%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU444+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 08:46:23 AM UTC 2026
% Result : Theorem 0.03s 0.39s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 31 ( 22 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 14 ~; 7 |; 5 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 18 ( 0 sgn 9 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t51_relset_2,axiom,
! [A,B,C] :
( m2_relset_1(C,B,A)
=> ( k2_funct_5(C) = k10_relset_1(B,A,C,B)
& k1_funct_5(C) = k10_relset_1(A,B,k6_relset_1(B,A,C),A) ) ),
file('theBenchmark.p',t51_relset_2) ).
fof(t56_relset_2,conjecture,
! [A,B,C] :
( m2_relset_1(C,B,A)
=> ( k10_relset_1(A,B,k6_relset_1(B,A,C),k10_relset_1(B,A,C,B)) = k10_relset_1(A,B,k6_relset_1(B,A,C),k2_funct_5(C))
& k1_funct_5(C) = k10_relset_1(A,B,k6_relset_1(B,A,C),A) ) ),
file('theBenchmark.p',t56_relset_2) ).
fof(t56_relset_2_neg,negated_conjecture,
~ ! [A,B,C] :
( m2_relset_1(C,B,A)
=> ( k10_relset_1(A,B,k6_relset_1(B,A,C),k10_relset_1(B,A,C,B)) = k10_relset_1(A,B,k6_relset_1(B,A,C),k2_funct_5(C))
& k1_funct_5(C) = k10_relset_1(A,B,k6_relset_1(B,A,C),A) ) ),
inference(assume_negation,[status(cth)],[t56_relset_2]) ).
cnf(c_51,plain,
( k10_relset_1(C,B,k6_relset_1(B,C,A),C) = k1_funct_5(A)
| ~ m2_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[t51_relset_2]) ).
cnf(c_52,plain,
( k2_funct_5(A) = k10_relset_1(B,C,A,B)
| ~ m2_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[t51_relset_2]) ).
fof(nnf_45,plain,
? [A,B,C] :
( ( k10_relset_1(A,B,k6_relset_1(B,A,C),k2_funct_5(C)) != k10_relset_1(A,B,k6_relset_1(B,A,C),k10_relset_1(B,A,C,B))
| k10_relset_1(A,B,k6_relset_1(B,A,C),A) != k1_funct_5(C) )
& m2_relset_1(C,B,A) ),
inference(fof_nnf,[status(thm)],[t56_relset_2_neg]) ).
fof(sk_t56_relset_2_neg,plain,
( ( k10_relset_1(sK2,sK1,k6_relset_1(sK1,sK2,sK0),k2_funct_5(sK0)) != k10_relset_1(sK2,sK1,k6_relset_1(sK1,sK2,sK0),k10_relset_1(sK1,sK2,sK0,sK1))
| k10_relset_1(sK2,sK1,k6_relset_1(sK1,sK2,sK0),sK2) != k1_funct_5(sK0) )
& m2_relset_1(sK0,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK2),skolemize(B,sK1),skolemize(C,sK0)],[nnf_45]) ).
cnf(c_53,negated_conjecture,
m2_relset_1(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t56_relset_2_neg]) ).
cnf(c_60,negated_conjecture,
k10_relset_1(sK2,sK1,k6_relset_1(sK1,sK2,sK0),sK2) = k1_funct_5(sK0),
inference(resolve,[status(thm)],[c_53,c_51]) ).
cnf(c_61,negated_conjecture,
k2_funct_5(sK0) = k10_relset_1(sK1,sK2,sK0,sK1),
inference(resolve,[status(thm)],[c_53,c_52]) ).
cnf(c_62,negated_conjecture,
k10_relset_1(sK1,sK2,sK0,sK1) = k2_funct_5(sK0),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_77,negated_conjecture,
( k10_relset_1(sK2,sK1,k6_relset_1(sK1,sK2,sK0),k2_funct_5(sK0)) != k10_relset_1(sK2,sK1,k6_relset_1(sK1,sK2,sK0),k10_relset_1(sK1,sK2,sK0,sK1))
| k10_relset_1(sK2,sK1,k6_relset_1(sK1,sK2,sK0),sK2) != k1_funct_5(sK0) ),
inference(split_conjunct,[status(thm)],[sk_t56_relset_2_neg]) ).
cnf(c_79,negated_conjecture,
( k10_relset_1(sK2,sK1,k6_relset_1(sK1,sK2,sK0),k2_funct_5(sK0)) != k10_relset_1(sK2,sK1,k6_relset_1(sK1,sK2,sK0),k10_relset_1(sK1,sK2,sK0,sK1))
| k1_funct_5(sK0) != k1_funct_5(sK0) ),
inference(paramod,[status(thm)],[c_60,c_77]) ).
cnf(c_80,negated_conjecture,
( k10_relset_1(sK2,sK1,k6_relset_1(sK1,sK2,sK0),k2_funct_5(sK0)) != k10_relset_1(sK2,sK1,k6_relset_1(sK1,sK2,sK0),k2_funct_5(sK0))
| k1_funct_5(sK0) != k1_funct_5(sK0) ),
inference(paramod,[status(thm)],[c_62,c_79]) ).
cnf(c_81,negated_conjecture,
k10_relset_1(sK2,sK1,k6_relset_1(sK1,sK2,sK0),k2_funct_5(sK0)) != k10_relset_1(sK2,sK1,k6_relset_1(sK1,sK2,sK0),k2_funct_5(sK0)),
inference(copy,[status(thm)],[c_80]) ).
cnf(c_78,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU444+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 09:57:48 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.37 % Process 1291299 was started by sandbox on n020,
% 0.03/0.37 % Sat Sep 26 09:57:48 2026
% 0.03/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.38
% 0.03/0.38 % From the command line: assign(max_seconds, 300).
% 0.03/0.39
% 0.03/0.39 % SZS status Theorem for theBenchmark
% 0.03/0.39
% 0.03/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.03/0.39 % Length of proof is 10.
% 0.03/0.39 % Level of proof is 4.
% 0.03/0.39 % Maximum clause weight is 11.000.
% 0.03/0.39 % Given clauses 0.
% 0.03/0.39
% 0.03/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------