TSTP Solution File: SYN353-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SYN353-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 : Thu Jul 21 12:20:40 EDT 2022
% Result : Unsatisfiable 0.21s 0.42s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 13
% Syntax : Number of clauses : 60 ( 7 unt; 37 nHn; 60 RR)
% Number of literals : 157 ( 0 equ; 47 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ f(u,v,w)
| ~ f(a,a,z__dfg(u,v,w))
| f(w,u,v)
| f(v,w,u) ),
file('SYN353-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ f(u,v,w)
| ~ f(w,v,z__dfg(v,w,u))
| f(v,w,u) ),
file('SYN353-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ f(u,v,w)
| ~ f(w,v,z__dfg(v,w,u))
| f(w,u,v) ),
file('SYN353-1.p',unknown),
[] ).
cnf(4,axiom,
( f(u,v,w)
| f(w,v,z__dfg(v,w,u)) ),
file('SYN353-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ f(u,v,w)
| ~ f(w,u,v)
| f(u,w,z__dfg(w,u,v)) ),
file('SYN353-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ f(u,v,w)
| ~ f(w,z__dfg(w,u,v),u)
| f(w,u,v) ),
file('SYN353-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ f(u,v,w)
| ~ f(w,z__dfg(w,u,v),u)
| f(v,w,u) ),
file('SYN353-1.p',unknown),
[] ).
cnf(8,axiom,
( f(u,v,w)
| f(w,z__dfg(w,u,v),u) ),
file('SYN353-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ f(u,v,w)
| ~ f(v,w,u)
| f(v,z__dfg(v,w,u),w) ),
file('SYN353-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ f(z__dfg(u,v,w),v,u)
| f(u,v,w)
| f(w,u,v) ),
file('SYN353-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ f(z__dfg(u,v,w),v,u)
| f(u,v,w)
| f(v,w,u) ),
file('SYN353-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ f(u,v,w)
| ~ f(v,w,u)
| f(z__dfg(w,u,v),u,w) ),
file('SYN353-1.p',unknown),
[] ).
cnf(17,axiom,
( ~ f(u,v,w)
| ~ f(w,u,v)
| ~ f(v,w,u)
| ~ f(z__dfg(v,w,u),z__dfg(v,w,u),z__dfg(v,w,u)) ),
file('SYN353-1.p',unknown),
[] ).
cnf(30,plain,
( ~ f(a,a,u)
| f(u,a,a)
| f(u,a,a)
| f(a,u,a) ),
inference(res,[status(thm),theory(equality)],[4,1]),
[iquote('0:Res:4.1,1.1')] ).
cnf(32,plain,
( ~ f(a,a,u)
| f(u,a,a)
| f(a,u,a) ),
inference(obv,[status(thm),theory(equality)],[30]),
[iquote('0:Obv:30.1')] ).
cnf(33,plain,
( f(u,a,a)
| f(z__dfg(a,a,u),a,a)
| f(a,z__dfg(a,a,u),a) ),
inference(res,[status(thm),theory(equality)],[4,32]),
[iquote('0:Res:4.1,32.0')] ).
cnf(35,plain,
( f(u,a,a)
| f(a,z__dfg(a,a,u),a)
| f(a,a,u)
| f(u,a,a) ),
inference(res,[status(thm),theory(equality)],[33,10]),
[iquote('0:Res:33.1,10.0')] ).
cnf(37,plain,
( f(a,z__dfg(a,a,u),a)
| f(a,a,u)
| f(u,a,a) ),
inference(obv,[status(thm),theory(equality)],[35]),
[iquote('0:Obv:35.0')] ).
cnf(38,plain,
( ~ f(a,u,a)
| f(a,a,u)
| f(u,a,a)
| f(a,a,u) ),
inference(res,[status(thm),theory(equality)],[37,6]),
[iquote('0:Res:37.0,6.1')] ).
cnf(40,plain,
( ~ f(a,u,a)
| f(u,a,a)
| f(a,a,u) ),
inference(obv,[status(thm),theory(equality)],[38]),
[iquote('0:Obv:38.1')] ).
cnf(45,plain,
( f(a,u,a)
| f(z__dfg(a,a,u),a,a)
| f(a,a,z__dfg(a,a,u)) ),
inference(res,[status(thm),theory(equality)],[8,40]),
[iquote('0:Res:8.1,40.0')] ).
cnf(49,plain,
( f(a,u,a)
| f(a,a,z__dfg(a,a,u))
| f(a,a,u)
| f(a,u,a) ),
inference(res,[status(thm),theory(equality)],[45,11]),
[iquote('0:Res:45.1,11.0')] ).
cnf(50,plain,
( f(a,a,z__dfg(a,a,u))
| f(a,a,u)
| f(a,u,a) ),
inference(obv,[status(thm),theory(equality)],[49]),
[iquote('0:Obv:49.0')] ).
