Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f80,plain,
! [X] :
( ( ? [Y] :
( ~ caxcomp(Y)
& rinvS(X,Y) )
| ca_Vx6(X) )
& ( ! [Y] :
( caxcomp(Y)
| ~ rinvS(X,Y) )
| ~ ca_Vx6(X) ) ),
inference(NNF_transformation,[status(thm)],[f79]) ).
fof(f81,plain,
( ! [X] :
( ? [Y] :
( ~ caxcomp(Y)
& rinvS(X,Y) )
| ca_Vx6(X) )
& ! [X] :
( ! [Y] :
( caxcomp(Y)
| ~ rinvS(X,Y) )
| ~ ca_Vx6(X) ) ),
inference(miniscoping,[status(thm)],[f80]) ).
fof(f82,plain,
( ! [X] :
( ( ~ caxcomp(sK8_skl(X))
& rinvS(X,sK8_skl(X)) )
| ca_Vx6(X) )
& ! [X] :
( ! [Y] :
( caxcomp(Y)
| ~ rinvS(X,Y) )
| ~ ca_Vx6(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(Y,sK8_skl(X))],[f81]) ).
fof(f83,plain,
! [X0,X1] :
( caxcomp(X1)
| ~ rinvS(X0,X1)
| ~ ca_Vx6(X0) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f86,plain,
! [X] :
( ca_Vx7(X)
<=> ! [Y] :
( ca_Vx6(Y)
| ~ rinvP(X,Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f87,plain,
! [X] :
( ( ? [Y] :
( ~ ca_Vx6(Y)
& rinvP(X,Y) )
| ca_Vx7(X) )
& ( ! [Y] :
( ca_Vx6(Y)
| ~ rinvP(X,Y) )
| ~ ca_Vx7(X) ) ),
inference(NNF_transformation,[status(thm)],[f86]) ).
fof(f88,plain,
( ! [X] :
( ? [Y] :
( ~ ca_Vx6(Y)
& rinvP(X,Y) )
| ca_Vx7(X) )
& ! [X] :
( ! [Y] :
( ca_Vx6(Y)
| ~ rinvP(X,Y) )
| ~ ca_Vx7(X) ) ),
inference(miniscoping,[status(thm)],[f87]) ).
fof(f89,plain,
( ! [X] :
( ( ~ ca_Vx6(sK9_skl(X))
& rinvP(X,sK9_skl(X)) )
| ca_Vx7(X) )
& ! [X] :
( ! [Y] :
( ca_Vx6(Y)
| ~ rinvP(X,Y) )
| ~ ca_Vx7(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(Y,sK9_skl(X))],[f88]) ).
fof(f90,plain,
! [X0,X1] :
( ca_Vx6(X1)
| ~ rinvP(X0,X1)
| ~ ca_Vx7(X0) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f93,plain,
! [X,Y] :
( ( ~ rp(Y,X)
| rinvP(X,Y) )
& ( rp(Y,X)
| ~ rinvP(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f94,plain,
( ! [X,Y] :
( ~ rp(Y,X)
| rinvP(X,Y) )
& ! [X,Y] :
( rp(Y,X)
| ~ rinvP(X,Y) ) ),
inference(miniscoping,[status(thm)],[f93]) ).
fof(f96,plain,
! [X0,X1] :
( ~ rp(X1,X0)
| rinvP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f97,plain,
! [X,Y] :
( ( ~ rr(Y,X)
| rinvR(X,Y) )
& ( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f98,plain,
( ! [X,Y] :
( ~ rr(Y,X)
| rinvR(X,Y) )
& ! [X,Y] :
( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(miniscoping,[status(thm)],[f97]) ).
fof(f100,plain,
! [X0,X1] :
( ~ rr(X1,X0)
| rinvR(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f101,plain,
! [X,Y] :
( ( ~ rs(Y,X)
| rinvS(X,Y) )
& ( rs(Y,X)
| ~ rinvS(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f16]) ).
fof(f102,plain,
( ! [X,Y] :
( ~ rs(Y,X)
| rinvS(X,Y) )
& ! [X,Y] :
( rs(Y,X)
| ~ rinvS(X,Y) ) ),
inference(miniscoping,[status(thm)],[f101]) ).
