%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COM007+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 06:59:37 AM UTC 2026
% Result : Theorem 0.20s 0.50s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 20 unt; 0 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 80 ( 34 ~; 31 |; 8 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 55 ( 0 sgn 28 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(assumption,axiom,
( reflexive_rewrite(a,c)
& reflexive_rewrite(a,b) ),
file('theBenchmark.p',assumption) ).
fof(goal_ax,axiom,
! [A] :
( ( reflexive_rewrite(c,A)
& reflexive_rewrite(b,A) )
=> goal ),
file('theBenchmark.p',goal_ax) ).
fof(reflexivity,axiom,
! [A] : equalish(A,A),
file('theBenchmark.p',reflexivity) ).
fof(symmtery,axiom,
! [A,B] :
( equalish(A,B)
=> equalish(B,A) ),
file('theBenchmark.p',symmtery) ).
fof(substitution,axiom,
! [A,B,C] :
( ( reflexive_rewrite(B,C)
& equalish(A,B) )
=> reflexive_rewrite(A,C) ),
file('theBenchmark.p',substitution) ).
fof(equalish_in_reflexive_rewrite,axiom,
! [A,B] :
( equalish(A,B)
=> reflexive_rewrite(A,B) ),
file('theBenchmark.p',equalish_in_reflexive_rewrite) ).
fof(rewrite_in_reflexive_rewrite,axiom,
! [A,B] :
( rewrite(A,B)
=> reflexive_rewrite(A,B) ),
file('theBenchmark.p',rewrite_in_reflexive_rewrite) ).
fof(equalish_or_rewrite,axiom,
! [A,B] :
( reflexive_rewrite(A,B)
=> ( rewrite(A,B)
| equalish(A,B) ) ),
file('theBenchmark.p',equalish_or_rewrite) ).
fof(rewrite_diamond,axiom,
! [A,B,C] :
( ( rewrite(A,C)
& rewrite(A,B) )
=> ? [D] :
( rewrite(C,D)
& rewrite(B,D) ) ),
file('theBenchmark.p',rewrite_diamond) ).
fof(goal_to_be_proved,conjecture,
goal,
file('theBenchmark.p',goal_to_be_proved) ).
fof(goal_to_be_proved_neg,negated_conjecture,
~ goal,
inference(assume_negation,[status(cth)],[goal_to_be_proved]) ).
cnf(c_11,plain,
reflexive_rewrite(a,b),
inference(clausify,[status(thm)],[assumption]) ).
cnf(c_12,plain,
reflexive_rewrite(a,c),
inference(clausify,[status(thm)],[assumption]) ).
cnf(c_13,plain,
( goal
| ~ reflexive_rewrite(c,A)
| ~ reflexive_rewrite(b,A) ),
inference(clausify,[status(thm)],[goal_ax]) ).
cnf(c_14,plain,
equalish(A,A),
inference(clausify,[status(thm)],[reflexivity]) ).
cnf(c_15,plain,
( equalish(B,A)
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[symmtery]) ).
cnf(c_16,plain,
( reflexive_rewrite(A,C)
| ~ reflexive_rewrite(B,C)
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[substitution]) ).
cnf(c_17,plain,
( reflexive_rewrite(A,B)
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[equalish_in_reflexive_rewrite]) ).
cnf(c_18,plain,
( reflexive_rewrite(A,B)
| ~ rewrite(A,B) ),
inference(clausify,[status(thm)],[rewrite_in_reflexive_rewrite]) ).
cnf(c_19,plain,
( rewrite(A,B)
| equalish(A,B)
| ~ reflexive_rewrite(A,B) ),
inference(clausify,[status(thm)],[equalish_or_rewrite]) ).
fof(nnf_9,plain,
! [A,B,C] :
( ? [D] :
( rewrite(C,D)
& rewrite(B,D) )
| ~ rewrite(A,C)
| ~ rewrite(A,B) ),
inference(fof_nnf,[status(thm)],[rewrite_diamond]) ).
fof(sk_rewrite_diamond_sk,plain,
! [A,B,C] :
( ( rewrite(C,sK0(A,B,C))
& rewrite(B,sK0(A,B,C)) )
| ~ rewrite(A,C)
| ~ rewrite(A,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(D,sK0(A,B,C))],[nnf_9]) ).
fof(sk_rewrite_diamond,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( rewrite(VAR_2,sK0(VAR_0,VAR_1,VAR_2))
| ~ rewrite(VAR_0,VAR_2)
| ~ rewrite(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( rewrite(VAR_1,sK0(VAR_0,VAR_1,VAR_2))
| ~ rewrite(VAR_0,VAR_2)
| ~ rewrite(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_rewrite_diamond_sk]) ).
cnf(c_20,plain,
( rewrite(B,sK0(A,B,C))
| ~ rewrite(A,C)
| ~ rewrite(A,B) ),
inference(split_conjunct,[status(thm)],[sk_rewrite_diamond]) ).
