%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KRS118+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 : n007.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 01:53:05 PM UTC 2026
% Result : Unsatisfiable 8.26s 1.58s
% Output : Proof 8.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 92 ( 40 unt; 0 def)
% Number of atoms : 220 ( 43 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 213 ( 85 ~; 75 |; 41 &)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 125 ( 3 sgn 66 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ccxcomp(X)
& ? [Y] :
( cd(Y)
& rinvF(X,Y) )
& ! [Y] :
( rinvR(X,Y)
=> ca_Vx3(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f21_nnf,plain,
! [X] :
( ( ~ ccxcomp(X)
| ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| ? [Y] :
( ~ ca_Vx3(Y)
& rinvR(X,Y) )
| cUnsatisfiable(X) )
& ( ( ccxcomp(X)
& ? [Y] :
( cd(Y)
& rinvF(X,Y) )
& ! [Y] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X,Y] :
( ( ~ ccxcomp(X)
| ~ cd(Y)
| ~ rinvF(X,Y)
| ( ~ ca_Vx3(sk1(X))
& rinvR(X,sk1(X)) )
| cUnsatisfiable(X) )
& ( ( ccxcomp(X)
& cd(sk0(X))
& rinvF(X,sk0(X))
& ( ca_Vx3(Y)
| ~ rinvR(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f21_nnf]) ).
cnf(c24,plain,
( rinvF(X0,sk0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi23,axiom,
ifeq(cUnsatisfiable(X0),true,rinvF(X0,sk0(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
fof(f30,axiom,
cUnsatisfiable(i2003_11_14_17_21_4056),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
fof(f30_nnf,plain,
cUnsatisfiable(i2003_11_14_17_21_4056),
inference(nnf_transformation,[status(thm)],[f30]) ).
cnf(c46,plain,
cUnsatisfiable(i2003_11_14_17_21_4056),
inference(cnf_transformation,[status(esa)],[f30_nnf]) ).
cnf(hi44,axiom,
cUnsatisfiable(i2003_11_14_17_21_4056) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(h2,plain,
rinvF(i2003_11_14_17_21_4056,sk0(i2003_11_14_17_21_4056)) = true,
inference(hyper_resolution,[status(thm)],[hi23,hi44]) ).
fof(f27,axiom,
! [X,Y] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
fof(f27_nnf,plain,
! [X,Y] :
( ( ~ rf(Y,X)
| rinvF(X,Y) )
& ( rf(Y,X)
| ~ rinvF(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [X,Y] :
( ( ~ rf(Y,X)
| rinvF(X,Y) )
& ( rf(Y,X)
| ~ rinvF(X,Y) ) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c41,plain,
( rf(X1,X0)
| ~ rinvF(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(hi39,axiom,
ifeq(rinvF(X0,X1),true,rf(X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c41]) ).
cnf(h15,plain,
rf(sk0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) = true,
inference(hyper_resolution,[status(thm)],[hi39,h2]) ).
fof(f31,axiom,
! [X,Y] :
( rf(X,Y)
=> rr(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).
fof(f31_nnf,plain,
! [X,Y] :
( rr(X,Y)
| ~ rf(X,Y) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [X,Y] :
( rr(X,Y)
| ~ rf(X,Y) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c47,plain,
( rr(X0,X1)
| ~ rf(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(hi45,axiom,
ifeq(rf(X0,X1),true,rr(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c47]) ).
cnf(h54,plain,
rr(sk0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) = true,
inference(hyper_resolution,[status(thm)],[hi45,h15]) ).
fof(f28,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
fof(f28_nnf,plain,
! [X,Y] :
( ( ~ rr(Y,X)
| rinvR(X,Y) )
& ( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [X,Y] :
( ( ~ rr(Y,X)
| rinvR(X,Y) )
& ( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c44,plain,
( ~ rr(X1,X0)
| rinvR(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(hi42,axiom,
ifeq(rr(X0,X1),true,rinvR(X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
cnf(h75,plain,
rinvR(i2003_11_14_17_21_4056,sk0(i2003_11_14_17_21_4056)) = true,
inference(hyper_resolution,[status(thm)],[hi42,h54]) ).
cnf(c23,plain,
( ca_Vx3(X1)
| ~ rinvR(X0,X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi22,axiom,
ifeq(cUnsatisfiable(X0),true,ifeq(rinvR(X0,X1),true,ca_Vx3(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(h85,plain,
ca_Vx3(sk0(i2003_11_14_17_21_4056)) = true,
inference(hyper_resolution,[status(thm)],[hi22,hi44,h75]) ).
fof(f25,axiom,
! [X] :
( ca_Vx3(X)
<=> ? [Y] :
( cd(Y)
& rinvF(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f25_nnf,plain,
! [X] :
( ( ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| ca_Vx3(X) )
& ( ? [Y] :
( cd(Y)
& rinvF(X,Y) )
| ~ ca_Vx3(X) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [X,Y] :
( ( ~ cd(Y)
| ~ rinvF(X,Y)
| ca_Vx3(X) )
& ( ( cd(sk5(X))
& rinvF(X,sk5(X)) )
| ~ ca_Vx3(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f25_nnf]) ).
cnf(c38,plain,
( cd(sk5(X0))
| ~ ca_Vx3(X0) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(hi36,axiom,
ifeq(ca_Vx3(X0),true,cd(sk5(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(h90,plain,
cd(sk5(sk0(i2003_11_14_17_21_4056))) = true,
inference(hyper_resolution,[status(thm)],[hi36,h85]) ).