fof(f104,plain,
! [X0,X1] :
( ~ rs(X1,X0)
| rinvS(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f108,plain,
cUnsatisfiable(i2003_11_14_17_21_33997),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f109,definition,
! [X] :
( sP1_prd(X)
<=> ( ! [Y] :
( ca_Vx5(Y)
| ~ rp(X,Y) )
& ! [Y] :
( ca_Vx3(Y)
| ~ rp(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f110,plain,
! [X] :
( sP0_prd(X)
<=> ( ? [Y] :
( cowlThing(Y)
& rp(X,Y) )
& ? [Y] :
( cowlThing(Y)
& rr(X,Y) )
& ! [Y] :
( cc(Y)
| ~ rr(X,Y) )
& sP1_prd(X) ) ),
inference(formula_renaming,[status(thm)],[f51,f109]) ).
fof(f111,plain,
! [X] :
( ( ! [Y] :
( ~ cowlThing(Y)
| ~ rp(X,Y) )
| ! [Y] :
( ~ cowlThing(Y)
| ~ rr(X,Y) )
| ? [Y] :
( ~ cc(Y)
& rr(X,Y) )
| ~ sP1_prd(X)
| sP0_prd(X) )
& ( ( ? [Y] :
( cowlThing(Y)
& rp(X,Y) )
& ? [Y] :
( cowlThing(Y)
& rr(X,Y) )
& ! [Y] :
( cc(Y)
| ~ rr(X,Y) )
& sP1_prd(X) )
| ~ sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f110]) ).
fof(f112,plain,
( ! [X] :
( ! [Y] :
( ~ cowlThing(Y)
| ~ rp(X,Y) )
| ! [Y] :
( ~ cowlThing(Y)
| ~ rr(X,Y) )
| ? [Y] :
( ~ cc(Y)
& rr(X,Y) )
| ~ sP1_prd(X)
| sP0_prd(X) )
& ! [X] :
( ( ? [Y] :
( cowlThing(Y)
& rp(X,Y) )
& ? [Y] :
( cowlThing(Y)
& rr(X,Y) )
& ! [Y] :
( cc(Y)
| ~ rr(X,Y) )
& sP1_prd(X) )
| ~ sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f111]) ).
fof(f113,plain,
( ! [X] :
( ! [Y] :
( ~ cowlThing(Y)
| ~ rp(X,Y) )
| ! [Y] :
( ~ cowlThing(Y)
| ~ rr(X,Y) )
| ( ~ cc(sK12_skl(X))
& rr(X,sK12_skl(X)) )
| ~ sP1_prd(X)
| sP0_prd(X) )
& ! [X] :
( ( cowlThing(sK11_skl(X))
& rp(X,sK11_skl(X))
& cowlThing(sK10_skl(X))
& rr(X,sK10_skl(X))
& ! [Y] :
( cc(Y)
| ~ rr(X,Y) )
& sP1_prd(X) )
| ~ sP0_prd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(Y,sK10_skl(X)),skolemize(Y,sK11_skl(X)),skolemize(Y,sK12_skl(X))],[f112]) ).
fof(f114,plain,
! [X0] :
( sP1_prd(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f118,plain,
! [X0] :
( rp(X0,sK11_skl(X0))
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f122,plain,
! [X] :
( ( ? [Y] :
( ~ ca_Vx5(Y)
& rp(X,Y) )
| ? [Y] :
( ~ ca_Vx3(Y)
& rp(X,Y) )
| sP1_prd(X) )
& ( ( ! [Y] :
( ca_Vx5(Y)
| ~ rp(X,Y) )
& ! [Y] :
( ca_Vx3(Y)
| ~ rp(X,Y) ) )
| ~ sP1_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f109]) ).
fof(f123,plain,
( ! [X] :
( ? [Y] :
( ~ ca_Vx5(Y)
& rp(X,Y) )
| ? [Y] :
( ~ ca_Vx3(Y)
& rp(X,Y) )
| sP1_prd(X) )
& ! [X] :
( ( ! [Y] :
( ca_Vx5(Y)
| ~ rp(X,Y) )
& ! [Y] :
( ca_Vx3(Y)
| ~ rp(X,Y) ) )
| ~ sP1_prd(X) ) ),
inference(miniscoping,[status(thm)],[f122]) ).
