%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KRS072+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 : n008.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 01:52:59 PM UTC 2026
% Result : Unsatisfiable 6.89s 1.32s
% Output : Proof 6.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 70 ( 25 unt; 0 def)
% Number of atoms : 181 ( 30 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 210 ( 99 ~; 63 |; 39 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 84 ( 1 sgn 43 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( cp2(X)
& ? [Y] :
( ? [Z] :
( cp1(Z)
& rr(Y,Z) )
& ! [Z0,Z1] :
( ( rr(Y,Z1)
& rr(Y,Z0) )
=> Z0 = Z1 )
& rinvR(X,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f16_nnf,plain,
! [X] :
( ( ~ cp2(X)
| ! [Y] :
( ! [Z] :
( ~ cp1(Z)
| ~ rr(Y,Z) )
| ? [Z0,Z1] :
( Z0 != Z1
& rr(Y,Z1)
& rr(Y,Z0) )
| ~ rinvR(X,Y) )
| cUnsatisfiable(X) )
& ( ( cp2(X)
& ? [Y] :
( ? [Z] :
( cp1(Z)
& rr(Y,Z) )
& ! [Z0,Z1] :
( Z0 = Z1
| ~ rr(Y,Z1)
| ~ rr(Y,Z0) )
& rinvR(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X,Z0,Z1,Y,Z] :
( ( ~ cp2(X)
| ~ cp1(Z)
| ~ rr(Y,Z)
| ( sk2(X,Y) != sk3(X,Y)
& rr(Y,sk3(X,Y))
& rr(Y,sk2(X,Y)) )
| ~ rinvR(X,Y)
| cUnsatisfiable(X) )
& ( ( cp2(X)
& cp1(sk1(X))
& rr(sk0(X),sk1(X))
& ( Z0 = Z1
| ~ rr(sk0(X),Z1)
| ~ rr(sk0(X),Z0) )
& rinvR(X,sk0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f16_nnf]) ).
cnf(c22,plain,
( cp2(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi21,axiom,
ifeq(cUnsatisfiable(X0),true,cp2(X0),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
fof(f22,axiom,
cUnsatisfiable(i2003_11_14_17_18_50190),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
fof(f22_nnf,plain,
cUnsatisfiable(i2003_11_14_17_18_50190),
inference(nnf_transformation,[status(thm)],[f22]) ).
cnf(c38,plain,
cUnsatisfiable(i2003_11_14_17_18_50190),
inference(cnf_transformation,[status(esa)],[f22_nnf]) ).
cnf(hi27,axiom,
cUnsatisfiable(i2003_11_14_17_18_50190) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(h0,plain,
cp2(i2003_11_14_17_18_50190) = true,
inference(hyper_resolution,[status(thm)],[hi21,hi27]) ).
cnf(c21,plain,
( cp1(sk1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi20,axiom,
ifeq(cUnsatisfiable(X0),true,cp1(sk1(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(h1,plain,
cp1(sk1(i2003_11_14_17_18_50190)) = true,
inference(hyper_resolution,[status(thm)],[hi20,hi27]) ).
cnf(c20,plain,
( rr(sk0(X0),sk1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi19,axiom,
ifeq(cUnsatisfiable(X0),true,rr(sk0(X0),sk1(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(h2,plain,
rr(sk0(i2003_11_14_17_18_50190),sk1(i2003_11_14_17_18_50190)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi27]) ).
cnf(c18,plain,
( rinvR(X0,sk0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi17,axiom,
ifeq(cUnsatisfiable(X0),true,rinvR(X0,sk0(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h3,plain,
rinvR(i2003_11_14_17_18_50190,sk0(i2003_11_14_17_18_50190)) = true,
inference(hyper_resolution,[status(thm)],[hi17,hi27]) ).
fof(f21,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
fof(f21_nnf,plain,
! [X,Y] :
( ( ~ rr(Y,X)
| rinvR(X,Y) )
& ( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X,Y] :
( ( ~ rr(Y,X)
| rinvR(X,Y) )
& ( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c36,plain,
( rr(X1,X0)
| ~ rinvR(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi25,axiom,
ifeq(rinvR(X0,X1),true,rr(X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c36]) ).
