%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KRS078+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 : n002.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 5.67s 1.30s
% Output : Proof 5.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 50 ( 25 unt; 0 def)
% Number of atoms : 139 ( 30 equ)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 149 ( 60 ~; 48 |; 35 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 78 ( 1 sgn 38 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( ~ cp(Y)
& ~ cq(Y)
& rs(X,Y) )
& ? [Y] :
( ! [Z0,Z1] :
( ( rinvR(Y,Z1)
& rinvR(Y,Z0) )
=> Z0 = Z1 )
& ? [Z] :
( ! [W] :
( rs(Z,W)
=> cp(W) )
& rinvR(Y,Z) )
& rr(X,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f15_nnf,plain,
! [X] :
( ( ! [Y] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) )
| ! [Y] :
( ? [Z0,Z1] :
( Z0 != Z1
& rinvR(Y,Z1)
& rinvR(Y,Z0) )
| ! [Z] :
( ? [W] :
( ~ cp(W)
& rs(Z,W) )
| ~ rinvR(Y,Z) )
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ( ( ? [Y] :
( ~ cp(Y)
& ~ cq(Y)
& rs(X,Y) )
& ? [Y] :
( ! [Z0,Z1] :
( Z0 = Z1
| ~ rinvR(Y,Z1)
| ~ rinvR(Y,Z0) )
& ? [Z] :
( ! [W] :
( cp(W)
| ~ rs(Z,W) )
& rinvR(Y,Z) )
& rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X,W,Z0,Z1,Y,Z] :
( ( cp(Y)
| cq(Y)
| ~ rs(X,Y)
| ( sk4(X,Y) != sk5(X,Y)
& rinvR(Y,sk5(X,Y))
& rinvR(Y,sk4(X,Y)) )
| ( ~ cp(sk3(X,Y,Z))
& rs(Z,sk3(X,Y,Z)) )
| ~ rinvR(Y,Z)
| ~ rr(X,Y)
| cUnsatisfiable(X) )
& ( ( ~ cp(sk2(X))
& ~ cq(sk2(X))
& rs(X,sk2(X))
& ( Z0 = Z1
| ~ rinvR(sk0(X),Z1)
| ~ rinvR(sk0(X),Z0) )
& ( cp(W)
| ~ rs(sk1(X),W) )
& rinvR(sk0(X),sk1(X))
& rr(X,sk0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3,sk4,sk5])],[f15_nnf]) ).
cnf(c21,plain,
( rs(X0,sk2(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi20,axiom,
ifeq(cUnsatisfiable(X0),true,rs(X0,sk2(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
fof(f17,axiom,
cUnsatisfiable(i2003_11_14_17_19_13721),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f17_nnf,plain,
cUnsatisfiable(i2003_11_14_17_19_13721),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c32,plain,
cUnsatisfiable(i2003_11_14_17_19_13721),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(hi29,axiom,
cUnsatisfiable(i2003_11_14_17_19_13721) = true,
inference(equality_encoding,[status(esa)],[c32]) ).
cnf(h0,plain,
rs(i2003_11_14_17_19_13721,sk2(i2003_11_14_17_19_13721)) = true,
inference(hyper_resolution,[status(thm)],[hi20,hi29]) ).
cnf(c18,plain,
( rinvR(sk0(X0),sk1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi17,axiom,
ifeq(cUnsatisfiable(X0),true,rinvR(sk0(X0),sk1(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h1,plain,
rinvR(sk0(i2003_11_14_17_19_13721),sk1(i2003_11_14_17_19_13721)) = true,
inference(hyper_resolution,[status(thm)],[hi17,hi29]) ).
cnf(c17,plain,
( rr(X0,sk0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi16,axiom,
ifeq(cUnsatisfiable(X0),true,rr(X0,sk0(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(h2,plain,
rr(i2003_11_14_17_19_13721,sk0(i2003_11_14_17_19_13721)) = true,
inference(hyper_resolution,[status(thm)],[hi16,hi29]) ).
fof(f16,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f16_nnf,plain,
! [X,Y] :
( ( ~ rr(Y,X)
| rinvR(X,Y) )
& ( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X,Y] :
( ( ~ rr(Y,X)
| rinvR(X,Y) )
& ( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c31,plain,
( ~ rr(X1,X0)
| rinvR(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi28,axiom,
ifeq(rr(X0,X1),true,rinvR(X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(h9,plain,
rinvR(sk0(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721) = true,
inference(hyper_resolution,[status(thm)],[hi28,h2]) ).
cnf(c20,plain,
( X4 = X5
| ~ rinvR(sk0(X0),X5)
| ~ rinvR(sk0(X0),X4)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi19,axiom,
ifeq(cUnsatisfiable(X0),true,ifeq(rinvR(sk0(X0),X1),true,ifeq(rinvR(sk0(X0),X2),true,X1,X2),X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(h29,plain,
i2003_11_14_17_19_13721 = sk1(i2003_11_14_17_19_13721),
inference(hyper_resolution,[status(thm)],[hi19,hi29,h9,h1]) ).
fof(f9,axiom,
! [A,B,C] :
( ( rs(A,C)
& A = B )
=> rs(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rs_substitution_1) ).
fof(f9_nnf,plain,
! [A,B,C] :
( rs(B,C)
| ~ rs(A,C)
| A != B ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B,C] :
( rs(B,C)
| ~ rs(A,C)
| A != B ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( rs(X1,X2)
| ~ rs(X0,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi11,axiom,
ifeq(X0,X1,ifeq(rs(X0,X2),true,rs(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h34,plain,
rs(sk1(i2003_11_14_17_19_13721),sk2(i2003_11_14_17_19_13721)) = true,
inference(hyper_resolution,[status(thm)],[hi11,h29,h0]) ).
cnf(c19,plain,
( cp(X3)
| ~ rs(sk1(X0),X3)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi18,axiom,
ifeq(cUnsatisfiable(X0),true,ifeq(rs(sk1(X0),X1),true,cp(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(h45,plain,
cp(sk2(i2003_11_14_17_19_13721)) = true,
inference(hyper_resolution,[status(thm)],[hi18,hi29,h34]) ).
cnf(c23,plain,
( ~ cp(sk2(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi33,axiom,
ifeq(cUnsatisfiable(X0),true,ifeq(cp(sk2(X0)),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi33,hi29,h45]) ).
cnf(t162,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f13,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
fof(f13_nnf,plain,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c14,plain,
~ cowlNothing(X0),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
fof(f14,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f14_nnf,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c15,plain,
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(c22,plain,
( ~ cq(sk2(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c14,c15,c22,c23]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t162]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS078+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 19:22:34 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.67/1.30 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.67/1.30 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------