fof(f124,plain,
( ! [X] :
( ( ~ ca_Vx5(sK14_skl(X))
& rp(X,sK14_skl(X)) )
| ( ~ ca_Vx3(sK13_skl(X))
& rp(X,sK13_skl(X)) )
| sP1_prd(X) )
& ! [X] :
( ( ! [Y] :
( ca_Vx5(Y)
| ~ rp(X,Y) )
& ! [Y] :
( ca_Vx3(Y)
| ~ rp(X,Y) ) )
| ~ sP1_prd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(Y,sK13_skl(X)),skolemize(Y,sK14_skl(X))],[f123]) ).
fof(f125,plain,
! [X0,X1] :
( ca_Vx3(X1)
| ~ rp(X0,X1)
| ~ sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f126,plain,
! [X0,X1] :
( ca_Vx5(X1)
| ~ rp(X0,X1)
| ~ sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f132,plain,
! [X0,X1] :
( ~ cUnsatisfiable(X0)
| ~ ra_Px1(X0,X1) ),
inference(resolution,[status(thm)],[f36,f27]) ).
fof(f133,plain,
! [X0] : ~ ra_Px1(i2003_11_14_17_21_33997,X0),
inference(resolution,[status(thm)],[f132,f108]) ).
fof(f134,plain,
! [X0] :
( sP0_prd(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(resolution,[status(thm)],[f31,f56]) ).
fof(f135,plain,
~ caxcomp(i2003_11_14_17_21_33997),
inference(resolution,[status(thm)],[f133,f41]) ).
fof(f140,plain,
! [X0] :
( sP1_prd(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(resolution,[status(thm)],[f134,f114]) ).
fof(f148,plain,
! [X0,X1,X2] :
( caxcomp(X2)
| ~ rinvS(X1,X2)
| ~ rinvP(X0,X1)
| ~ ca_Vx7(X0) ),
inference(resolution,[status(thm)],[f90,f83]) ).
fof(f151,plain,
! [X0,X1] :
( ~ cUnsatisfiable(X0)
| ca_Vx5(X1)
| ~ rp(sK0_skl(X0),X1) ),
inference(resolution,[status(thm)],[f126,f140]) ).
fof(f157,plain,
! [X0] :
( ca_Vx5(X0)
| ~ rp(sK0_skl(i2003_11_14_17_21_33997),X0) ),
inference(resolution,[status(thm)],[f151,f108]) ).
fof(f159,plain,
! [X0,X1] :
( cc(X1)
| ~ rr(X0,X1)
| ~ rp(sK0_skl(i2003_11_14_17_21_33997),X0) ),
inference(resolution,[status(thm)],[f157,f76]) ).
fof(f169,plain,
! [X0,X1,X2,X3] :
( ~ rinvR(X3,X0)
| ~ cc(X3)
| caxcomp(X2)
| ~ rinvS(X1,X2)
| ~ rinvP(X0,X1) ),
inference(resolution,[status(thm)],[f148,f47]) ).
fof(f177,definition,
( sQ1_spl
<=> cUnsatisfiable(i2003_11_14_17_21_33997) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f179,plain,
( sQ1_spl
| ~ cUnsatisfiable(i2003_11_14_17_21_33997) ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f221,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f179,f108]) ).
fof(f222,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f221]) ).
fof(f231,plain,
! [X0,X1,X2,X3] :
( ~ rp(X0,X3)
| ~ rinvR(X2,X3)
| ~ cc(X2)
| caxcomp(X1)
| ~ rinvS(X0,X1) ),
inference(resolution,[status(thm)],[f169,f96]) ).
fof(f266,plain,
! [X0,X1,X2,X3] :
( ~ rs(X0,X3)
| ~ rp(X3,X2)
| ~ rinvR(X1,X2)
| ~ cc(X1)
| caxcomp(X0) ),
inference(resolution,[status(thm)],[f231,f104]) ).
fof(f297,plain,
! [X0,X1,X2,X3] :
( ~ rr(X3,X1)
| ~ rs(X0,X2)
| ~ rp(X2,X3)
| ~ cc(X1)
| caxcomp(X0) ),
inference(resolution,[status(thm)],[f266,f100]) ).
fof(f314,plain,
! [X0,X1,X2] :
( ~ cUnsatisfiable(X0)
| ~ rr(X2,X1)
| ~ rp(sK0_skl(X0),X2)
| ~ cc(X1)
| caxcomp(X0) ),
inference(resolution,[status(thm)],[f297,f30]) ).
