%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KRS082+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 : Fri Sep 25 01:53:00 PM UTC 2026
% Result : Unsatisfiable 4.10s 0.94s
% Output : Proof 4.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 27 unt; 0 def)
% Number of atoms : 181 ( 22 equ)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 186 ( 66 ~; 56 |; 49 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 105 ( 1 sgn 54 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( cUnsatisfiable(X)
=> ca(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f3_nnf,plain,
! [X] :
( ca(X)
| ~ cUnsatisfiable(X) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] :
( ca(X)
| ~ cUnsatisfiable(X) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c15,plain,
( ca(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi13,axiom,
ifeq(cUnsatisfiable(X0),true,ca(X0),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
fof(f9,axiom,
cUnsatisfiable(i2003_11_14_17_19_28752),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
fof(f9_nnf,plain,
cUnsatisfiable(i2003_11_14_17_19_28752),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c28,plain,
cUnsatisfiable(i2003_11_14_17_19_28752),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(hi25,axiom,
cUnsatisfiable(i2003_11_14_17_19_28752) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(h0,plain,
ca(i2003_11_14_17_19_28752) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi25]) ).
fof(f2,axiom,
! [X] :
( cUnsatisfiable(X)
=> ? [Y] :
( ? [Z] :
( cowlThing(Z)
& rr(Y,Z) )
& ! [Z] :
( rp(Y,Z)
=> ! [W] :
( rr(Z,W)
=> cc(W) ) )
& ! [Z] :
( rp(Y,Z)
=> ? [W] :
( cowlThing(W)
& rp(Z,W) ) )
& ! [Z] :
( rp(Y,Z)
=> ? [W] :
( cowlThing(W)
& rr(Z,W) ) )
& ! [Z] :
( rr(Y,Z)
=> cc(Z) )
& ? [Z] :
( cowlThing(Z)
& rp(Y,Z) )
& rs(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f2_nnf,plain,
! [X] :
( ? [Y] :
( ? [Z] :
( cowlThing(Z)
& rr(Y,Z) )
& ! [Z] :
( ! [W] :
( cc(W)
| ~ rr(Z,W) )
| ~ rp(Y,Z) )
& ! [Z] :
( ? [W] :
( cowlThing(W)
& rp(Z,W) )
| ~ rp(Y,Z) )
& ! [Z] :
( ? [W] :
( cowlThing(W)
& rr(Z,W) )
| ~ rp(Y,Z) )
& ! [Z] :
( cc(Z)
| ~ rr(Y,Z) )
& ? [Z] :
( cowlThing(Z)
& rp(Y,Z) )
& rs(X,Y) )
| ~ cUnsatisfiable(X) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Z,W] :
( ( cowlThing(sk4(X))
& rr(sk0(X),sk4(X))
& ( cc(W)
| ~ rr(Z,W)
| ~ rp(sk0(X),Z) )
& ( ( cowlThing(sk3(X,Z))
& rp(Z,sk3(X,Z)) )
| ~ rp(sk0(X),Z) )
& ( ( cowlThing(sk2(X,Z))
& rr(Z,sk2(X,Z)) )
| ~ rp(sk0(X),Z) )
& ( cc(Z)
| ~ rr(sk0(X),Z) )
& cowlThing(sk1(X))
& rp(sk0(X),sk1(X))
& rs(X,sk0(X)) )
| ~ cUnsatisfiable(X) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3,sk4])],[f2_nnf]) ).
cnf(c4,plain,
( rs(X0,sk0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi1,axiom,
ifeq(cUnsatisfiable(X0),true,rs(X0,sk0(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h3,plain,
rs(i2003_11_14_17_19_28752,sk0(i2003_11_14_17_19_28752)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi25]) ).
fof(f7,axiom,
! [X,Y] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
fof(f7_nnf,plain,
! [X,Y] :
( ( ~ rs(Y,X)
| rinvS(X,Y) )
& ( rs(Y,X)
| ~ rinvS(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] :
( ( ~ rs(Y,X)
| rinvS(X,Y) )
& ( rs(Y,X)
| ~ rinvS(X,Y) ) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c26,plain,
( ~ rs(X1,X0)
| rinvS(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi23,axiom,
ifeq(rs(X0,X1),true,rinvS(X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(h4,plain,
rinvS(sk0(i2003_11_14_17_19_28752),i2003_11_14_17_19_28752) = true,
inference(hyper_resolution,[status(thm)],[hi23,h3]) ).
