TSTP Solution File: SEU142+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU142+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 : Tue Jul 19 14:34:17 EDT 2022
% Result : Theorem 0.52s 0.69s
% Output : Refutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of clauses : 19 ( 4 unt; 6 nHn; 19 RR)
% Number of literals : 43 ( 0 equ; 18 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(unordered_pair(skc1,skc1),singleton(skc1)),
file('SEU142+1.p',unknown),
[] ).
cnf(2,axiom,
equal(unordered_pair(u,v),unordered_pair(v,u)),
file('SEU142+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ equal(skf3(u,v),u)
| ~ in(skf3(u,v),v) ),
file('SEU142+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(u,v)
| ~ equal(w,unordered_pair(x,v))
| in(u,w) ),
file('SEU142+1.p',unknown),
[] ).
cnf(11,axiom,
( equal(u,singleton(v))
| equal(skf3(v,u),v)
| in(skf3(v,u),u) ),
file('SEU142+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ in(u,v)
| ~ equal(v,unordered_pair(w,x))
| equal(u,x)
| equal(u,w) ),
file('SEU142+1.p',unknown),
[] ).
cnf(40,plain,
( ~ equal(u,v)
| in(u,unordered_pair(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[9]),
[iquote('0:EqR:9.1')] ).
cnf(43,plain,
( ~ equal(u,v)
| in(u,unordered_pair(v,w)) ),
inference(spr,[status(thm),theory(equality)],[2,40]),
[iquote('0:SpR:2.0,40.1')] ).
cnf(55,plain,
( ~ equal(skf3(u,unordered_pair(v,w)),v)
| ~ equal(skf3(u,unordered_pair(v,w)),u) ),
inference(res,[status(thm),theory(equality)],[43,4]),
[iquote('0:Res:43.1,4.1')] ).
cnf(122,plain,
( ~ in(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[14]),
[iquote('0:EqR:14.1')] ).
cnf(129,plain,
( equal(unordered_pair(u,v),singleton(w))
| equal(skf3(w,unordered_pair(u,v)),w)
| equal(skf3(w,unordered_pair(u,v)),v)
| equal(skf3(w,unordered_pair(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[11,122]),
[iquote('0:Res:11.2,122.0')] ).
cnf(140,plain,
( ~ equal(skf3(u,unordered_pair(v,w)),w)
| ~ equal(skf3(u,unordered_pair(w,v)),u) ),
inference(spl,[status(thm),theory(equality)],[2,55]),
[iquote('0:SpL:2.0,55.0')] ).
cnf(409,plain,
( equal(unordered_pair(u,u),singleton(v))
| equal(skf3(v,unordered_pair(u,u)),v)
| equal(skf3(v,unordered_pair(u,u)),u) ),
inference(fac,[status(thm)],[129]),
[iquote('0:Fac:129.2,129.3')] ).
cnf(1255,plain,
( equal(unordered_pair(u,u),singleton(u))
| equal(skf3(u,unordered_pair(u,u)),u) ),
inference(fac,[status(thm)],[409]),
[iquote('0:Fac:409.1,409.2')] ).
cnf(1295,plain,
( ~ equal(u,u)
| ~ equal(skf3(u,unordered_pair(u,u)),u)
| equal(unordered_pair(u,u),singleton(u)) ),
inference(spl,[status(thm),theory(equality)],[1255,140]),
[iquote('0:SpL:1255.1,140.0')] ).
cnf(1300,plain,
( ~ equal(skf3(u,unordered_pair(u,u)),u)
| equal(unordered_pair(u,u),singleton(u)) ),
inference(obv,[status(thm),theory(equality)],[1295]),
[iquote('0:Obv:1295.0')] ).
cnf(1301,plain,
( ~ equal(u,u)
| equal(unordered_pair(u,u),singleton(u)) ),
inference(rew,[status(thm),theory(equality)],[1255,1300]),
[iquote('0:Rew:1255.1,1300.0')] ).
cnf(1302,plain,
equal(unordered_pair(u,u),singleton(u)),
inference(obv,[status(thm),theory(equality)],[1301]),
[iquote('0:Obv:1301.0')] ).
cnf(1303,plain,
$false,
inference(unc,[status(thm)],[1302,1]),
[iquote('0:UnC:1302.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU142+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n003.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 : Mon Jun 20 09:41:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.52/0.69
% 0.52/0.69 SPASS V 3.9
% 0.52/0.69 SPASS beiseite: Proof found.
% 0.52/0.69 % SZS status Theorem
% 0.52/0.69 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.52/0.69 SPASS derived 1001 clauses, backtracked 0 clauses, performed 0 splits and kept 310 clauses.
% 0.52/0.69 SPASS allocated 86270 KBytes.
% 0.52/0.69 SPASS spent 0:00:00.33 on the problem.
% 0.52/0.69 0:00:00.03 for the input.
% 0.52/0.69 0:00:00.03 for the FLOTTER CNF translation.
% 0.52/0.69 0:00:00.03 for inferences.
% 0.52/0.69 0:00:00.00 for the backtracking.
% 0.52/0.69 0:00:00.21 for the reduction.
% 0.52/0.69
% 0.52/0.69
% 0.52/0.69 Here is a proof with depth 5, length 19 :
% 0.52/0.69 % SZS output start Refutation
% See solution above
% 0.52/0.69 Formulae used in the proof : t69_enumset1 commutativity_k2_tarski d1_tarski antisymmetry_r2_hidden d2_tarski
% 0.52/0.69
%------------------------------------------------------------------------------