%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LDA004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 08:00:19 AM UTC 2026
% Result : Unsatisfiable 50.63s 22.00s
% Output : CNFRefutation 50.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 110 ( 105 unt; 0 def)
% Number of atoms : 117 ( 83 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 69 ( 8 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a1,axiom,
! [VAR_0,VAR_1,VAR_2] : f(VAR_0,f(VAR_1,VAR_2)) = f(f(VAR_0,VAR_1),f(VAR_0,VAR_2)),
file('theBenchmark.p',a1) ).
cnf(c_1,plain,
f(A,f(B,C)) = f(f(A,B),f(A,C)),
inference(clausify,[status(thm)],[a1]) ).
cnf(c_2,plain,
f(f(A,B),f(A,C)) = f(A,f(B,C)),
inference(copy,[status(thm)],[c_1]) ).
fof(a2,axiom,
! [VAR_0,VAR_1] : left(VAR_0,f(VAR_0,VAR_1)),
file('theBenchmark.p',a2) ).
cnf(c_3,plain,
left(A,f(A,B)),
inference(clausify,[status(thm)],[a2]) ).
fof(a3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( left(VAR_0,VAR_2)
| ~ left(VAR_1,VAR_2)
| ~ left(VAR_0,VAR_1) ),
file('theBenchmark.p',a3) ).
cnf(c_4,plain,
( left(A,C)
| ~ left(B,C)
| ~ left(A,B) ),
inference(clausify,[status(thm)],[a3]) ).
fof(clause_4,axiom,
n2 = f(n1,n1),
file('theBenchmark.p',clause_4) ).
cnf(c_5,plain,
n2 = f(n1,n1),
inference(clausify,[status(thm)],[clause_4]) ).
cnf(c_6,plain,
f(n1,n1) = n2,
inference(copy,[status(thm)],[c_5]) ).
fof(clause_5,axiom,
n3 = f(n2,n1),
file('theBenchmark.p',clause_5) ).
cnf(c_7,plain,
n3 = f(n2,n1),
inference(clausify,[status(thm)],[clause_5]) ).
cnf(c_8,plain,
f(n2,n1) = n3,
inference(copy,[status(thm)],[c_7]) ).
fof(clause_6,axiom,
u = f(n2,n2),
file('theBenchmark.p',clause_6) ).
cnf(c_9,plain,
u = f(n2,n2),
inference(clausify,[status(thm)],[clause_6]) ).
cnf(c_10,plain,
f(n2,n2) = u,
inference(copy,[status(thm)],[c_9]) ).
fof(clause_7,axiom,
u1 = f(u,n1),
file('theBenchmark.p',clause_7) ).
cnf(c_11,plain,
u1 = f(u,n1),
inference(clausify,[status(thm)],[clause_7]) ).
cnf(c_12,plain,
f(u,n1) = u1,
inference(copy,[status(thm)],[c_11]) ).
fof(clause_8,axiom,
u2 = f(u,n2),
file('theBenchmark.p',clause_8) ).
cnf(c_13,plain,
u2 = f(u,n2),
inference(clausify,[status(thm)],[clause_8]) ).
cnf(c_14,plain,
f(u,n2) = u2,
inference(copy,[status(thm)],[c_13]) ).
fof(clause_9,axiom,
u3 = f(u,n3),
file('theBenchmark.p',clause_9) ).
cnf(c_15,plain,
u3 = f(u,n3),
inference(clausify,[status(thm)],[clause_9]) ).
cnf(c_16,plain,
f(u,n3) = u3,
inference(copy,[status(thm)],[c_15]) ).
fof(clause_10,axiom,
a = f(f(n3,n2),u2),
file('theBenchmark.p',clause_10) ).
cnf(c_17,plain,
a = f(f(n3,n2),u2),
inference(clausify,[status(thm)],[clause_10]) ).
cnf(c_18,plain,
f(f(n3,n2),u2) = a,
inference(copy,[status(thm)],[c_17]) ).
fof(clause_11,axiom,
b = f(u1,u3),
file('theBenchmark.p',clause_11) ).
cnf(c_19,plain,
b = f(u1,u3),
inference(clausify,[status(thm)],[clause_11]) ).
cnf(c_20,plain,
f(u1,u3) = b,
inference(copy,[status(thm)],[c_19]) ).
fof(prove_equation,axiom,
~ left(a,b),
file('theBenchmark.p',prove_equation) ).
cnf(c_21,plain,
~ left(a,b),
inference(clausify,[status(thm)],[prove_equation]) ).