cnf(51,plain,
( ~ f(u,a,a)
| f(a,a,u)
| f(a,u,a)
| f(a,a,u) ),
inference(res,[status(thm),theory(equality)],[50,2]),
[iquote('0:Res:50.0,2.1')] ).
cnf(55,plain,
( ~ f(u,a,a)
| f(a,u,a)
| f(a,a,u) ),
inference(obv,[status(thm),theory(equality)],[51]),
[iquote('0:Obv:51.1')] ).
cnf(58,plain,
( ~ f(a,u,a)
| ~ f(u,a,a)
| f(a,z__dfg(a,a,u),a)
| f(a,a,z__dfg(a,a,u)) ),
inference(res,[status(thm),theory(equality)],[12,55]),
[iquote('0:Res:12.2,55.0')] ).
cnf(61,plain,
( f(a,z__dfg(a,a,u),a)
| f(a,a,z__dfg(a,a,u)) ),
inference(mrr,[status(thm)],[58,8,4]),
[iquote('0:MRR:58.0,58.1,8.0,4.0')] ).
cnf(64,plain,
( ~ f(a,u,a)
| f(a,a,z__dfg(a,a,u))
| f(a,a,u) ),
inference(res,[status(thm),theory(equality)],[61,6]),
[iquote('0:Res:61.0,6.1')] ).
cnf(66,plain,
( f(a,a,z__dfg(a,a,u))
| f(z__dfg(a,a,u),a,a)
| f(a,a,z__dfg(a,a,u)) ),
inference(res,[status(thm),theory(equality)],[61,40]),
[iquote('0:Res:61.0,40.0')] ).
cnf(67,plain,
( f(a,a,z__dfg(a,a,u))
| f(a,a,u) ),
inference(mrr,[status(thm)],[64,50]),
[iquote('0:MRR:64.0,50.2')] ).
cnf(68,plain,
( f(z__dfg(a,a,u),a,a)
| f(a,a,z__dfg(a,a,u)) ),
inference(obv,[status(thm),theory(equality)],[66]),
[iquote('0:Obv:66.0')] ).
cnf(69,plain,
( ~ f(u,a,a)
| f(a,a,u)
| f(a,a,u) ),
inference(res,[status(thm),theory(equality)],[67,2]),
[iquote('0:Res:67.0,2.1')] ).
cnf(73,plain,
( ~ f(u,a,a)
| f(a,a,u) ),
inference(obv,[status(thm),theory(equality)],[69]),
[iquote('0:Obv:69.1')] ).
cnf(76,plain,
f(a,a,z__dfg(a,a,u)),
inference(mrr,[status(thm)],[68,73]),
[iquote('0:MRR:68.0,73.0')] ).
cnf(78,plain,
( ~ f(u,a,a)
| f(a,u,a) ),
inference(res,[status(thm),theory(equality)],[76,3]),
[iquote('0:Res:76.0,3.1')] ).
cnf(80,plain,
( f(z__dfg(a,a,u),a,a)
| f(a,z__dfg(a,a,u),a) ),
inference(res,[status(thm),theory(equality)],[76,32]),
[iquote('0:Res:76.0,32.0')] ).
cnf(83,plain,
f(a,z__dfg(a,a,u),a),
inference(mrr,[status(thm)],[80,78]),
[iquote('0:MRR:80.0,78.0')] ).
cnf(85,plain,
( ~ f(a,u,a)
| f(u,a,a) ),
inference(res,[status(thm),theory(equality)],[83,7]),
[iquote('0:Res:83.0,7.1')] ).
cnf(98,plain,
f(z__dfg(a,a,u),a,a),
inference(res,[status(thm),theory(equality)],[83,85]),
[iquote('0:Res:83.0,85.0')] ).
cnf(99,plain,
( f(a,a,u)
| f(u,a,a) ),
inference(res,[status(thm),theory(equality)],[98,10]),
[iquote('0:Res:98.0,10.0')] ).
cnf(103,plain,
f(a,a,u),
inference(mrr,[status(thm)],[99,73]),
[iquote('0:MRR:99.1,73.0')] ).
cnf(104,plain,
( ~ f(u,v,w)
| f(w,u,v)
| f(v,w,u) ),
inference(mrr,[status(thm)],[1,103]),
[iquote('0:MRR:1.1,103.0')] ).
cnf(108,plain,
( f(u,v,w)
| f(u,w,z__dfg(w,u,v))
| f(z__dfg(w,u,v),u,w) ),
inference(res,[status(thm),theory(equality)],[8,104]),
[iquote('0:Res:8.1,104.0')] ).
cnf(109,plain,
( f(u,v,w)
| f(z__dfg(v,w,u),w,v)
| f(v,z__dfg(v,w,u),w) ),
inference(res,[status(thm),theory(equality)],[4,104]),
[iquote('0:Res:4.1,104.0')] ).