fof(f24,axiom,
! [X] :
( cd(X)
<=> ( cc(X)
& ? [Y] :
( ccxcomp(Y)
& rf(X,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f24_nnf,plain,
! [X] :
( ( ~ cc(X)
| ! [Y] :
( ~ ccxcomp(Y)
| ~ rf(X,Y) )
| cd(X) )
& ( ( cc(X)
& ? [Y] :
( ccxcomp(Y)
& rf(X,Y) ) )
| ~ cd(X) ) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [X,Y] :
( ( ~ cc(X)
| ~ ccxcomp(Y)
| ~ rf(X,Y)
| cd(X) )
& ( ( cc(X)
& ccxcomp(sk4(X))
& rf(X,sk4(X)) )
| ~ cd(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f24_nnf]) ).
cnf(c34,plain,
( ccxcomp(sk4(X0))
| ~ cd(X0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi32,axiom,
ifeq(cd(X0),true,ccxcomp(sk4(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c34]) ).
cnf(h100,plain,
ccxcomp(sk4(sk5(sk0(i2003_11_14_17_21_4056)))) = true,
inference(hyper_resolution,[status(thm)],[hi32,h90]) ).
cnf(c33,plain,
( rf(X0,sk4(X0))
| ~ cd(X0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi31,axiom,
ifeq(cd(X0),true,rf(X0,sk4(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c33]) ).
cnf(h101,plain,
rf(sk5(sk0(i2003_11_14_17_21_4056)),sk4(sk5(sk0(i2003_11_14_17_21_4056)))) = true,
inference(hyper_resolution,[status(thm)],[hi31,h90]) ).
cnf(c37,plain,
( rinvF(X0,sk5(X0))
| ~ ca_Vx3(X0) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(hi35,axiom,
ifeq(ca_Vx3(X0),true,rinvF(X0,sk5(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(h91,plain,
rinvF(sk0(i2003_11_14_17_21_4056),sk5(sk0(i2003_11_14_17_21_4056))) = true,
inference(hyper_resolution,[status(thm)],[hi35,h85]) ).
cnf(h423,plain,
rf(sk5(sk0(i2003_11_14_17_21_4056)),sk0(i2003_11_14_17_21_4056)) = true,
inference(hyper_resolution,[status(thm)],[hi39,h91]) ).
fof(f26,axiom,
! [X,Y,Z] :
( ( rf(X,Z)
& rf(X,Y) )
=> Y = Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
fof(f26_nnf,plain,
! [X,Y,Z] :
( Y = Z
| ~ rf(X,Z)
| ~ rf(X,Y) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [X,Y,Z] :
( Y = Z
| ~ rf(X,Z)
| ~ rf(X,Y) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c40,plain,
( X1 = X2
| ~ rf(X0,X2)
| ~ rf(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(hi38,axiom,
ifeq(rf(X0,X1),true,ifeq(rf(X0,X2),true,X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(h1316,plain,
sk0(i2003_11_14_17_21_4056) = sk4(sk5(sk0(i2003_11_14_17_21_4056))),
inference(hyper_resolution,[status(thm)],[hi38,h423,h101]) ).
fof(f3,axiom,
! [A,B] :
( ( ccxcomp(A)
& A = B )
=> ccxcomp(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ccxcomp_substitution_1) ).
fof(f3_nnf,plain,
! [A,B] :
( ccxcomp(B)
| ~ ccxcomp(A)
| A != B ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( ccxcomp(B)
| ~ ccxcomp(A)
| A != B ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( ccxcomp(X1)
| ~ ccxcomp(X0)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(X0,X1,ifeq(ccxcomp(X0),true,ccxcomp(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h1345,plain,
ccxcomp(sk0(i2003_11_14_17_21_4056)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h1316,h100]) ).
fof(f23,axiom,
! [X] :
( ccxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f23_nnf,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| ccxcomp(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ ccxcomp(X) ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [X,Y0] :
( ( ~ ra_Px1(X,Y0)
| ccxcomp(X) )
& ( ra_Px1(X,sk3(X))
| ~ ccxcomp(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f23_nnf]) ).
cnf(c31,plain,
( ra_Px1(X0,sk3(X0))
| ~ ccxcomp(X0) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(hi29,axiom,
ifeq(ccxcomp(X0),true,ra_Px1(X0,sk3(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(h1346,plain,
ra_Px1(sk0(i2003_11_14_17_21_4056),sk3(sk0(i2003_11_14_17_21_4056))) = true,
inference(hyper_resolution,[status(thm)],[hi29,h1345]) ).
cnf(c25,plain,
( cd(sk0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi24,axiom,
ifeq(cUnsatisfiable(X0),true,cd(sk0(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(h1,plain,
cd(sk0(i2003_11_14_17_21_4056)) = true,
inference(hyper_resolution,[status(thm)],[hi24,hi44]) ).
cnf(c35,plain,
( cc(X0)
| ~ cd(X0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi33,axiom,
ifeq(cd(X0),true,cc(X0),true) = true,
inference(equality_encoding,[status(esa)],[c35]) ).
cnf(h8,plain,
cc(sk0(i2003_11_14_17_21_4056)) = true,
inference(hyper_resolution,[status(thm)],[hi33,h1]) ).
fof(f22,axiom,
! [X] :
( cc(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f22_nnf,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| cc(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ cc(X) ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [X,Y] :
( ( ra_Px1(X,sk2(X))
| cc(X) )
& ( ~ ra_Px1(X,Y)
| ~ cc(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f22_nnf]) ).
cnf(c29,plain,
( ~ ra_Px1(X0,X1)
| ~ cc(X0) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi48,axiom,
ifeq(cc(X0),true,ifeq(ra_Px1(X0,X1),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi48,h8,h1346]) ).
cnf(t261,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f19,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
fof(f19_nnf,plain,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c20,plain,
~ cowlNothing(X0),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
fof(f20,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f20_nnf,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c21,plain,
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c20,c21,c29]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t261]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS118+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 19:24:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.26/1.58 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.26/1.58 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------