fof(f333,plain,
! [X0,X1] :
( ~ rr(X1,X0)
| ~ rp(sK0_skl(i2003_11_14_17_21_33997),X1)
| ~ cc(X0)
| caxcomp(i2003_11_14_17_21_33997) ),
inference(resolution,[status(thm)],[f314,f108]) ).
fof(f334,definition,
( sQ7_spl
<=> caxcomp(i2003_11_14_17_21_33997) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f335,plain,
( ~ sQ7_spl
| caxcomp(i2003_11_14_17_21_33997) ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f337,definition,
! [X0,X1] :
( sQ8_spl
<=> ( ~ rr(X1,X0)
| ~ rp(sK0_skl(i2003_11_14_17_21_33997),X1)
| ~ cc(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f338,plain,
! [X0,X1] :
( ~ sQ8_spl
| ~ rr(X1,X0)
| ~ rp(sK0_skl(i2003_11_14_17_21_33997),X1)
| ~ cc(X0) ),
inference(component_clause,[status(thm)],[f337]) ).
fof(f340,plain,
( sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f333,f334,f337]) ).
fof(f341,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f335,f135]) ).
fof(f342,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f341]) ).
fof(f343,plain,
! [X0,X1] :
( ~ sQ8_spl
| ~ rr(X0,X1)
| ~ rp(sK0_skl(i2003_11_14_17_21_33997),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f338,f159]) ).
fof(f345,plain,
! [X0] :
( ~ sQ8_spl
| ~ ca_Vx3(X0)
| ~ rp(sK0_skl(i2003_11_14_17_21_33997),X0) ),
inference(resolution,[status(thm)],[f343,f63]) ).
fof(f351,plain,
! [X0,X1] :
( ~ sQ8_spl
| ~ rp(X1,X0)
| ~ sP1_prd(X1)
| ~ rp(sK0_skl(i2003_11_14_17_21_33997),X0) ),
inference(resolution,[status(thm)],[f345,f125]) ).
fof(f365,plain,
! [X0,X1] :
( ~ sQ8_spl
| ~ cUnsatisfiable(X1)
| ~ rp(sK0_skl(X1),X0)
| ~ rp(sK0_skl(i2003_11_14_17_21_33997),X0) ),
inference(resolution,[status(thm)],[f351,f140]) ).
fof(f383,plain,
! [X0] :
( ~ sQ8_spl
| ~ rp(sK0_skl(i2003_11_14_17_21_33997),X0)
| ~ rp(sK0_skl(i2003_11_14_17_21_33997),X0) ),
inference(resolution,[status(thm)],[f365,f108]) ).
fof(f384,plain,
! [X0] :
( ~ sQ8_spl
| ~ rp(sK0_skl(i2003_11_14_17_21_33997),X0) ),
inference(duplicate_literals_removal,[status(thm)],[f383]) ).
fof(f385,plain,
( ~ sQ8_spl
| ~ sP0_prd(sK0_skl(i2003_11_14_17_21_33997)) ),
inference(resolution,[status(thm)],[f384,f118]) ).
fof(f425,plain,
( ~ sQ8_spl
| ~ cUnsatisfiable(i2003_11_14_17_21_33997) ),
inference(resolution,[status(thm)],[f385,f134]) ).
fof(f426,plain,
( ~ sQ8_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f425,f177,f337]) ).
fof(f427,plain,
$false,
inference(sat_refutation,[status(thm)],[f222,f340,f342,f426]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.23 % Problem : KRS116+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.24 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.78 % Computer : n017.cluster.edu
% 0.13/0.78 % Model : x86_64 x86_64
% 0.13/0.78 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.78 % Memory : 8046.5625MB
% 0.13/0.78 % OS : Linux 6.8.0-71-generic
% 0.13/0.78 % CPULimit : 300
% 0.13/0.78 % WCLimit : 300
% 0.13/0.78 % DateTime : Sun Sep 20 22:49:13 UTC 2026
% 0.13/0.78 % CPUTime :
% 0.13/0.79 % Drodi V4.1.1
% 0.15/0.84 % Refutation found
% 0.15/0.84 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.87 % Elapsed time: 0.079372 seconds
% 0.15/0.87 % CPU time: 0.383902 seconds
% 0.15/0.87 % Total memory used: 9.840 MB
% 0.15/0.87 % Net memory used: 8.713 MB
%------------------------------------------------------------------------------