%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG210+2 : TPTP v9.3.1. Released v3.1.0.
% 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 06:49:47 AM UTC 2026
% Result : Theorem 0.15s 10.61s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 3
% Syntax : Number of formulae : 50 ( 37 unt; 0 def)
% Number of atoms : 86 ( 57 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 75 ( 39 ~; 16 |; 17 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 18 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
! [A,B,C] : times(times(A,B),C) = times(B,times(C,A)),
file('theBenchmark.p',axiom_1) ).
fof(axiom_2,axiom,
! [B] :
( element(B)
<=> ? [C] :
( times(B,B) = C
& times(B,C) = B ) ),
file('theBenchmark.p',axiom_2) ).
fof(conjecture_1,conjecture,
! [A,B,C] :
( ( C = times(A,B)
& element(B)
& element(A) )
=> element(C) ),
file('theBenchmark.p',conjecture_1) ).
fof(conjecture_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( C = times(A,B)
& element(B)
& element(A) )
=> element(C) ),
inference(assume_negation,[status(cth)],[conjecture_1]) ).
cnf(c_4,plain,
times(times(A,B),C) = times(B,times(C,A)),
inference(clausify,[status(thm)],[axiom_1]) ).
fof(nnf_2,plain,
! [B] :
( ( ! [C] :
( times(B,B) != C
| times(B,C) != B )
| element(B) )
& ( ? [X0] :
( times(B,B) = X0
& times(B,X0) = B )
| ~ element(B) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [B] :
( ( ! [C] :
( times(B,B) != C
| times(B,C) != B )
| element(B) )
& ( ( times(B,B) = sK0(B)
& times(B,sK0(B)) = B )
| ~ element(B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(B))],[nnf_2]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( times(VAR_0,VAR_0) != VAR_1
| times(VAR_0,VAR_1) != VAR_0
| element(VAR_0) )
& ! [VAR_0] :
( times(VAR_0,VAR_0) = sK0(VAR_0)
| ~ element(VAR_0) )
& ! [VAR_0] :
( times(VAR_0,sK0(VAR_0)) = VAR_0
| ~ element(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_5,plain,
( times(A,sK0(A)) = A
| ~ element(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_6,plain,
( times(A,A) = sK0(A)
| ~ element(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_7,plain,
( sK0(A) = times(A,A)
| ~ element(A) ),
inference(copy,[status(thm)],[c_6]) ).
cnf(c_8,plain,
( times(A,A) != B
| times(A,B) != A
| element(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
fof(nnf_3,plain,
? [A,B,C] :
( ~ element(C)
& times(A,B) = C
& element(B)
& element(A) ),
inference(fof_nnf,[status(thm)],[conjecture_1_neg]) ).
fof(sk_conjecture_1_neg,plain,
( ~ element(sK3)
& times(sK1,sK2) = sK3
& element(sK2)
& element(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK3)],[nnf_3]) ).
cnf(c_9,negated_conjecture,
element(sK1),
inference(split_conjunct,[status(thm)],[sk_conjecture_1_neg]) ).
cnf(c_10,negated_conjecture,
element(sK2),
inference(split_conjunct,[status(thm)],[sk_conjecture_1_neg]) ).
cnf(c_11,negated_conjecture,
times(sK1,sK2) = sK3,
inference(split_conjunct,[status(thm)],[sk_conjecture_1_neg]) ).
cnf(c_12,negated_conjecture,
sK3 = times(sK1,sK2),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_13,negated_conjecture,
~ element(sK3),
inference(split_conjunct,[status(thm)],[sk_conjecture_1_neg]) ).
cnf(c_14,negated_conjecture,
~ element(times(sK1,sK2)),
inference(paramod,[status(thm)],[c_12,c_13]) ).
cnf(c_15,plain,
times(times(A,times(B,C)),D) = times(B,times(D,times(C,A))),
inference(paramod,[status(thm)],[c_4,c_4]) ).
cnf(c_23,negated_conjecture,
sK0(sK1) = times(sK1,sK1),
inference(resolve,[status(thm)],[c_7,c_9]) ).
cnf(c_74,negated_conjecture,
times(sK1,sK0(sK1)) = sK1,
inference(resolve,[status(thm)],[c_5,c_9]) ).
cnf(c_24,negated_conjecture,
times(sK1,times(sK1,sK1)) = sK1,
inference(paramod,[status(thm)],[c_23,c_74]) ).
cnf(c_25,negated_conjecture,
sK0(sK2) = times(sK2,sK2),
inference(resolve,[status(thm)],[c_7,c_10]) ).
cnf(c_75,negated_conjecture,
times(sK2,sK0(sK2)) = sK2,
inference(resolve,[status(thm)],[c_5,c_10]) ).
cnf(c_26,negated_conjecture,
times(sK2,times(sK2,sK2)) = sK2,
inference(paramod,[status(thm)],[c_25,c_75]) ).
cnf(c_76,negated_conjecture,
( times(times(sK1,sK2),times(sK1,sK2)) != A
| times(times(sK1,sK2),A) != times(sK1,sK2) ),
inference(resolve,[status(thm)],[c_8,c_14]) ).
cnf(c_77,negated_conjecture,
times(times(sK1,sK2),times(sK2,times(times(sK1,sK2),sK1))) != times(sK1,sK2),
inference(resolve,[status(thm)],[c_76,c_4]) ).
