%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU306+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 08:45:45 AM UTC 2026
% Result : Theorem 16.90s 3.17s
% Output : CNFRefutation 16.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 4 unt; 0 def)
% Number of atoms : 16 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 5 ~; 1 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 5 ( 0 sgn 3 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_pre_topc,axiom,
! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
file('theBenchmark.p',d3_pre_topc) ).
fof(t12_pre_topc,conjecture,
! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
file('theBenchmark.p',t12_pre_topc) ).
fof(t12_pre_topc_neg,negated_conjecture,
~ ! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
inference(assume_negation,[status(cth)],[t12_pre_topc]) ).
cnf(c_816,plain,
( cast_as_carrier_subset(A) = the_carrier(A)
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[d3_pre_topc]) ).
fof(nnf_472,plain,
? [A] :
( cast_as_carrier_subset(A) != the_carrier(A)
& one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[t12_pre_topc_neg]) ).
fof(sk_t12_pre_topc_neg,plain,
( cast_as_carrier_subset(sK0) != the_carrier(sK0)
& one_sorted_str(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_472]) ).
cnf(c_2822,negated_conjecture,
one_sorted_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t12_pre_topc_neg]) ).
cnf(c_2823,negated_conjecture,
cast_as_carrier_subset(sK0) != the_carrier(sK0),
inference(split_conjunct,[status(thm)],[sk_t12_pre_topc_neg]) ).
cnf(c_4949,negated_conjecture,
cast_as_carrier_subset(sK0) = the_carrier(sK0),
inference(resolve,[status(thm)],[c_816,c_2822]) ).
cnf(c_4948,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2823,c_4949]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU306+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n008.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 : Sat Sep 26 09:10:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3275214 was started by sandbox on n008,
% 0.10/0.37 % Sat Sep 26 09:10:24 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.39/0.66
% 0.39/0.66 % From the command line: assign(max_seconds, 300).
% 0.39/0.66
% 0.39/0.66 % SInE: 369 to sos, 104 to usable, of 473 axioms (tolerance 2.00, depth 0 fixpoint).
% 16.90/3.17
% 16.90/3.17 % SZS status Theorem for theBenchmark
% 16.90/3.17
% 16.90/3.17 % Proof 1 at 2.22 (+ 0.14) seconds.
% 16.90/3.17 % Length of proof is 6.
% 16.90/3.17 % Level of proof is 2.
% 16.90/3.17 % Maximum clause weight is 17.000.
% 16.90/3.17 % Given clauses 61.
% 16.90/3.17
% 16.90/3.17 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------