%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWX186+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 : Fri Sep 25 03:32:03 PM UTC 2026
% Result : Theorem 4.48s 1.70s
% Output : Proof 4.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 39 unt; 0 def)
% Number of atoms : 49 ( 48 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 16 ~; 3 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 80 ( 24 sgn 27 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,X2] : nil != cons(X,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
fof(f2_nnf,plain,
! [X,X2] : nil != cons(X,X2),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,X2] : nil != cons(X,X2),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
nil != cons(X0,X1),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t7,plain,
ifeq(nil,cons(X1,X2),false,true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t25,plain,
ifeq(nil,cons(X1,X2),false,true) = true,
inference(orient,[status(thm)],[t7]) ).
fof(f8,conjecture,
? [N,Xs,Ys] :
~ ( drop(N,Xs) = drop(N,Ys)
=> Xs = Ys ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_009) ).
fof(f8_neg,negated_conjecture,
~ ? [N,Xs,Ys] :
~ ( drop(N,Xs) = drop(N,Ys)
=> Xs = Ys ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
! [N,Xs,Ys] :
( Xs = Ys
| drop(N,Xs) != drop(N,Ys) ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
! [N,Xs,Ys] :
( Xs = Ys
| drop(N,Xs) != drop(N,Ys) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( X1 = X2
| drop(X0,X1) != drop(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t9,plain,
ifeq(drop(X1,X2),drop(X1,X3),X2,X3) = X3,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t12,plain,
ifeq(drop(X1,X2),drop(X1,X3),X2,X3) = X3,
inference(orient,[status(thm)],[t9]) ).
fof(f5,axiom,
! [Z] : drop(s(Z),nil) = nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
fof(f5_nnf,plain,
! [Z] : drop(s(Z),nil) = nil,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [Z] : drop(s(Z),nil) = nil,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
drop(s(X0),nil) = nil,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t2,plain,
drop(s(X1),nil) = nil,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t21,plain,
drop(s(X1),nil) = nil,
inference(orient,[status(thm)],[t2]) ).
cnf(t23,plain,
nil = ifeq(drop(s(X1),X2),nil,X2,nil),
inference(cp,[status(thm)],[t12,t21]) ).
cnf(t29,plain,
ifeq(drop(s(X1),X2),nil,X2,nil) = nil,
inference(orient,[status(thm)],[t23]) ).
fof(f6,axiom,
! [Z,X2,X3] : drop(s(Z),cons(X2,X3)) = drop(Z,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
fof(f6_nnf,plain,
! [Z,X2,X3] : drop(s(Z),cons(X2,X3)) = drop(Z,X3),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [Z,X2,X3] : drop(s(Z),cons(X2,X3)) = drop(Z,X3),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
drop(s(X0),cons(X1,X2)) = drop(X0,X2),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t8,plain,
drop(s(X1),cons(X2,X3)) = drop(X1,X3),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t18,plain,
drop(s(X1),cons(X2,X3)) = drop(X1,X3),
inference(orient,[status(thm)],[t8]) ).
cnf(t30,plain,
nil = ifeq(drop(X1,X2),nil,cons(X3,X2),nil),
inference(cp,[status(thm)],[t29,t18]) ).
cnf(t31,plain,
ifeq(drop(X1,X2),nil,cons(X3,X2),nil) = nil,
inference(orient,[status(thm)],[t30]) ).
cnf(t34,plain,
nil = ifeq(nil,nil,cons(X1,nil),nil),
inference(cp,[status(thm)],[t31,t21]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t45,plain,
nil = cons(X1,nil),
inference(step,[status(thm)],[t34,t11]) ).
cnf(t35,plain,
cons(X1,nil) = nil,
inference(orient,[status(thm)],[t45]) ).
cnf(t37,plain,
true = ifeq(nil,nil,false,true),
inference(cp,[status(thm)],[t25,t35]) ).
cnf(t46,plain,
true = false,
inference(step,[status(thm)],[t37,t11]) ).
cnf(t41,plain,
false = true,
inference(orient,[status(thm)],[t46]) ).
fof(f4,axiom,
! [X] : s(X) != z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
fof(f4_nnf,plain,
! [X] : s(X) != z,
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] : s(X) != z,
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
s(X0) != z,
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2,c4]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t41]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX186+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 23:38:24 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.48/1.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.48/1.70 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------