cnf(c_22,plain,
f(f(A,f(B,C)),f(f(A,B),D)) = f(f(A,B),f(f(A,C),D)),
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_23,plain,
f(f(f(A,B),C),f(A,f(B,D))) = f(f(A,B),f(C,f(A,D))),
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_24,plain,
left(f(A,B),f(A,f(B,C))),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_16175,plain,
f(n2,f(n1,A)) = f(n1,f(n1,A)),
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_26,plain,
f(n1,f(n1,A)) = f(n2,f(n1,A)),
inference(copy,[status(thm)],[c_16175]) ).
cnf(c_27,plain,
f(f(n1,A),n2) = f(n1,f(A,n1)),
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_29,plain,
f(n3,f(n2,A)) = f(n2,f(n1,A)),
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_30,plain,
f(f(n2,A),n3) = f(n2,f(A,n1)),
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_33,plain,
f(f(n2,A),u) = f(n2,f(A,n2)),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_36,plain,
f(f(u,A),u1) = f(u,f(A,n1)),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_39,plain,
f(f(u,A),u2) = f(u,f(A,n2)),
inference(paramod,[status(thm)],[c_14,c_2]) ).
cnf(c_42,plain,
f(f(u,A),u3) = f(u,f(A,n3)),
inference(paramod,[status(thm)],[c_16,c_2]) ).
cnf(c_45,plain,
f(f(f(n3,n2),A),a) = f(f(n3,n2),f(A,u2)),
inference(paramod,[status(thm)],[c_18,c_2]) ).
cnf(c_55,plain,
left(f(A,f(B,C)),f(f(A,B),f(f(A,C),D))),
inference(paramod,[status(thm)],[c_22,c_3]) ).
cnf(c_59,plain,
f(f(A,u),f(f(A,n2),B)) = f(f(A,n2),f(f(A,n2),B)),
inference(paramod,[status(thm)],[c_10,c_22]) ).
cnf(c_16176,plain,
f(f(A,u2),f(f(A,u),B)) = f(f(A,u),f(f(A,n2),B)),
inference(paramod,[status(thm)],[c_14,c_22]) ).
cnf(c_63,plain,
f(f(A,u2),f(f(A,u),B)) = f(f(A,n2),f(f(A,n2),B)),
inference(paramod,[status(thm)],[c_59,c_16176]) ).
cnf(c_16177,plain,
f(n1,n2) = f(n2,f(n1,n1)),
inference(paramod,[status(thm)],[c_6,c_26]) ).
cnf(c_16178,plain,
f(n1,n2) = f(n2,n2),
inference(paramod,[status(thm)],[c_6,c_16177]) ).
cnf(c_225,plain,
f(n1,n2) = u,
inference(paramod,[status(thm)],[c_10,c_16178]) ).
cnf(c_16179,plain,
f(f(n1,n2),n2) = f(n1,n3),
inference(paramod,[status(thm)],[c_8,c_27]) ).
cnf(c_16180,plain,
f(u,n2) = f(n1,n3),
inference(paramod,[status(thm)],[c_225,c_16179]) ).
cnf(c_16181,plain,
u2 = f(n1,n3),
inference(paramod,[status(thm)],[c_14,c_16180]) ).
cnf(c_239,plain,
f(n1,n3) = u2,
inference(copy,[status(thm)],[c_16181]) ).
cnf(c_16182,plain,
f(n3,f(n2,n1)) = f(n2,n2),
inference(paramod,[status(thm)],[c_6,c_29]) ).
cnf(c_16183,plain,
f(n3,n3) = f(n2,n2),
inference(paramod,[status(thm)],[c_8,c_16182]) ).
cnf(c_250,plain,
f(n3,n3) = u,
inference(paramod,[status(thm)],[c_10,c_16183]) ).
cnf(c_16184,plain,
f(f(n2,n2),n3) = f(n2,n3),
inference(paramod,[status(thm)],[c_8,c_30]) ).
cnf(c_16185,plain,
f(u,n3) = f(n2,n3),
inference(paramod,[status(thm)],[c_10,c_16184]) ).
cnf(c_16186,plain,
u3 = f(n2,n3),
inference(paramod,[status(thm)],[c_16,c_16185]) ).
cnf(c_268,plain,
f(n2,n3) = u3,
inference(copy,[status(thm)],[c_16186]) ).
cnf(c_274,plain,
f(f(n1,A),u) = f(n1,f(A,n2)),
inference(paramod,[status(thm)],[c_225,c_2]) ).
