%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS131+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 : Sun Sep 27 07:46:06 AM UTC 2026
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 79 ( 6 unt; 0 def)
% Number of atoms : 339 ( 0 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 443 ( 183 ~; 223 |; 27 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 59 ( 6 sgn 31 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_0,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('theBenchmark.p',axiom_0) ).
fof(axiom_1,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ),
file('theBenchmark.p',axiom_1) ).
fof(axiom_2,axiom,
! [X] :
( cA(X)
<=> ? [Y] :
( cowlThing(Y)
& rq(X,Y) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cNothing(X)
=> ~ ? [Y] : rp(X,Y) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( cNothing(X)
=> ? [Y0] : rp(X,Y0) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X] :
( cnotA(X)
<=> ! [Y] :
( rq(X,Y)
=> cNothing(Y) ) ),
file('theBenchmark.p',axiom_5) ).
fof(the_axiom,conjecture,
( ! [X] :
( cnotA(X)
<=> ~ cA(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('theBenchmark.p',the_axiom) ).
fof(the_axiom_neg,negated_conjecture,
~ ( ! [X] :
( cnotA(X)
<=> ~ cA(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(assume_negation,[status(cth)],[the_axiom]) ).
fof(nnf_3,plain,
! [X] :
( ( ! [Y] :
( ~ cowlThing(Y)
| ~ rq(X,Y) )
| cA(X) )
& ( ? [X0] :
( cowlThing(X0)
& rq(X,X0) )
| ~ cA(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ! [Y] :
( ~ cowlThing(Y)
| ~ rq(X,Y) )
| cA(X) )
& ( ( cowlThing(sK4(X))
& rq(X,sK4(X)) )
| ~ cA(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4(X))],[nnf_3]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( ~ cowlThing(VAR_1)
| ~ rq(VAR_0,VAR_1)
| cA(VAR_0) )
& ! [VAR_0] :
( cowlThing(sK4(VAR_0))
| ~ cA(VAR_0) )
& ! [VAR_0] :
( rq(VAR_0,sK4(VAR_0))
| ~ cA(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_8,plain,
( ~ cowlThing(B)
| ~ rq(A,B)
| cA(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_10,plain,
cowlThing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
fof(nnf_7,plain,
( ? [X] :
( ( cA(X)
| ~ cnotA(X) )
& ( ~ cA(X)
| cnotA(X) ) )
| ? [X0] :
( ( xsd_integer(X0)
| ~ xsd_string(X0) )
& ( ~ xsd_integer(X0)
| xsd_string(X0) ) )
| ? [X1] :
( cowlNothing(X1)
| ~ cowlThing(X1) ) ),
inference(fof_nnf,[status(thm)],[the_axiom_neg]) ).
fof(sk_the_axiom_neg_sk,plain,
( ( ( cA(sK2)
| ~ cnotA(sK2) )
& ( ~ cA(sK2)
| cnotA(sK2) ) )
| ( ( xsd_integer(sK1)
| ~ xsd_string(sK1) )
& ( ~ xsd_integer(sK1)
| xsd_string(sK1) ) )
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X1,sK0),skolemize(X0,sK1),skolemize(X,sK2)],[nnf_7]) ).
fof(sk_the_axiom_neg,plain,
( ( cA(sK2)
| ~ cnotA(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ cA(sK2)
| cnotA(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( cA(sK2)
| ~ cnotA(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ cA(sK2)
| cnotA(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_the_axiom_neg_sk]) ).
cnf(c_11,negated_conjecture,
( ~ cA(sK2)
| cnotA(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_12,negated_conjecture,
( cA(sK2)
| ~ cnotA(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_13,negated_conjecture,
( ~ cA(sK2)
| cnotA(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_14,negated_conjecture,
( cA(sK2)
| ~ cnotA(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_15,plain,
~ cowlNothing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_16,negated_conjecture,
( ~ cA(sK2)
| cnotA(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_11,c_10]) ).
cnf(c_17,negated_conjecture,
( cA(sK2)
| ~ cnotA(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_12,c_10]) ).
cnf(c_18,negated_conjecture,
( ~ cA(sK2)
| cnotA(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_13,c_10]) ).
cnf(c_19,negated_conjecture,
( cA(sK2)
| ~ cnotA(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_14,c_10]) ).