cnf(c5,plain,
( rp(sk0(X0),sk1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(cUnsatisfiable(X0),true,rp(sk0(X0),sk1(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h2,plain,
rp(sk0(i2003_11_14_17_19_28752),sk1(i2003_11_14_17_19_28752)) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi25]) ).
fof(f5,axiom,
! [X,Y] :
( rinvP(X,Y)
<=> rp(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f5_nnf,plain,
! [X,Y] :
( ( ~ rp(Y,X)
| rinvP(X,Y) )
& ( rp(Y,X)
| ~ rinvP(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] :
( ( ~ rp(Y,X)
| rinvP(X,Y) )
& ( rp(Y,X)
| ~ rinvP(X,Y) ) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c22,plain,
( ~ rp(X1,X0)
| rinvP(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi19,axiom,
ifeq(rp(X0,X1),true,rinvP(X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(h7,plain,
rinvP(sk1(i2003_11_14_17_19_28752),sk0(i2003_11_14_17_19_28752)) = true,
inference(hyper_resolution,[status(thm)],[hi19,h2]) ).
cnf(c8,plain,
( rr(X2,sk2(X0,X2))
| ~ rp(sk0(X0),X2)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi6,axiom,
ifeq(cUnsatisfiable(X0),true,ifeq(rp(sk0(X0),X1),true,rr(X1,sk2(X0,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h9,plain,
rr(sk1(i2003_11_14_17_19_28752),sk2(i2003_11_14_17_19_28752,sk1(i2003_11_14_17_19_28752))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi25,h2]) ).
fof(f6,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f6_nnf,plain,
! [X,Y] :
( ( ~ rr(Y,X)
| rinvR(X,Y) )
& ( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( ( ~ rr(Y,X)
| rinvR(X,Y) )
& ( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c24,plain,
( ~ rr(X1,X0)
| rinvR(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi21,axiom,
ifeq(rr(X0,X1),true,rinvR(X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(h12,plain,
rinvR(sk2(i2003_11_14_17_19_28752,sk1(i2003_11_14_17_19_28752)),sk1(i2003_11_14_17_19_28752)) = true,
inference(hyper_resolution,[status(thm)],[hi21,h9]) ).
cnf(c12,plain,
( cc(X3)
| ~ rr(X2,X3)
| ~ rp(sk0(X0),X2)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi10,axiom,
ifeq(cUnsatisfiable(X0),true,ifeq(rp(sk0(X0),X1),true,ifeq(rr(X1,X2),true,cc(X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h13,plain,
cc(sk2(i2003_11_14_17_19_28752,sk1(i2003_11_14_17_19_28752))) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi25,h2,h9]) ).
fof(f4,axiom,
! [X] :
( cc(X)
<=> ! [Y] :
( rinvR(X,Y)
=> ! [Z] :
( rinvP(Y,Z)
=> ! [W] :
( rinvS(Z,W)
=> ~ ca(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f4_nnf,plain,
! [X] :
( ( ? [Y] :
( ? [Z] :
( ? [W] :
( ca(W)
& rinvS(Z,W) )
& rinvP(Y,Z) )
& rinvR(X,Y) )
| cc(X) )
& ( ! [Y] :
( ! [Z] :
( ! [W] :
( ~ ca(W)
| ~ rinvS(Z,W) )
| ~ rinvP(Y,Z) )
| ~ rinvR(X,Y) )
| ~ cc(X) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Z,W] :
( ( ( ca(sk7(X))
& rinvS(sk6(X),sk7(X))
& rinvP(sk5(X),sk6(X))
& rinvR(X,sk5(X)) )
| cc(X) )
& ( ~ ca(W)
| ~ rinvS(Z,W)
| ~ rinvP(Y,Z)
| ~ rinvR(X,Y)
| ~ cc(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5,sk6,sk7])],[f4_nnf]) ).
cnf(c16,plain,
( ~ ca(X3)
| ~ rinvS(X2,X3)
| ~ rinvP(X1,X2)
| ~ rinvR(X0,X1)
| ~ cc(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi29,axiom,
ifeq(cc(X0),true,ifeq(rinvR(X0,X1),true,ifeq(rinvP(X1,X2),true,ifeq(rinvS(X2,X3),true,ifeq(ca(X3),true,false,true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi29,h13,h12,h7,h4,h0]) ).
cnf(t141,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f0,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
fof(f0_nnf,plain,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c1,plain,
~ cowlNothing(X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f1,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f1_nnf,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c2,plain,
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c1,c2,c16]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t141]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS082+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n005.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 19:20:18 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.10/0.94 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.10/0.94 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------