cnf(c_299,plain,
f(f(n3,A),u) = f(n3,f(A,n3)),
inference(paramod,[status(thm)],[c_250,c_2]) ).
cnf(c_16187,plain,
f(u3,u) = f(n2,f(n3,n2)),
inference(paramod,[status(thm)],[c_268,c_33]) ).
cnf(c_351,plain,
f(n2,f(n3,n2)) = f(u3,u),
inference(copy,[status(thm)],[c_16187]) ).
cnf(c_16188,plain,
f(f(u,n1),u1) = f(u,n2),
inference(paramod,[status(thm)],[c_6,c_36]) ).
cnf(c_16189,plain,
f(u1,u1) = f(u,n2),
inference(paramod,[status(thm)],[c_12,c_16188]) ).
cnf(c_364,plain,
f(u1,u1) = u2,
inference(paramod,[status(thm)],[c_14,c_16189]) ).
cnf(c_16190,plain,
f(f(u,n2),u1) = f(u,n3),
inference(paramod,[status(thm)],[c_8,c_36]) ).
cnf(c_16191,plain,
f(u2,u1) = f(u,n3),
inference(paramod,[status(thm)],[c_14,c_16190]) ).
cnf(c_365,plain,
f(u2,u1) = u3,
inference(paramod,[status(thm)],[c_16,c_16191]) ).
cnf(c_381,plain,
left(f(A,u1),f(A,u2)),
inference(paramod,[status(thm)],[c_364,c_24]) ).
cnf(c_390,plain,
left(f(A,u2),f(A,u3)),
inference(paramod,[status(thm)],[c_365,c_24]) ).
cnf(c_16192,plain,
f(u3,u2) = f(u,f(n3,n2)),
inference(paramod,[status(thm)],[c_16,c_39]) ).
cnf(c_464,plain,
f(u,f(n3,n2)) = f(u3,u2),
inference(copy,[status(thm)],[c_16192]) ).
cnf(c_16193,plain,
f(u1,u3) = f(u,f(n1,n3)),
inference(paramod,[status(thm)],[c_12,c_42]) ).
cnf(c_16194,plain,
b = f(u,f(n1,n3)),
inference(paramod,[status(thm)],[c_20,c_16193]) ).
cnf(c_16195,plain,
b = f(u,u2),
inference(paramod,[status(thm)],[c_239,c_16194]) ).
cnf(c_522,plain,
f(u,u2) = b,
inference(copy,[status(thm)],[c_16195]) ).
cnf(c_1562,plain,
left(f(u,u1),b),
inference(paramod,[status(thm)],[c_522,c_381]) ).
cnf(c_16196,plain,
( left(A,b)
| ~ left(A,f(u,u1)) ),
inference(resolve,[status(thm)],[c_4,c_1562]) ).
cnf(c_1577,plain,
~ left(a,f(u,u1)),
inference(resolve,[status(thm)],[c_16196,c_21]) ).
cnf(c_16197,plain,
( left(f(A,u2),B)
| ~ left(f(A,u3),B) ),
inference(resolve,[status(thm)],[c_4,c_390]) ).
cnf(c_1633,plain,
left(f(A,u2),f(f(A,u3),B)),
inference(resolve,[status(thm)],[c_16197,c_3]) ).
cnf(c_16198,plain,
f(n3,f(u3,u)) = f(n2,f(n1,f(n3,n2))),
inference(paramod,[status(thm)],[c_351,c_29]) ).
cnf(c_11536,plain,
f(n2,f(n1,f(n3,n2))) = f(n3,f(u3,u)),
inference(copy,[status(thm)],[c_16198]) ).
cnf(c_16199,plain,
f(u2,u) = f(n1,f(n3,n2)),
inference(paramod,[status(thm)],[c_239,c_274]) ).
cnf(c_12066,plain,
f(n1,f(n3,n2)) = f(u2,u),
inference(copy,[status(thm)],[c_16199]) ).
cnf(c_16200,plain,
f(n2,f(u2,u)) = f(n3,f(u3,u)),
inference(paramod,[status(thm)],[c_12066,c_11536]) ).
cnf(c_12087,plain,
f(n3,f(u3,u)) = f(n2,f(u2,u)),
inference(copy,[status(thm)],[c_16200]) ).
cnf(c_16201,plain,
f(f(f(n3,A),u),f(n3,f(A,n2))) = f(f(n3,A),f(u3,u2)),
inference(paramod,[status(thm)],[c_464,c_23]) ).