cnf(c_20,negated_conjecture,
( cA(sK2)
| ~ cnotA(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_15,c_17]) ).
cnf(c_21,negated_conjecture,
( ~ cA(sK2)
| cnotA(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_15,c_18]) ).
cnf(c_22,negated_conjecture,
( cA(sK2)
| ~ cnotA(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_15,c_19]) ).
cnf(c_23,negated_conjecture,
( ~ cA(sK2)
| cnotA(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_15,c_16]) ).
cnf(c_24,plain,
( ~ xsd_integer(A)
| ~ xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_25,plain,
( xsd_integer(A)
| xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
fof(nnf_6,plain,
! [X] :
( ( ? [Y] :
( ~ cNothing(Y)
& rq(X,Y) )
| cnotA(X) )
& ( ! [X0] :
( cNothing(X0)
| ~ rq(X,X0) )
| ~ cnotA(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_5]) ).
fof(sk_axiom_5_sk,plain,
! [X] :
( ( ( ~ cNothing(sK3(X))
& rq(X,sK3(X)) )
| cnotA(X) )
& ( ! [X0] :
( cNothing(X0)
| ~ rq(X,X0) )
| ~ cnotA(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(Y,sK3(X))],[nnf_6]) ).
fof(sk_axiom_5,plain,
( ! [VAR_0] :
( ~ cNothing(sK3(VAR_0))
| cnotA(VAR_0) )
& ! [VAR_0] :
( rq(VAR_0,sK3(VAR_0))
| cnotA(VAR_0) )
& ! [VAR_0,VAR_1] :
( cNothing(VAR_1)
| ~ rq(VAR_0,VAR_1)
| ~ cnotA(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_5_sk]) ).
cnf(c_26,plain,
( rq(A,sK3(A))
| cnotA(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_5]) ).
cnf(c_28,plain,
( ~ rq(A,B)
| cA(A) ),
inference(resolve,[status(thm)],[c_8,c_10]) ).
cnf(c_29,plain,
( cNothing(B)
| ~ rq(A,B)
| ~ cnotA(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_5]) ).
cnf(c_30,plain,
( rq(A,sK4(A))
| ~ cA(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_31,plain,
( cA(A)
| cnotA(A) ),
inference(resolve,[status(thm)],[c_26,c_28]) ).
cnf(c_32,plain,
( cNothing(sK4(A))
| ~ cnotA(A)
| ~ cA(A) ),
inference(resolve,[status(thm)],[c_30,c_29]) ).
cnf(c_33,negated_conjecture,
( ~ cA(sK2)
| cnotA(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_24,c_23]) ).
cnf(c_34,negated_conjecture,
( cA(sK2)
| ~ cnotA(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_24,c_20]) ).
cnf(c_35,negated_conjecture,
( ~ cA(sK2)
| cnotA(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_25,c_21]) ).
cnf(c_36,negated_conjecture,
( cA(sK2)
| ~ cnotA(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_25,c_22]) ).
cnf(c_38,negated_conjecture,
( cNothing(sK4(sK2))
| ~ cnotA(sK2)
| ~ cnotA(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_34,c_32]) ).
cnf(c_39,negated_conjecture,
( cNothing(sK4(sK2))
| ~ cnotA(sK2)
| ~ cnotA(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_36,c_32]) ).
fof(nnf_5,plain,
! [X] :
( ? [Y0] : rp(X,Y0)
| ~ cNothing(X) ),
inference(fof_nnf,[status(thm)],[axiom_4]) ).
fof(sk_axiom_4,plain,
! [X] :
( rp(X,sK5(X))
| ~ cNothing(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(Y0,sK5(X))],[nnf_5]) ).
cnf(c_40,plain,
( rp(A,sK5(A))
| ~ cNothing(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
cnf(c_41,plain,
( ~ rp(A,B)
| ~ cNothing(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
cnf(c_42,negated_conjecture,
( ~ cnotA(sK2)
| ~ cnotA(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1)
| rp(sK4(sK2),sK5(sK4(sK2))) ),
inference(resolve,[status(thm)],[c_40,c_39]) ).
cnf(c_43,negated_conjecture,
( ~ cnotA(sK2)
| ~ cnotA(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1)
| ~ rp(sK4(sK2),A) ),
inference(resolve,[status(thm)],[c_41,c_38]) ).