cnf(c_21,plain,
( rewrite(C,sK0(A,B,C))
| ~ rewrite(A,C)
| ~ rewrite(A,B) ),
inference(split_conjunct,[status(thm)],[sk_rewrite_diamond]) ).
cnf(c_22,negated_conjecture,
~ goal,
inference(clausify,[status(thm)],[goal_to_be_proved_neg]) ).
cnf(c_24,negated_conjecture,
( ~ reflexive_rewrite(c,A)
| ~ reflexive_rewrite(b,A) ),
inference(resolve,[status(thm)],[c_22,c_13]) ).
cnf(c_25,plain,
( reflexive_rewrite(A,c)
| ~ equalish(A,a) ),
inference(resolve,[status(thm)],[c_16,c_12]) ).
cnf(c_26,plain,
( reflexive_rewrite(A,b)
| ~ equalish(A,a) ),
inference(resolve,[status(thm)],[c_16,c_11]) ).
cnf(c_27,plain,
reflexive_rewrite(A,A),
inference(resolve,[status(thm)],[c_17,c_14]) ).
cnf(c_28,plain,
( rewrite(a,c)
| equalish(a,c) ),
inference(resolve,[status(thm)],[c_19,c_12]) ).
cnf(c_29,plain,
( rewrite(a,b)
| equalish(a,b) ),
inference(resolve,[status(thm)],[c_19,c_11]) ).
cnf(c_30,plain,
~ reflexive_rewrite(b,c),
inference(resolve,[status(thm)],[c_27,c_24]) ).
cnf(c_31,plain,
~ reflexive_rewrite(c,b),
inference(resolve,[status(thm)],[c_27,c_24]) ).
cnf(c_33,plain,
( equalish(c,a)
| rewrite(a,c) ),
inference(resolve,[status(thm)],[c_28,c_15]) ).
cnf(c_35,plain,
( equalish(b,a)
| rewrite(a,b) ),
inference(resolve,[status(thm)],[c_29,c_15]) ).
cnf(c_36,plain,
~ equalish(b,a),
inference(resolve,[status(thm)],[c_25,c_30]) ).
cnf(c_39,plain,
rewrite(a,b),
inference(resolve,[status(thm)],[c_36,c_35]) ).
cnf(c_40,plain,
~ equalish(c,a),
inference(resolve,[status(thm)],[c_26,c_31]) ).
cnf(c_43,plain,
rewrite(a,c),
inference(resolve,[status(thm)],[c_40,c_33]) ).
cnf(c_47,plain,
( rewrite(b,sK0(a,A,b))
| ~ rewrite(a,A) ),
inference(resolve,[status(thm)],[c_39,c_21]) ).
cnf(c_49,plain,
( rewrite(A,sK0(a,A,b))
| ~ rewrite(a,A) ),
inference(resolve,[status(thm)],[c_39,c_20]) ).
cnf(c_72,plain,
rewrite(b,sK0(a,c,b)),
inference(resolve,[status(thm)],[c_47,c_43]) ).
cnf(c_78,plain,
reflexive_rewrite(b,sK0(a,c,b)),
inference(resolve,[status(thm)],[c_72,c_18]) ).
cnf(c_86,plain,
~ reflexive_rewrite(c,sK0(a,c,b)),
inference(resolve,[status(thm)],[c_78,c_24]) ).
cnf(c_96,plain,
rewrite(c,sK0(a,c,b)),
inference(resolve,[status(thm)],[c_49,c_43]) ).
cnf(c_99,plain,
~ rewrite(c,sK0(a,c,b)),
inference(resolve,[status(thm)],[c_18,c_86]) ).
cnf(c_98,plain,
$false,
inference(resolve,[status(thm)],[c_96,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COM007+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48 % Computer : n009.cluster.edu
% 0.20/0.48 % Model : x86_64 x86_64
% 0.20/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.48 % Memory : 8046.5625MB
% 0.20/0.48 % OS : Linux 6.8.0-71-generic
% 0.20/0.48 % CPULimit : 300
% 0.20/0.48 % WCLimit : 300
% 0.20/0.48 % DateTime : Sat Sep 26 23:20:00 UTC 2026
% 0.20/0.48 % CPUTime :
% 0.20/0.48 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.48 % Process 1406729 was started by sandbox2 on n009,
% 0.20/0.48 % Sat Sep 26 23:20:00 2026
% 0.20/0.48 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.49
% 0.20/0.49 % From the command line: assign(max_seconds, 300).
% 0.20/0.50
% 0.20/0.50 % SZS status Theorem for theBenchmark
% 0.20/0.50
% 0.20/0.50 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.20/0.50 % Length of proof is 43.
% 0.20/0.50 % Level of proof is 10.
% 0.20/0.50 % Maximum clause weight is 22.000.
% 0.20/0.50 % Given clauses 51.
% 0.20/0.50
% 0.20/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------