%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWX185+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 09:16:15 AM UTC 2026
% Result : Theorem 13.92s 7.28s
% Output : CNFRefutation 13.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 42 unt; 0 def)
% Number of atoms : 56 ( 55 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 4 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 74 ( 10 sgn 15 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_021,axiom,
! [X,X2] : proj12(x2(X,X2)) = X,
file('theBenchmark.p',axiom_021) ).
fof(axiom_024,axiom,
! [X,X2] : z(X,X2) != eX,
file('theBenchmark.p',axiom_024) ).
fof(axiom_026,axiom,
! [X,X2] : x2(X,X2) != eX,
file('theBenchmark.p',axiom_026) ).
fof(axiom_029,axiom,
! [X] :
( X != z(proj1(X),proj2(X))
=> ( X != x2(proj12(X),proj22(X))
=> assoc(X) = X ) ),
file('theBenchmark.p',axiom_029) ).
fof(axiom_032,axiom,
! [A2,B2] : assoc(x2(A2,B2)) = x2(assoc(A2),assoc(B2)),
file('theBenchmark.p',axiom_032) ).
fof(axiom_033,axiom,
! [Y] : append(nil,Y) = Y,
file('theBenchmark.p',axiom_033) ).
fof(axiom_034,axiom,
! [Y,Z,Xs] : append(cons(Z,Xs),Y) = cons(Z,append(Xs,Y)),
file('theBenchmark.p',axiom_034) ).
fof(axiom_038,axiom,
! [A3,B2] : lin(x2(A3,B2)) = append(lin(A3),append(cons(mul,nil),lin(B2))),
file('theBenchmark.p',axiom_038) ).
fof(goal_041,conjecture,
? [U,V] :
~ ( lin(U) = lin(V)
=> assoc(U) = assoc(V) ),
file('theBenchmark.p',goal_041) ).
fof(goal_041_neg,negated_conjecture,
~ ? [U,V] :
~ ( lin(U) = lin(V)
=> assoc(U) = assoc(V) ),
inference(assume_negation,[status(cth)],[goal_041]) ).
cnf(c_54,plain,
proj12(x2(A,B)) = A,
inference(clausify,[status(thm)],[axiom_021]) ).
cnf(c_57,plain,
z(A,B) != eX,
inference(clausify,[status(thm)],[axiom_024]) ).
cnf(c_59,plain,
x2(A,B) != eX,
inference(clausify,[status(thm)],[axiom_026]) ).
cnf(c_63,plain,
( assoc(A) = A
| x2(proj12(A),proj22(A)) = A
| z(proj1(A),proj2(A)) = A ),
inference(clausify,[status(thm)],[axiom_029]) ).
cnf(c_67,plain,
assoc(x2(A,B)) = x2(assoc(A),assoc(B)),
inference(clausify,[status(thm)],[axiom_032]) ).
cnf(c_68,plain,
x2(assoc(A),assoc(B)) = assoc(x2(A,B)),
inference(copy,[status(thm)],[c_67]) ).
cnf(c_69,plain,
append(nil,A) = A,
inference(clausify,[status(thm)],[axiom_033]) ).
cnf(c_70,plain,
append(cons(A,B),C) = cons(A,append(B,C)),
inference(clausify,[status(thm)],[axiom_034]) ).
cnf(c_77,plain,
lin(x2(A,B)) = append(lin(A),append(cons(mul,nil),lin(B))),
inference(clausify,[status(thm)],[axiom_038]) ).
cnf(c_5581,plain,
lin(x2(A,B)) = append(lin(A),cons(mul,append(nil,lin(B)))),
inference(paramod,[status(thm)],[c_70,c_77]) ).
cnf(c_5582,plain,
lin(x2(A,B)) = append(lin(A),cons(mul,lin(B))),
inference(paramod,[status(thm)],[c_69,c_5581]) ).
cnf(c_78,plain,
append(lin(A),cons(mul,lin(B))) = lin(x2(A,B)),
inference(copy,[status(thm)],[c_5582]) ).
fof(axiom_039,axiom,
lin(eX) = cons(x,nil),
file('theBenchmark.p',axiom_039) ).
cnf(c_79,plain,
lin(eX) = cons(x,nil),
inference(clausify,[status(thm)],[axiom_039]) ).
cnf(c_80,plain,
cons(x,nil) = lin(eX),
inference(copy,[status(thm)],[c_79]) ).
cnf(c_83,negated_conjecture,
( assoc(A) = assoc(B)
| lin(A) != lin(B) ),
inference(clausify,[status(thm)],[goal_041_neg]) ).
