%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWX207+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 09:16:20 AM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 27 unt; 0 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 7 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 1 sgn 8 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_017,axiom,
! [X,X2] : proj1C(c2(X,X2)) = X,
file('theBenchmark.p',axiom_017) ).
fof(axiom_019,axiom,
! [Y] : append(nil,Y) = Y,
file('theBenchmark.p',axiom_019) ).
fof(axiom_020,axiom,
! [Y,Z,Xs] : append(cons(Z,Xs),Y) = cons(Z,append(Xs,Y)),
file('theBenchmark.p',axiom_020) ).
fof(axiom_026,axiom,
! [P,Q] : linC(c2(P,Q)) = append(linP(P),linP(Q)),
file('theBenchmark.p',axiom_026) ).
fof(goal_027,conjecture,
? [U,V] :
~ ( linC(U) = linC(V)
=> U = V ),
file('theBenchmark.p',goal_027) ).
fof(goal_027_neg,negated_conjecture,
~ ? [U,V] :
~ ( linC(U) = linC(V)
=> U = V ),
inference(assume_negation,[status(cth)],[goal_027]) ).
fof(axiom_016,axiom,
pB != pE,
file('theBenchmark.p',axiom_016) ).
cnf(c_39,plain,
pB != pE,
inference(clausify,[status(thm)],[axiom_016]) ).
cnf(c_40,plain,
pE != pB,
inference(copy,[status(thm)],[c_39]) ).
cnf(c_41,plain,
proj1C(c2(A,B)) = A,
inference(clausify,[status(thm)],[axiom_017]) ).
cnf(c_43,plain,
append(nil,A) = A,
inference(clausify,[status(thm)],[axiom_019]) ).
cnf(c_44,plain,
append(cons(A,B),C) = cons(A,append(B,C)),
inference(clausify,[status(thm)],[axiom_020]) ).
fof(axiom_024,axiom,
linP(pB) = cons(b,nil),
file('theBenchmark.p',axiom_024) ).
cnf(c_50,plain,
linP(pB) = cons(b,nil),
inference(clausify,[status(thm)],[axiom_024]) ).
fof(axiom_025,axiom,
linP(pE) = nil,
file('theBenchmark.p',axiom_025) ).
cnf(c_51,plain,
linP(pE) = nil,
inference(clausify,[status(thm)],[axiom_025]) ).
cnf(c_52,plain,
nil = linP(pE),
inference(copy,[status(thm)],[c_51]) ).
cnf(c_53,plain,
linC(c2(A,B)) = append(linP(A),linP(B)),
inference(clausify,[status(thm)],[axiom_026]) ).
cnf(c_54,negated_conjecture,
( A = B
| linC(A) != linC(B) ),
inference(clausify,[status(thm)],[goal_027_neg]) ).
cnf(c_142,plain,
linP(pB) = cons(b,linP(pE)),
inference(paramod,[status(thm)],[c_52,c_50]) ).
cnf(c_55,plain,
cons(b,linP(pE)) = linP(pB),
inference(copy,[status(thm)],[c_142]) ).
cnf(c_59,plain,
append(linP(pE),A) = A,
inference(paramod,[status(thm)],[c_52,c_43]) ).
cnf(c_143,plain,
( c2(A,B) = C
| append(linP(A),linP(B)) != linC(C) ),
inference(paramod,[status(thm)],[c_53,c_54]) ).
cnf(c_72,plain,
( c2(B,C) = A
| linC(A) != append(linP(B),linP(C)) ),
inference(copy,[status(thm)],[c_143]) ).
cnf(c_144,plain,
append(linP(pB),A) = cons(b,append(linP(pE),A)),
inference(paramod,[status(thm)],[c_55,c_44]) ).
cnf(c_75,plain,
append(linP(pB),A) = cons(b,A),
inference(paramod,[status(thm)],[c_59,c_144]) ).
cnf(c_97,plain,
( c2(pE,B) = A
| linC(A) != linP(B) ),
inference(paramod,[status(thm)],[c_59,c_72]) ).
cnf(c_145,plain,
( c2(pE,C) = c2(A,B)
| append(linP(A),linP(B)) != linP(C) ),
inference(paramod,[status(thm)],[c_53,c_97]) ).
cnf(c_100,plain,
( c2(pE,A) = c2(B,C)
| linP(A) != append(linP(B),linP(C)) ),
inference(copy,[status(thm)],[c_145]) ).
cnf(c_130,plain,
( c2(pE,A) = c2(pB,B)
| linP(A) != cons(b,linP(B)) ),
inference(paramod,[status(thm)],[c_75,c_100]) ).
cnf(c_146,plain,
linP(pB) = cons(b,linP(pE)),
inference(copy,[status(thm)],[c_55]) ).
cnf(c_134,plain,
c2(pE,pB) = c2(pB,pE),
inference(resolve,[status(thm)],[c_130,c_146]) ).
cnf(c_147,plain,
proj1C(c2(pB,pE)) = pE,
inference(paramod,[status(thm)],[c_134,c_41]) ).
cnf(c_148,plain,
pB = pE,
inference(paramod,[status(thm)],[c_41,c_147]) ).
cnf(c_140,plain,
pE = pB,
inference(copy,[status(thm)],[c_148]) ).
cnf(c_141,plain,
$false,
inference(resolve,[status(thm)],[c_140,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX207+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.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 : Sat Sep 26 16:55:15 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 658931 was started by sandbox on n009,
% 0.10/0.37 % Sat Sep 26 16:55:15 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.40
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40
% 0.14/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/0.40 % Length of proof is 25.
% 0.14/0.40 % Level of proof is 8.
% 0.14/0.40 % Maximum clause weight is 15.000.
% 0.14/0.40 % Given clauses 63.
% 0.14/0.40
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------