cnf(c_44,negated_conjecture,
( ~ cnotA(sK2)
| ~ cnotA(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1)
| ~ rp(sK4(sK2),A) ),
inference(resolve,[status(thm)],[c_41,c_39]) ).
cnf(c_45,negated_conjecture,
( ~ cnotA(sK2)
| ~ cnotA(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1)
| rp(sK4(sK2),sK5(sK4(sK2))) ),
inference(resolve,[status(thm)],[c_40,c_38]) ).
cnf(c_46,negated_conjecture,
( ~ cnotA(sK2)
| ~ cnotA(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1)
| ~ cnotA(sK2)
| ~ cnotA(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_45,c_43]) ).
cnf(c_57,negated_conjecture,
( ~ cnotA(sK2)
| ~ cnotA(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1)
| ~ cnotA(sK2)
| ~ cnotA(sK2)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_58,negated_conjecture,
( ~ cnotA(sK2)
| ~ cnotA(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1)
| ~ cnotA(sK2)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_57]) ).
cnf(c_59,negated_conjecture,
( ~ cnotA(sK2)
| ~ cnotA(sK2)
| ~ xsd_integer(sK1)
| ~ cnotA(sK2)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_60,negated_conjecture,
( ~ cnotA(sK2)
| ~ cnotA(sK2)
| ~ cnotA(sK2)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_59]) ).
cnf(c_61,negated_conjecture,
( ~ cnotA(sK2)
| ~ cnotA(sK2)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_47,negated_conjecture,
( ~ cnotA(sK2)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_48,negated_conjecture,
( ~ cnotA(sK2)
| ~ cnotA(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1)
| ~ cnotA(sK2)
| ~ cnotA(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_42,c_44]) ).
cnf(c_62,negated_conjecture,
( ~ cnotA(sK2)
| ~ cnotA(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1)
| ~ cnotA(sK2)
| ~ cnotA(sK2)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_63,negated_conjecture,
( ~ cnotA(sK2)
| ~ cnotA(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1)
| ~ cnotA(sK2)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_62]) ).
cnf(c_64,negated_conjecture,
( ~ cnotA(sK2)
| ~ cnotA(sK2)
| xsd_integer(sK1)
| ~ cnotA(sK2)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_63]) ).
cnf(c_65,negated_conjecture,
( ~ cnotA(sK2)
| ~ cnotA(sK2)
| ~ cnotA(sK2)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_66,negated_conjecture,
( ~ cnotA(sK2)
| ~ cnotA(sK2)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_65]) ).
cnf(c_49,negated_conjecture,
( ~ cnotA(sK2)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_66]) ).
cnf(c_50,negated_conjecture,
( cnotA(sK2)
| cnotA(sK2)
| xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_35,c_31]) ).
cnf(c_67,negated_conjecture,
( cnotA(sK2)
| cnotA(sK2)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_50]) ).
cnf(c_51,negated_conjecture,
( cnotA(sK2)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_67]) ).
cnf(c_52,negated_conjecture,
( cnotA(sK2)
| cnotA(sK2)
| ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_33,c_31]) ).
cnf(c_68,negated_conjecture,
( cnotA(sK2)
| cnotA(sK2)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_52]) ).
cnf(c_53,negated_conjecture,
( cnotA(sK2)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_69,negated_conjecture,
( cnotA(sK2)
| cnotA(sK2) ),
inference(resolve,[status(thm)],[c_53,c_51]) ).
cnf(c_54,negated_conjecture,
cnotA(sK2),
inference(copy,[status(thm)],[c_69]) ).
cnf(c_55,negated_conjecture,
xsd_integer(sK1),
inference(resolve,[status(thm)],[c_54,c_49]) ).
cnf(c_70,negated_conjecture,
~ cnotA(sK2),
inference(resolve,[status(thm)],[c_55,c_47]) ).
cnf(c_56,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_54,c_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS131+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n012.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 19:40:21 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 2817388 was started by sandbox on n012,
% 0.07/0.35 % Fri Sep 25 19:40:21 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 0.12/0.36
% 0.12/0.36 % SZS status Theorem for theBenchmark
% 0.12/0.36
% 0.12/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.36 % Length of proof is 53.
% 0.12/0.36 % Level of proof is 10.
% 0.12/0.36 % Maximum clause weight is 4.000.
% 0.12/0.36 % Given clauses 4.
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
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