cnf(h10,plain,
rr(sk0(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190) = true,
inference(hyper_resolution,[status(thm)],[hi25,h3]) ).
cnf(c19,plain,
( X2 = X3
| ~ rr(sk0(X0),X3)
| ~ rr(sk0(X0),X2)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi18,axiom,
ifeq(cUnsatisfiable(X0),true,ifeq(rr(sk0(X0),X1),true,ifeq(rr(sk0(X0),X2),true,X1,X2),X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(h34,plain,
i2003_11_14_17_18_50190 = sk1(i2003_11_14_17_18_50190),
inference(hyper_resolution,[status(thm)],[hi18,hi27,h10,h2]) ).
fof(f3,axiom,
! [A,B] :
( ( cp1(A)
& A = B )
=> cp1(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1_substitution_1) ).
fof(f3_nnf,plain,
! [A,B] :
( cp1(B)
| ~ cp1(A)
| A != B ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( cp1(B)
| ~ cp1(A)
| A != B ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( cp1(X1)
| ~ cp1(X0)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi5,axiom,
ifeq(X0,X1,ifeq(cp1(X0),true,cp1(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h41,plain,
cp1(i2003_11_14_17_18_50190) = true,
inference(hyper_resolution,[status(thm)],[hi5,h34,h1]) ).
fof(f17,axiom,
! [X] :
( cp1(X)
=> ~ ( cp5(X)
| cp4(X)
| cp2(X)
| cp3(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f17_nnf,plain,
! [X] :
( ( ~ cp5(X)
& ~ cp4(X)
& ~ cp2(X)
& ~ cp3(X) )
| ~ cp1(X) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X] :
( ( ~ cp5(X)
& ~ cp4(X)
& ~ cp2(X)
& ~ cp3(X) )
| ~ cp1(X) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c27,plain,
( ~ cp2(X0)
| ~ cp1(X0) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi31,axiom,
ifeq(cp1(X0),true,ifeq(cp2(X0),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi31,h41,h0]) ).
cnf(t170,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f14,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
fof(f14_nnf,plain,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c15,plain,
~ cowlNothing(X0),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f15,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f15_nnf,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c16,plain,
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(c26,plain,
( ~ cp3(X0)
| ~ cp1(X0) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(c28,plain,
( ~ cp4(X0)
| ~ cp1(X0) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(c29,plain,
( ~ cp5(X0)
| ~ cp1(X0) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
fof(f18,axiom,
! [X] :
( cp2(X)
=> ~ ( cp5(X)
| cp4(X)
| cp3(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f18_nnf,plain,
! [X] :
( ( ~ cp5(X)
& ~ cp4(X)
& ~ cp3(X) )
| ~ cp2(X) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X] :
( ( ~ cp5(X)
& ~ cp4(X)
& ~ cp3(X) )
| ~ cp2(X) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c30,plain,
( ~ cp3(X0)
| ~ cp2(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(c31,plain,
( ~ cp4(X0)
| ~ cp2(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(c32,plain,
( ~ cp5(X0)
| ~ cp2(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f19,axiom,
! [X] :
( cp3(X)
=> ~ ( cp5(X)
| cp4(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f19_nnf,plain,
! [X] :
( ( ~ cp5(X)
& ~ cp4(X) )
| ~ cp3(X) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X] :
( ( ~ cp5(X)
& ~ cp4(X) )
| ~ cp3(X) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c33,plain,
( ~ cp4(X0)
| ~ cp3(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(c34,plain,
( ~ cp5(X0)
| ~ cp3(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
fof(f20,axiom,
! [X] :
( cp4(X)
=> ~ cp5(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f20_nnf,plain,
! [X] :
( ~ cp5(X)
| ~ cp4(X) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X] :
( ~ cp5(X)
| ~ cp4(X) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c35,plain,
( ~ cp5(X0)
| ~ cp4(X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c15,c16,c26,c27,c28,c29,c30,c31,c32,c33,c34,c35]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t170]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS072+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 19:19:38 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.89/1.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.89/1.32 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------