%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP658+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 07:31:05 AM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 33 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 3 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 0 con; 1-2 aty)
% Number of variables : 84 ( 0 sgn 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [B,A] : mult(A,ld(A,B)) = B,
file('theBenchmark.p',f01) ).
fof(f02,axiom,
! [B,A] : ld(A,mult(A,B)) = B,
file('theBenchmark.p',f02) ).
fof(f03,axiom,
! [B,A] : mult(rd(A,B),B) = A,
file('theBenchmark.p',f03) ).
fof(f04,axiom,
! [B,A] : rd(mult(A,B),B) = A,
file('theBenchmark.p',f04) ).
fof(f05,axiom,
! [C,B,A] : mult(mult(A,mult(B,B)),C) = mult(mult(A,B),mult(B,C)),
file('theBenchmark.p',f05) ).
fof(goals,conjecture,
? [X0] :
! [X1] :
( mult(X0,X1) = X1
& mult(X1,X0) = X1 ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ? [X0] :
! [X1] :
( mult(X0,X1) = X1
& mult(X1,X0) = X1 ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_7,plain,
mult(A,ld(A,B)) = B,
inference(clausify,[status(thm)],[f01]) ).
cnf(c_8,plain,
ld(A,mult(A,B)) = B,
inference(clausify,[status(thm)],[f02]) ).
cnf(c_9,plain,
mult(rd(A,B),B) = A,
inference(clausify,[status(thm)],[f03]) ).
cnf(c_10,plain,
rd(mult(A,B),B) = A,
inference(clausify,[status(thm)],[f04]) ).
cnf(c_11,plain,
mult(mult(A,mult(B,B)),C) = mult(mult(A,B),mult(B,C)),
inference(clausify,[status(thm)],[f05]) ).
fof(nnf_6,plain,
! [X0] :
? [X1] :
( mult(X0,X1) != X1
| mult(X1,X0) != X1 ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
! [X0] :
( mult(X0,sK0(X0)) != sK0(X0)
| mult(sK0(X0),X0) != sK0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[nnf_6]) ).
cnf(c_12,negated_conjecture,
( mult(A,sK0(A)) != sK0(A)
| mult(sK0(A),A) != sK0(A) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_13,plain,
ld(rd(A,B),A) = B,
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_14,plain,
rd(A,ld(B,A)) = B,
inference(paramod,[status(thm)],[c_7,c_10]) ).
cnf(c_15,plain,
mult(mult(A,B),mult(B,ld(mult(A,mult(B,B)),C))) = C,
inference(paramod,[status(thm)],[c_11,c_7]) ).
cnf(c_91,plain,
ld(mult(A,B),C) = mult(B,ld(mult(A,mult(B,B)),C)),
inference(paramod,[status(thm)],[c_15,c_8]) ).
cnf(c_21,plain,
mult(A,ld(mult(B,mult(A,A)),C)) = ld(mult(B,A),C),
inference(copy,[status(thm)],[c_91]) ).
cnf(c_92,plain,
mult(A,ld(B,C)) = ld(mult(rd(B,mult(A,A)),A),C),
inference(paramod,[status(thm)],[c_9,c_21]) ).
cnf(c_24,plain,
ld(mult(rd(A,mult(B,B)),B),C) = mult(B,ld(A,C)),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_27,plain,
rd(A,mult(B,ld(C,A))) = mult(rd(C,mult(B,B)),B),
inference(paramod,[status(thm)],[c_24,c_14]) ).
cnf(c_28,plain,
rd(A,A) = mult(rd(B,mult(B,B)),B),
inference(paramod,[status(thm)],[c_7,c_27]) ).
cnf(c_93,plain,
rd(A,mult(B,C)) = mult(rd(rd(A,C),mult(B,B)),B),
inference(paramod,[status(thm)],[c_13,c_27]) ).
cnf(c_36,plain,
mult(rd(rd(A,B),mult(C,C)),C) = rd(A,mult(C,B)),
inference(copy,[status(thm)],[c_93]) ).
cnf(c_43,plain,
ld(rd(A,mult(A,A)),rd(B,B)) = A,
inference(paramod,[status(thm)],[c_28,c_8]) ).
cnf(c_94,plain,
ld(rd(A,A),B) = mult(C,ld(C,B)),
inference(paramod,[status(thm)],[c_28,c_24]) ).
cnf(c_51,plain,
ld(rd(A,A),B) = B,
inference(paramod,[status(thm)],[c_7,c_94]) ).
cnf(c_95,plain,
rd(A,mult(B,ld(B,A))) = rd(C,C),
inference(paramod,[status(thm)],[c_28,c_27]) ).
cnf(c_53,plain,
rd(A,A) = rd(B,B),
inference(paramod,[status(thm)],[c_7,c_95]) ).
cnf(c_55,plain,
mult(rd(A,A),B) = B,
inference(paramod,[status(thm)],[c_53,c_9]) ).
cnf(c_96,plain,
ld(mult(rd(rd(A,A),mult(B,B)),B),C) = mult(B,C),
inference(paramod,[status(thm)],[c_51,c_24]) ).
cnf(c_57,plain,
ld(rd(A,mult(B,A)),C) = mult(B,C),
inference(paramod,[status(thm)],[c_36,c_96]) ).
cnf(c_59,plain,
mult(A,rd(B,B)) = A,
inference(paramod,[status(thm)],[c_57,c_43]) ).
cnf(c_97,negated_conjecture,
mult(sK0(rd(A,A)),rd(A,A)) != sK0(rd(A,A)),
inference(resolve,[status(thm)],[c_12,c_55]) ).
cnf(c_98,negated_conjecture,
sK0(rd(A,A)) != sK0(rd(A,A)),
inference(paramod,[status(thm)],[c_59,c_97]) ).
cnf(c_90,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP658+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n011.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 : Fri Sep 25 15:31:59 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 2359779 was started by sandbox2 on n011,
% 0.10/0.38 % Fri Sep 25 15:31:59 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Theorem for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 27.
% 0.10/0.39 % Level of proof is 10.
% 0.10/0.39 % Maximum clause weight is 60.000.
% 0.10/0.39 % Given clauses 19.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------