cnf(c_5583,plain,
( assoc(eX) = eX
| z(proj1(eX),proj2(eX)) = eX ),
inference(resolve,[status(thm)],[c_63,c_59]) ).
cnf(c_85,plain,
assoc(eX) = eX,
inference(resolve,[status(thm)],[c_57,c_5583]) ).
cnf(c_89,plain,
proj12(assoc(x2(A,B))) = assoc(A),
inference(paramod,[status(thm)],[c_68,c_54]) ).
cnf(c_5584,plain,
append(lin(eX),A) = cons(x,append(nil,A)),
inference(paramod,[status(thm)],[c_80,c_70]) ).
cnf(c_108,plain,
append(lin(eX),A) = cons(x,A),
inference(paramod,[status(thm)],[c_69,c_5584]) ).
cnf(c_5585,plain,
x2(eX,assoc(A)) = assoc(x2(eX,A)),
inference(paramod,[status(thm)],[c_85,c_68]) ).
cnf(c_117,plain,
assoc(x2(eX,A)) = x2(eX,assoc(A)),
inference(copy,[status(thm)],[c_5585]) ).
cnf(c_130,plain,
cons(x,cons(mul,lin(A))) = lin(x2(eX,A)),
inference(paramod,[status(thm)],[c_108,c_78]) ).
cnf(c_5586,plain,
append(lin(x2(eX,A)),B) = cons(x,append(cons(mul,lin(A)),B)),
inference(paramod,[status(thm)],[c_130,c_70]) ).
cnf(c_5587,plain,
append(lin(x2(eX,A)),B) = cons(x,cons(mul,append(lin(A),B))),
inference(paramod,[status(thm)],[c_70,c_5586]) ).
cnf(c_217,plain,
cons(x,cons(mul,append(lin(A),B))) = append(lin(x2(eX,A)),B),
inference(copy,[status(thm)],[c_5587]) ).
cnf(c_5588,plain,
cons(x,cons(mul,lin(x2(A,B)))) = append(lin(x2(eX,A)),cons(mul,lin(B))),
inference(paramod,[status(thm)],[c_78,c_217]) ).
cnf(c_5589,plain,
lin(x2(eX,x2(A,B))) = append(lin(x2(eX,A)),cons(mul,lin(B))),
inference(paramod,[status(thm)],[c_130,c_5588]) ).
cnf(c_5590,plain,
lin(x2(eX,x2(A,B))) = lin(x2(x2(eX,A),B)),
inference(paramod,[status(thm)],[c_78,c_5589]) ).
cnf(c_5028,plain,
lin(x2(x2(eX,A),B)) = lin(x2(eX,x2(A,B))),
inference(copy,[status(thm)],[c_5590]) ).
cnf(c_5591,negated_conjecture,
assoc(x2(x2(eX,A),B)) = assoc(x2(eX,x2(A,B))),
inference(resolve,[status(thm)],[c_5028,c_83]) ).
cnf(c_5232,negated_conjecture,
assoc(x2(x2(eX,A),B)) = x2(eX,assoc(x2(A,B))),
inference(paramod,[status(thm)],[c_117,c_5591]) ).
cnf(c_5592,plain,
proj12(x2(eX,assoc(x2(A,B)))) = assoc(x2(eX,A)),
inference(paramod,[status(thm)],[c_5232,c_89]) ).
cnf(c_5593,plain,
eX = assoc(x2(eX,A)),
inference(paramod,[status(thm)],[c_54,c_5592]) ).
cnf(c_5594,plain,
eX = x2(eX,assoc(A)),
inference(paramod,[status(thm)],[c_117,c_5593]) ).
cnf(c_5595,plain,
x2(eX,assoc(A)) = eX,
inference(copy,[status(thm)],[c_5594]) ).
cnf(c_5580,plain,
$false,
inference(resolve,[status(thm)],[c_59,c_5595]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX185+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n026.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 26 16:54:31 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 1496107 was started by sandbox2 on n026,
% 0.09/5.37 % Sat Sep 26 16:54:31 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.38
% 0.09/5.38 % From the command line: assign(max_seconds, 300).
% 13.92/7.28
% 13.92/7.28 % SZS status Theorem for theBenchmark
% 13.92/7.28
% 13.92/7.28 % Proof 1 at 1.20 (+ 0.36) seconds.
% 13.92/7.28 % Length of proof is 31.
% 13.92/7.28 % Level of proof is 7.
% 13.92/7.28 % Maximum clause weight is 42.000.
% 13.92/7.28 % Given clauses 389.
% 13.92/7.28
% 13.92/7.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------