%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU047+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 08:44:57 AM UTC 2026
% Result : Theorem 0.15s 0.46s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 48 ( 23 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 47 ( 18 ~; 11 |; 10 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 12 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t129_relat_1,axiom,
! [A,B,C] :
( relation(C)
=> ( subset(A,B)
=> relation_rng_restriction(B,relation_rng_restriction(A,C)) = relation_rng_restriction(A,C) ) ),
file('theBenchmark.p',t129_relat_1) ).
fof(t130_relat_1,axiom,
! [A,B,C] :
( relation(C)
=> ( subset(A,B)
=> relation_rng_restriction(A,relation_rng_restriction(B,C)) = relation_rng_restriction(A,C) ) ),
file('theBenchmark.p',t130_relat_1) ).
fof(t97_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( subset(A,B)
=> ( relation_rng_restriction(A,relation_rng_restriction(B,C)) = relation_rng_restriction(A,C)
& relation_rng_restriction(B,relation_rng_restriction(A,C)) = relation_rng_restriction(A,C) ) ) ),
file('theBenchmark.p',t97_funct_1) ).
fof(t97_funct_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( subset(A,B)
=> ( relation_rng_restriction(A,relation_rng_restriction(B,C)) = relation_rng_restriction(A,C)
& relation_rng_restriction(B,relation_rng_restriction(A,C)) = relation_rng_restriction(A,C) ) ) ),
inference(assume_negation,[status(cth)],[t97_funct_1]) ).
cnf(c_36,plain,
( relation_rng_restriction(C,relation_rng_restriction(B,A)) = relation_rng_restriction(B,A)
| ~ subset(B,C)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t129_relat_1]) ).
cnf(c_37,plain,
( relation_rng_restriction(B,relation_rng_restriction(C,A)) = relation_rng_restriction(B,A)
| ~ subset(B,C)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t130_relat_1]) ).
fof(nnf_32,plain,
? [A,B,C] :
( ( relation_rng_restriction(A,relation_rng_restriction(B,C)) != relation_rng_restriction(A,C)
| relation_rng_restriction(B,relation_rng_restriction(A,C)) != relation_rng_restriction(A,C) )
& subset(A,B)
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[t97_funct_1_neg]) ).
fof(sk_t97_funct_1_neg,plain,
( ( relation_rng_restriction(sK0,relation_rng_restriction(sK1,sK2)) != relation_rng_restriction(sK0,sK2)
| relation_rng_restriction(sK1,relation_rng_restriction(sK0,sK2)) != relation_rng_restriction(sK0,sK2) )
& subset(sK0,sK1)
& function(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_32]) ).
cnf(c_38,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t97_funct_1_neg]) ).
cnf(c_40,negated_conjecture,
( relation_rng_restriction(sK1,relation_rng_restriction(sK0,A)) = relation_rng_restriction(sK0,A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_38,c_36]) ).
cnf(c_41,negated_conjecture,
( relation_rng_restriction(sK0,relation_rng_restriction(sK1,A)) = relation_rng_restriction(sK0,A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_38,c_37]) ).
cnf(c_46,negated_conjecture,
( relation_rng_restriction(sK0,relation_rng_restriction(sK1,sK2)) != relation_rng_restriction(sK0,sK2)
| relation_rng_restriction(sK1,relation_rng_restriction(sK0,sK2)) != relation_rng_restriction(sK0,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t97_funct_1_neg]) ).
cnf(c_48,negated_conjecture,
relation(sK2),
inference(split_conjunct,[status(thm)],[sk_t97_funct_1_neg]) ).
cnf(c_86,plain,
relation_rng_restriction(sK0,relation_rng_restriction(sK1,sK2)) = relation_rng_restriction(sK0,sK2),
inference(resolve,[status(thm)],[c_48,c_41]) ).
cnf(c_87,plain,
relation_rng_restriction(sK1,relation_rng_restriction(sK0,sK2)) = relation_rng_restriction(sK0,sK2),
inference(resolve,[status(thm)],[c_48,c_40]) ).
cnf(c_89,negated_conjecture,
( relation_rng_restriction(sK0,relation_rng_restriction(sK1,sK2)) != relation_rng_restriction(sK0,sK2)
| relation_rng_restriction(sK0,sK2) != relation_rng_restriction(sK0,sK2) ),
inference(paramod,[status(thm)],[c_87,c_46]) ).
cnf(c_90,negated_conjecture,
( relation_rng_restriction(sK0,sK2) != relation_rng_restriction(sK0,sK2)
| relation_rng_restriction(sK0,sK2) != relation_rng_restriction(sK0,sK2) ),
inference(paramod,[status(thm)],[c_86,c_89]) ).
cnf(c_91,negated_conjecture,
relation_rng_restriction(sK0,sK2) != relation_rng_restriction(sK0,sK2),
inference(copy,[status(thm)],[c_90]) ).
cnf(c_88,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU047+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n009.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 08:32:14 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 3851216 was started by sandbox2 on n009,
% 0.15/0.43 % Sat Sep 26 08:32:14 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.45
% 0.15/0.45 % From the command line: assign(max_seconds, 300).
% 0.15/0.46
% 0.15/0.46 % SZS status Theorem for theBenchmark
% 0.15/0.46
% 0.15/0.46 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/0.46 % Length of proof is 13.
% 0.15/0.46 % Level of proof is 4.
% 0.15/0.46 % Maximum clause weight is 18.000.
% 0.15/0.46 % Given clauses 10.
% 0.15/0.46
% 0.15/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------