%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HWC001-1 : TPTP v8.1.0. Bugfixed v1.1.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 13:07:36 EDT 2022
% Result : Unsatisfiable 0.60s 0.80s
% Output : Refutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 28 ( 20 unt; 0 nHn; 28 RR)
% Number of literals : 38 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(not__dfg(and__dfg(u,v)),nand__dfg(u,v)),
file('HWC001-1.p',unknown),
[] ).
cnf(2,axiom,
equal(and__dfg(u,n0),n0),
file('HWC001-1.p',unknown),
[] ).
cnf(3,axiom,
equal(and__dfg(u,n1),u),
file('HWC001-1.p',unknown),
[] ).
cnf(4,axiom,
equal(not__dfg(n0),n1),
file('HWC001-1.p',unknown),
[] ).
cnf(5,axiom,
equal(not__dfg(n1),n0),
file('HWC001-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ output(u,v,w,x)
| ~ output(y,z,x1,x2)
| output(nand__dfg(y,u),nand__dfg(z,v),nand__dfg(x1,w),nand__dfg(x2,x)) ),
file('HWC001-1.p',unknown),
[] ).
cnf(7,axiom,
output(n0,n0,n1,n1),
file('HWC001-1.p',unknown),
[] ).
cnf(8,axiom,
output(n0,n1,n0,n1),
file('HWC001-1.p',unknown),
[] ).
cnf(9,axiom,
~ output(n0,n1,n1,n1),
file('HWC001-1.p',unknown),
[] ).
cnf(11,plain,
( ~ output(u,v,w,x)
| output(nand__dfg(u,n0),nand__dfg(v,n1),nand__dfg(w,n0),nand__dfg(x,n1)) ),
inference(res,[status(thm),theory(equality)],[8,6]),
[iquote('0:Res:8.0,6.1')] ).
cnf(13,plain,
( ~ output(u,v,w,x)
| output(nand__dfg(u,n0),nand__dfg(v,n0),nand__dfg(w,n1),nand__dfg(x,n1)) ),
inference(res,[status(thm),theory(equality)],[7,6]),
[iquote('0:Res:7.0,6.1')] ).
cnf(18,plain,
output(nand__dfg(n0,n0),nand__dfg(n0,n0),nand__dfg(n1,n1),nand__dfg(n1,n1)),
inference(res,[status(thm),theory(equality)],[7,13]),
[iquote('0:Res:7.0,13.0')] ).
cnf(29,plain,
equal(nand__dfg(u,n0),not__dfg(n0)),
inference(spr,[status(thm),theory(equality)],[2,1]),
[iquote('0:SpR:2.0,1.0')] ).
cnf(30,plain,
equal(nand__dfg(u,n1),not__dfg(u)),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(31,plain,
equal(nand__dfg(u,n0),n1),
inference(rew,[status(thm),theory(equality)],[4,29]),
[iquote('0:Rew:4.0,29.0')] ).
cnf(32,plain,
output(n1,n1,nand__dfg(n1,n1),nand__dfg(n1,n1)),
inference(rew,[status(thm),theory(equality)],[31,18]),
[iquote('0:Rew:31.0,18.0')] ).
cnf(36,plain,
( ~ output(u,v,w,x)
| output(nand__dfg(u,n0),nand__dfg(v,n1),n1,nand__dfg(x,n1)) ),
inference(rew,[status(thm),theory(equality)],[31,11]),
[iquote('0:Rew:31.0,11.1')] ).
cnf(37,plain,
output(n1,n1,not__dfg(n1),not__dfg(n1)),
inference(rew,[status(thm),theory(equality)],[30,32]),
[iquote('0:Rew:30.0,32.0')] ).
cnf(38,plain,
output(n1,n1,n0,n0),
inference(rew,[status(thm),theory(equality)],[5,37]),
[iquote('0:Rew:5.0,37.0')] ).
cnf(44,plain,
( ~ output(u,v,w,x)
| output(n1,not__dfg(v),n1,not__dfg(x)) ),
inference(rew,[status(thm),theory(equality)],[31,36,30]),
[iquote('0:Rew:31.0,36.1,30.0,36.1,30.0,36.1')] ).
cnf(47,plain,
( ~ output(u,v,n0,w)
| ~ output(x,y,z,x1)
| output(nand__dfg(x,u),nand__dfg(y,v),n1,nand__dfg(x1,w)) ),
inference(spr,[status(thm),theory(equality)],[31,6]),
[iquote('0:SpR:31.0,6.2')] ).
cnf(64,plain,
output(n1,not__dfg(n1),n1,not__dfg(n1)),
inference(res,[status(thm),theory(equality)],[8,44]),
[iquote('0:Res:8.0,44.0')] ).
cnf(69,plain,
output(n1,n0,n1,n0),
inference(rew,[status(thm),theory(equality)],[5,64]),
[iquote('0:Rew:5.0,64.0')] ).
cnf(3460,plain,
( ~ output(u,v,w,x)
| output(nand__dfg(u,n1),nand__dfg(v,n1),n1,nand__dfg(x,n0)) ),
inference(res,[status(thm),theory(equality)],[38,47]),
[iquote('0:Res:38.0,47.0')] ).
cnf(3482,plain,
( ~ output(u,v,w,x)
| output(not__dfg(u),not__dfg(v),n1,n1) ),
inference(rew,[status(thm),theory(equality)],[30,3460,31]),
[iquote('0:Rew:30.0,3460.1,30.0,3460.1,31.0,3460.1')] ).
cnf(3582,plain,
output(not__dfg(n1),not__dfg(n0),n1,n1),
inference(res,[status(thm),theory(equality)],[69,3482]),
[iquote('0:Res:69.0,3482.0')] ).
cnf(3676,plain,
output(n0,n1,n1,n1),
inference(rew,[status(thm),theory(equality)],[5,3582,4]),
[iquote('0:Rew:5.0,3582.0,4.0,3582.0')] ).
cnf(3677,plain,
$false,
inference(mrr,[status(thm)],[3676,9]),
[iquote('0:MRR:3676.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HWC001-1 : TPTP v8.1.0. Bugfixed v1.1.1.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 12:54:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.60/0.80
% 0.60/0.80 SPASS V 3.9
% 0.60/0.80 SPASS beiseite: Proof found.
% 0.60/0.80 % SZS status Theorem
% 0.60/0.80 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.60/0.80 SPASS derived 2233 clauses, backtracked 0 clauses, performed 0 splits and kept 400 clauses.
% 0.60/0.80 SPASS allocated 65122 KBytes.
% 0.60/0.80 SPASS spent 0:00:00.45 on the problem.
% 0.60/0.80 0:00:00.04 for the input.
% 0.60/0.80 0:00:00.00 for the FLOTTER CNF translation.
% 0.60/0.80 0:00:00.03 for inferences.
% 0.60/0.80 0:00:00.00 for the backtracking.
% 0.60/0.80 0:00:00.36 for the reduction.
% 0.60/0.80
% 0.60/0.80
% 0.60/0.80 Here is a proof with depth 4, length 28 :
% 0.60/0.80 % SZS output start Refutation
% See solution above
% 0.60/0.80 Formulae used in the proof : nand_definition and_definition1 and_definition2 not_definition1 not_definition2 nand_table_definition input1 input2 prove_cannot_make_or
% 0.60/0.80
%------------------------------------------------------------------------------