cnf(c_16202,plain,
f(f(n3,f(A,n3)),f(n3,f(A,n2))) = f(f(n3,A),f(u3,u2)),
inference(paramod,[status(thm)],[c_299,c_16201]) ).
cnf(c_16203,plain,
f(n3,f(f(A,n3),f(A,n2))) = f(f(n3,A),f(u3,u2)),
inference(paramod,[status(thm)],[c_2,c_16202]) ).
cnf(c_16204,plain,
f(n3,f(A,f(n3,n2))) = f(f(n3,A),f(u3,u2)),
inference(paramod,[status(thm)],[c_2,c_16203]) ).
cnf(c_12439,plain,
f(f(n3,A),f(u3,u2)) = f(n3,f(A,f(n3,n2))),
inference(copy,[status(thm)],[c_16204]) ).
cnf(c_16205,plain,
left(f(f(n3,n2),u2),f(f(n3,n2),f(u3,u2))),
inference(paramod,[status(thm)],[c_45,c_1633]) ).
cnf(c_16206,plain,
left(a,f(f(n3,n2),f(u3,u2))),
inference(paramod,[status(thm)],[c_18,c_16205]) ).
cnf(c_16207,plain,
left(a,f(n3,f(n2,f(n3,n2)))),
inference(paramod,[status(thm)],[c_12439,c_16206]) ).
cnf(c_16208,plain,
left(a,f(n3,f(u3,u))),
inference(paramod,[status(thm)],[c_351,c_16207]) ).
cnf(c_16072,plain,
left(a,f(n2,f(u2,u))),
inference(paramod,[status(thm)],[c_12087,c_16208]) ).
cnf(c_16209,plain,
( left(a,A)
| ~ left(f(n2,f(u2,u)),A) ),
inference(resolve,[status(thm)],[c_4,c_16072]) ).
cnf(c_16210,plain,
left(a,f(f(n2,u2),f(f(n2,u),A))),
inference(resolve,[status(thm)],[c_16209,c_55]) ).
cnf(c_16211,plain,
left(a,f(f(n2,n2),f(f(n2,n2),A))),
inference(paramod,[status(thm)],[c_63,c_16210]) ).
cnf(c_16212,plain,
left(a,f(u,f(f(n2,n2),A))),
inference(paramod,[status(thm)],[c_10,c_16211]) ).
cnf(c_16090,plain,
left(a,f(u,f(u,A))),
inference(paramod,[status(thm)],[c_10,c_16212]) ).
cnf(c_16213,plain,
left(a,f(u,u1)),
inference(paramod,[status(thm)],[c_12,c_16090]) ).
cnf(c_16174,plain,
$false,
inference(resolve,[status(thm)],[c_1577,c_16213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LDA004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/15.54 % Computer : n012.cluster.edu
% 0.03/15.54 % Model : x86_64 x86_64
% 0.03/15.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/15.54 % Memory : 8046.5625MB
% 0.03/15.54 % OS : Linux 6.8.0-71-generic
% 0.03/15.54 % CPULimit : 300
% 0.03/15.54 % WCLimit : 300
% 0.03/15.54 % DateTime : Fri Sep 25 23:55:41 UTC 2026
% 0.03/15.54 % CPUTime :
% 0.03/15.54 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/15.54 % Process 3360723 was started by sandbox on n012,
% 0.03/15.54 % Fri Sep 25 23:55:41 2026
% 0.03/15.54 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/15.54
% 0.03/15.54 % From the command line: assign(max_seconds, 300).
% 50.63/22.00
% 50.63/22.00 % given #500 (F,wt=71): 1570 -left(f(f(f(f(f(f(f(a,A),B),C),D),E),F),V6),f(u,u1)). [ur(4,b,1562,a,c,107,a)].
% 50.63/22.00
% 50.63/22.00 % given #1000 (T,wt=24): 410 left(u1,f(n2,f(n2,A))). [para(38(a,1),361(a,2))].
% 50.63/22.00
% 50.63/22.00 % given #1500 (F,wt=26): 10061 -left(f(n2,f(a,a)),f(u2,u)). [ur(4,b,1267,a,c,10045,a)].
% 50.63/22.00
% 50.63/22.00 % SZS status Unsatisfiable for theBenchmark
% 50.63/22.00
% 50.63/22.00 % Proof 1 at 4.54 (+ 1.88) seconds.
% 50.63/22.00 % Length of proof is 59.
% 50.63/22.00 % Level of proof is 9.
% 50.63/22.00 % Maximum clause weight is 55.000.
% 50.63/22.00 % Given clauses 1902.
% 50.63/22.00
% 50.63/22.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------