%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO082+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Sun Sep 27 07:17:00 AM UTC 2026
% Result : Theorem 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 7 unt; 0 def)
% Number of atoms : 71 ( 20 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 60 ( 17 ~; 28 |; 9 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 18 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(part_of_defn,axiom,
! [C,C1] :
( part_of(C1,C)
<=> ! [P] :
( incident_c(P,C1)
=> incident_c(P,C) ) ),
file('theBenchmark.p',part_of_defn) ).
fof(c9,axiom,
! [C,C1] :
( ! [P] :
( incident_c(P,C)
<=> incident_c(P,C1) )
=> C = C1 ),
file('theBenchmark.p',c9) ).
fof(part_of_antisymmetry,conjecture,
! [C1,C2] :
( ( part_of(C2,C1)
& part_of(C1,C2) )
=> C1 = C2 ),
file('theBenchmark.p',part_of_antisymmetry) ).
fof(part_of_antisymmetry_neg,negated_conjecture,
~ ! [C1,C2] :
( ( part_of(C2,C1)
& part_of(C1,C2) )
=> C1 = C2 ),
inference(assume_negation,[status(cth)],[part_of_antisymmetry]) ).
fof(nnf_17,plain,
? [C1,C2] :
( C2 != C1
& part_of(C2,C1)
& part_of(C1,C2) ),
inference(fof_nnf,[status(thm)],[part_of_antisymmetry_neg]) ).
fof(sk_part_of_antisymmetry_neg,plain,
( sK0 != sK1
& part_of(sK0,sK1)
& part_of(sK1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(C1,sK1),skolemize(C2,sK0)],[nnf_17]) ).
cnf(c_38,negated_conjecture,
sK0 != sK1,
inference(split_conjunct,[status(thm)],[sk_part_of_antisymmetry_neg]) ).
cnf(c_39,negated_conjecture,
part_of(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_part_of_antisymmetry_neg]) ).
cnf(c_40,negated_conjecture,
part_of(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_part_of_antisymmetry_neg]) ).
fof(nnf_16,plain,
! [C,C1] :
( C = C1
| ? [P] :
( ( ~ incident_c(P,C1)
| ~ incident_c(P,C) )
& ( incident_c(P,C1)
| incident_c(P,C) ) ) ),
inference(fof_nnf,[status(thm)],[c9]) ).
fof(sk_c9_sk,plain,
! [C,C1] :
( C = C1
| ( ( ~ incident_c(sK2(C,C1),C1)
| ~ incident_c(sK2(C,C1),C) )
& ( incident_c(sK2(C,C1),C1)
| incident_c(sK2(C,C1),C) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(P,sK2(C,C1))],[nnf_16]) ).
fof(sk_c9,plain,
( ! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ incident_c(sK2(VAR_0,VAR_1),VAR_1)
| ~ incident_c(sK2(VAR_0,VAR_1),VAR_0) )
& ! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| incident_c(sK2(VAR_0,VAR_1),VAR_1)
| incident_c(sK2(VAR_0,VAR_1),VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_c9_sk]) ).
cnf(c_41,plain,
( A = B
| ~ incident_c(sK2(A,B),B)
| ~ incident_c(sK2(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_c9]) ).
cnf(c_42,plain,
( A = B
| incident_c(sK2(A,B),B)
| incident_c(sK2(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_c9]) ).
cnf(c_72,plain,
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
inference(clausify,[status(thm)],[part_of_defn]) ).
cnf(c_389,plain,
( incident_c(A,sK0)
| ~ incident_c(A,sK1) ),
inference(resolve,[status(thm)],[c_72,c_40]) ).
cnf(c_390,plain,
( incident_c(A,sK1)
| ~ incident_c(A,sK0) ),
inference(resolve,[status(thm)],[c_72,c_39]) ).
cnf(c_819,plain,
( A = sK1
| incident_c(sK2(A,sK1),A)
| incident_c(sK2(A,sK1),sK0) ),
inference(resolve,[status(thm)],[c_389,c_42]) ).
cnf(c_482,plain,
( sK1 = A
| incident_c(sK2(A,sK1),A)
| incident_c(sK2(A,sK1),sK0) ),
inference(copy,[status(thm)],[c_819]) ).
cnf(c_820,plain,
( sK1 = sK0
| incident_c(sK2(sK0,sK1),sK0) ),
inference(factor,[status(thm)],[c_482]) ).
cnf(c_821,plain,
( sK0 = sK1
| incident_c(sK2(sK0,sK1),sK0) ),
inference(copy,[status(thm)],[c_820]) ).
cnf(c_495,negated_conjecture,
incident_c(sK2(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_38,c_821]) ).
cnf(c_505,plain,
( sK0 = A
| incident_c(sK2(sK0,A),A)
| incident_c(sK2(sK0,A),sK1) ),
inference(resolve,[status(thm)],[c_390,c_42]) ).
cnf(c_822,plain,
( sK0 = sK1
| incident_c(sK2(sK0,sK1),sK1) ),
inference(factor,[status(thm)],[c_505]) ).
cnf(c_518,negated_conjecture,
incident_c(sK2(sK0,sK1),sK1),
inference(resolve,[status(thm)],[c_38,c_822]) ).
cnf(c_823,plain,
( sK0 = sK1
| ~ incident_c(sK2(sK0,sK1),sK1) ),
inference(resolve,[status(thm)],[c_495,c_41]) ).
cnf(c_824,plain,
sK0 = sK1,
inference(resolve,[status(thm)],[c_518,c_823]) ).
cnf(c_818,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_38,c_824]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO082+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n007.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 12:38:38 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.35 % Process 1013256 was started by sandbox2 on n007,
% 0.10/0.35 % Fri Sep 25 12:38:38 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 0.14/0.44
% 0.14/0.44 % SZS status Theorem for theBenchmark
% 0.14/0.44
% 0.14/0.44 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.14/0.44 % Length of proof is 16.
% 0.14/0.44 % Level of proof is 5.
% 0.14/0.44 % Maximum clause weight is 23.000.
% 0.14/0.44 % Given clauses 94.
% 0.14/0.44
% 0.14/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------