cnf(111,plain,
( ~ f(u,v,w)
| ~ f(v,w,u)
| f(w,z__dfg(w,u,v),u)
| f(u,w,z__dfg(w,u,v)) ),
inference(res,[status(thm),theory(equality)],[12,104]),
[iquote('0:Res:12.2,104.0')] ).
cnf(116,plain,
( f(u,z__dfg(u,v,w),v)
| f(v,u,z__dfg(u,v,w)) ),
inference(mrr,[status(thm)],[111,8,4]),
[iquote('0:MRR:111.0,111.1,8.0,4.0')] ).
cnf(130,plain,
( ~ f(u,v,w)
| f(u,w,z__dfg(w,u,v))
| f(w,u,v) ),
inference(res,[status(thm),theory(equality)],[116,6]),
[iquote('0:Res:116.0,6.1')] ).
cnf(133,plain,
( ~ f(u,v,w)
| f(v,z__dfg(v,w,u),w)
| f(v,w,u) ),
inference(res,[status(thm),theory(equality)],[116,2]),
[iquote('0:Res:116.1,2.1')] ).
cnf(135,plain,
( ~ f(u,v,w)
| f(u,w,z__dfg(w,u,v)) ),
inference(mrr,[status(thm)],[130,5]),
[iquote('0:MRR:130.2,5.1')] ).
cnf(136,plain,
( f(u,v,z__dfg(v,u,w))
| f(z__dfg(v,u,w),u,v) ),
inference(mrr,[status(thm)],[108,135]),
[iquote('0:MRR:108.0,135.0')] ).
cnf(137,plain,
( ~ f(u,v,w)
| f(v,z__dfg(v,w,u),w) ),
inference(mrr,[status(thm)],[133,9]),
[iquote('0:MRR:133.2,9.1')] ).
cnf(138,plain,
( f(z__dfg(u,v,w),v,u)
| f(u,z__dfg(u,v,w),v) ),
inference(mrr,[status(thm)],[109,137]),
[iquote('0:MRR:109.0,137.0')] ).
cnf(143,plain,
( f(u,v,z__dfg(v,u,w))
| f(v,u,w)
| f(u,w,v) ),
inference(res,[status(thm),theory(equality)],[136,11]),
[iquote('0:Res:136.1,11.0')] ).
cnf(144,plain,
( f(u,v,z__dfg(v,u,w))
| f(v,u,w) ),
inference(mrr,[status(thm)],[143,135]),
[iquote('0:MRR:143.2,135.0')] ).
cnf(145,plain,
( ~ f(u,v,w)
| f(v,w,u) ),
inference(mrr,[status(thm)],[2,144]),
[iquote('0:MRR:2.1,144.0')] ).
cnf(146,plain,
( ~ f(z__dfg(u,v,w),v,u)
| f(v,w,u) ),
inference(mrr,[status(thm)],[11,145]),
[iquote('0:MRR:11.1,145.0')] ).
cnf(150,plain,
( ~ f(u,v,w)
| ~ f(w,u,v)
| ~ f(z__dfg(w,u,v),z__dfg(w,u,v),z__dfg(w,u,v)) ),
inference(mrr,[status(thm)],[17,145]),
[iquote('0:MRR:17.0,145.1')] ).
cnf(154,plain,
f(z__dfg(u,v,w),v,u),
inference(mrr,[status(thm)],[138,145]),
[iquote('0:MRR:138.1,145.0')] ).
cnf(157,plain,
f(u,v,w),
inference(mrr,[status(thm)],[146,154]),
[iquote('0:MRR:146.0,154.0')] ).
cnf(159,plain,
$false,
inference(mrr,[status(thm)],[150,157]),
[iquote('0:MRR:150.0,150.1,150.2,157.0,157.0,157.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN353-1 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 12 02:17:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.21/0.42
% 0.21/0.42 SPASS V 3.9
% 0.21/0.42 SPASS beiseite: Proof found.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.42 SPASS derived 115 clauses, backtracked 0 clauses, performed 0 splits and kept 60 clauses.
% 0.21/0.42 SPASS allocated 63175 KBytes.
% 0.21/0.42 SPASS spent 0:00:00.06 on the problem.
% 0.21/0.42 0:00:00.04 for the input.
% 0.21/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.42 0:00:00.00 for inferences.
% 0.21/0.42 0:00:00.00 for the backtracking.
% 0.21/0.42 0:00:00.01 for the reduction.
% 0.21/0.42
% 0.21/0.42
% 0.21/0.42 Here is a proof with depth 13, length 60 :
% 0.21/0.42 % SZS output start Refutation
% See solution above
% 0.21/0.42 Formulae used in the proof : clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause9 clause10 clause11 clause12 clause17
% 0.21/0.42
%------------------------------------------------------------------------------