%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COM007+2 : 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 : n013.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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 11 unt; 0 def)
% Number of atoms : 95 ( 29 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 83 ( 28 ~; 43 |; 7 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 41 ( 0 sgn 22 !; 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(equal_in_reflexive_rewrite,axiom,
! [A,B] :
( A = B
=> reflexive_rewrite(A,B) ),
file('theBenchmark.p',equal_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(equal_or_rewrite,axiom,
! [A,B] :
( reflexive_rewrite(A,B)
=> ( rewrite(A,B)
| A = B ) ),
file('theBenchmark.p',equal_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_8,plain,
reflexive_rewrite(a,b),
inference(clausify,[status(thm)],[assumption]) ).
cnf(c_9,plain,
reflexive_rewrite(a,c),
inference(clausify,[status(thm)],[assumption]) ).
cnf(c_10,plain,
( goal
| ~ reflexive_rewrite(c,A)
| ~ reflexive_rewrite(b,A) ),
inference(clausify,[status(thm)],[goal_ax]) ).
cnf(c_11,plain,
( reflexive_rewrite(B,A)
| A != B ),
inference(clausify,[status(thm)],[equal_in_reflexive_rewrite]) ).
cnf(c_12,plain,
( reflexive_rewrite(A,B)
| ~ rewrite(A,B) ),
inference(clausify,[status(thm)],[rewrite_in_reflexive_rewrite]) ).
cnf(c_13,plain,
( rewrite(A,B)
| B = A
| ~ reflexive_rewrite(A,B) ),
inference(clausify,[status(thm)],[equal_or_rewrite]) ).
fof(nnf_6,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_6]) ).
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_14,plain,
( rewrite(B,sK0(A,B,C))
| ~ rewrite(A,C)
| ~ rewrite(A,B) ),
inference(split_conjunct,[status(thm)],[sk_rewrite_diamond]) ).
cnf(c_15,plain,
( rewrite(C,sK0(A,B,C))
| ~ rewrite(A,C)
| ~ rewrite(A,B) ),
inference(split_conjunct,[status(thm)],[sk_rewrite_diamond]) ).
cnf(c_16,negated_conjecture,
~ goal,
inference(clausify,[status(thm)],[goal_to_be_proved_neg]) ).
cnf(c_18,negated_conjecture,
( ~ reflexive_rewrite(c,A)
| ~ reflexive_rewrite(b,A) ),
inference(resolve,[status(thm)],[c_16,c_10]) ).
cnf(c_19,plain,
reflexive_rewrite(A,A),
inference(xxres,[status(thm)],[c_11]) ).
cnf(c_20,plain,
( rewrite(a,c)
| c = a ),
inference(resolve,[status(thm)],[c_13,c_9]) ).
cnf(c_21,plain,
( rewrite(a,b)
| b = a ),
inference(resolve,[status(thm)],[c_13,c_8]) ).
cnf(c_22,plain,
~ reflexive_rewrite(b,c),
inference(resolve,[status(thm)],[c_19,c_18]) ).
cnf(c_23,plain,
~ reflexive_rewrite(c,b),
inference(resolve,[status(thm)],[c_18,c_19]) ).
cnf(c_28,plain,
( rewrite(c,sK0(a,A,c))
| ~ rewrite(a,A)
| c = a ),
inference(resolve,[status(thm)],[c_20,c_15]) ).
cnf(c_30,plain,
( rewrite(A,sK0(a,A,c))
| ~ rewrite(a,A)
| c = a ),
inference(resolve,[status(thm)],[c_20,c_14]) ).
cnf(c_50,plain,
( b = a
| rewrite(c,sK0(a,b,c))
| c = a ),
inference(resolve,[status(thm)],[c_28,c_21]) ).
cnf(c_52,plain,
( b = a
| rewrite(b,sK0(a,b,c))
| c = a ),
inference(resolve,[status(thm)],[c_30,c_21]) ).
cnf(c_59,plain,
( reflexive_rewrite(c,sK0(a,b,c))
| b = a
| c = a ),
inference(resolve,[status(thm)],[c_50,c_12]) ).
cnf(c_71,plain,
( reflexive_rewrite(b,sK0(a,b,c))
| b = a
| c = a ),
inference(resolve,[status(thm)],[c_52,c_12]) ).
cnf(c_84,plain,
( ~ reflexive_rewrite(b,sK0(a,b,c))
| b = a
| c = a ),
inference(resolve,[status(thm)],[c_59,c_18]) ).
cnf(c_99,plain,
( b = a
| c = a
| b = a
| c = a ),
inference(resolve,[status(thm)],[c_84,c_71]) ).
cnf(c_100,plain,
( b = a
| b = a
| c = a ),
inference(copy,[status(thm)],[c_99]) ).
cnf(c_88,plain,
( b = a
| c = a ),
inference(copy,[status(thm)],[c_100]) ).
cnf(c_101,plain,
( ~ reflexive_rewrite(a,b)
| b = a ),
inference(paramod,[status(thm)],[c_88,c_23]) ).
cnf(c_92,plain,
b = a,
inference(resolve,[status(thm)],[c_8,c_101]) ).
cnf(c_102,plain,
~ reflexive_rewrite(a,c),
inference(paramod,[status(thm)],[c_92,c_22]) ).
cnf(c_98,plain,
$false,
inference(resolve,[status(thm)],[c_9,c_102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM007+2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 23:19:51 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 3808606 was started by sandbox2 on n013,
% 0.13/0.36 % Sat Sep 26 23:19:51 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 32.
% 0.13/0.38 % Level of proof is 9.
% 0.13/0.38 % Maximum clause weight is 12.000.
% 0.13/0.38 % Given clauses 43.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------