cnf(c_27,negated_conjecture,
times(times(sK1,sK2),times(sK2,times(sK2,times(sK1,sK1)))) != times(sK1,sK2),
inference(paramod,[status(thm)],[c_4,c_77]) ).
cnf(c_78,plain,
times(times(sK1,sK2),times(times(times(sK1,sK1),sK2),sK2)) != times(sK1,sK2),
inference(paramod,[status(thm)],[c_4,c_27]) ).
cnf(c_79,plain,
times(times(sK1,sK2),times(times(sK1,times(sK2,sK1)),sK2)) != times(sK1,sK2),
inference(paramod,[status(thm)],[c_4,c_78]) ).
cnf(c_80,plain,
times(times(sK1,sK2),times(times(sK2,sK1),times(sK2,sK1))) != times(sK1,sK2),
inference(paramod,[status(thm)],[c_4,c_79]) ).
cnf(c_81,plain,
times(times(sK1,sK2),times(sK1,times(times(sK2,sK1),sK2))) != times(sK1,sK2),
inference(paramod,[status(thm)],[c_4,c_80]) ).
cnf(c_56,plain,
times(times(sK1,sK2),times(sK1,times(sK1,times(sK2,sK2)))) != times(sK1,sK2),
inference(paramod,[status(thm)],[c_4,c_81]) ).
cnf(c_82,plain,
times(times(times(sK1,times(sK2,sK2)),times(sK1,sK2)),sK1) != times(sK1,sK2),
inference(paramod,[status(thm)],[c_4,c_56]) ).
cnf(c_83,plain,
times(times(times(sK2,sK2),times(times(sK1,sK2),sK1)),sK1) != times(sK1,sK2),
inference(paramod,[status(thm)],[c_4,c_82]) ).
cnf(c_84,plain,
times(times(times(sK2,sK2),times(sK2,times(sK1,sK1))),sK1) != times(sK1,sK2),
inference(paramod,[status(thm)],[c_4,c_83]) ).
cnf(c_85,plain,
times(times(sK2,times(sK1,sK1)),times(sK1,times(sK2,sK2))) != times(sK1,sK2),
inference(paramod,[status(thm)],[c_4,c_84]) ).
cnf(c_86,plain,
times(times(sK1,sK1),times(times(sK1,times(sK2,sK2)),sK2)) != times(sK1,sK2),
inference(paramod,[status(thm)],[c_4,c_85]) ).
cnf(c_87,plain,
times(times(sK1,sK1),times(times(sK2,sK2),times(sK2,sK1))) != times(sK1,sK2),
inference(paramod,[status(thm)],[c_4,c_86]) ).
cnf(c_88,plain,
times(times(sK1,sK1),times(sK2,times(times(sK2,sK1),sK2))) != times(sK1,sK2),
inference(paramod,[status(thm)],[c_4,c_87]) ).
cnf(c_62,plain,
times(times(sK1,sK1),times(sK2,times(sK1,times(sK2,sK2)))) != times(sK1,sK2),
inference(paramod,[status(thm)],[c_4,c_88]) ).
cnf(c_89,plain,
times(sK1,A) = times(times(sK1,sK1),times(A,sK1)),
inference(paramod,[status(thm)],[c_24,c_4]) ).
cnf(c_64,plain,
times(times(sK1,sK1),times(A,sK1)) = times(sK1,A),
inference(copy,[status(thm)],[c_89]) ).
cnf(c_90,plain,
times(sK2,A) = times(sK2,times(A,times(sK2,sK2))),
inference(paramod,[status(thm)],[c_26,c_15]) ).
cnf(c_71,plain,
times(sK2,times(A,times(sK2,sK2))) = times(sK2,A),
inference(copy,[status(thm)],[c_90]) ).
cnf(c_91,plain,
times(times(sK1,sK1),times(sK2,sK1)) != times(sK1,sK2),
inference(paramod,[status(thm)],[c_71,c_62]) ).
cnf(c_92,plain,
times(sK1,sK2) != times(sK1,sK2),
inference(paramod,[status(thm)],[c_64,c_91]) ).
cnf(c_73,plain,
$false,
inference(copy,[status(thm)],[c_92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG210+2 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.59 % Computer : n013.cluster.edu
% 0.10/10.59 % Model : x86_64 x86_64
% 0.10/10.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.59 % Memory : 8046.5625MB
% 0.10/10.59 % OS : Linux 6.8.0-71-generic
% 0.10/10.60 % CPULimit : 300
% 0.10/10.60 % WCLimit : 300
% 0.10/10.60 % DateTime : Sat Sep 26 21:25:34 UTC 2026
% 0.15/10.60 % CPUTime :
% 0.15/10.60 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/10.60 % Process 3587437 was started by sandbox2 on n013,
% 0.15/10.60 % Sat Sep 26 21:25:34 2026
% 0.15/10.60 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/10.60
% 0.15/10.60 % From the command line: assign(max_seconds, 300).
% 0.15/10.61
% 0.15/10.61 % SZS status Theorem for theBenchmark
% 0.15/10.61
% 0.15/10.61 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/10.61 % Length of proof is 25.
% 0.15/10.61 % Level of proof is 7.
% 0.15/10.61 % Maximum clause weight is 15.000.
% 0.15/10.61 % Given clauses 17.
% 0.15/10.61
% 0.15/10.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------