TSTP Solution File: HAL003+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HAL003+3 : TPTP v8.1.0. Released v2.6.0.
% 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 12:46:00 EDT 2022
% Result : Theorem 0.69s 0.86s
% Output : Refutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 19 ( 7 unt; 1 nHn; 19 RR)
% Number of literals : 44 ( 0 equ; 30 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(7,axiom,
~ surjection(g),
file('HAL003+3.p',unknown),
[] ).
cnf(15,axiom,
morphism(g,b,e),
file('HAL003+3.p',unknown),
[] ).
cnf(22,axiom,
( ~ element(u,e)
| element(skf17(v),b) ),
file('HAL003+3.p',unknown),
[] ).
cnf(23,axiom,
( ~ element(u,e)
| element(skf16(v),b) ),
file('HAL003+3.p',unknown),
[] ).
cnf(30,axiom,
( ~ morphism(u,v,w)
| surjection(u)
| element(skf22(w,x,y),w) ),
file('HAL003+3.p',unknown),
[] ).
cnf(33,axiom,
( ~ element(u,e)
| equal(apply(g,subtract(b,skf17(u),skf16(u))),u) ),
file('HAL003+3.p',unknown),
[] ).
cnf(35,axiom,
( ~ element(u,v)
| ~ element(w,v)
| element(subtract(v,w,u),v) ),
file('HAL003+3.p',unknown),
[] ).
cnf(42,axiom,
( ~ element(u,v)
| ~ equal(apply(w,u),skf22(x,w,v))
| ~ morphism(w,v,x)
| surjection(w) ),
file('HAL003+3.p',unknown),
[] ).
cnf(62,plain,
( ~ morphism(g,u,v)
| element(skf22(v,w,x),v) ),
inference(res,[status(thm),theory(equality)],[30,7]),
[iquote('0:Res:30.2,7.0')] ).
cnf(65,plain,
element(skf22(e,u,v),e),
inference(res,[status(thm),theory(equality)],[15,62]),
[iquote('0:Res:15.0,62.0')] ).
cnf(68,plain,
element(skf17(u),b),
inference(res,[status(thm),theory(equality)],[65,22]),
[iquote('0:Res:65.0,22.0')] ).
cnf(69,plain,
element(skf16(u),b),
inference(res,[status(thm),theory(equality)],[65,23]),
[iquote('0:Res:65.0,23.0')] ).
cnf(273,plain,
( ~ element(u,e)
| ~ element(subtract(b,skf17(u),skf16(u)),v)
| ~ equal(u,skf22(w,g,v))
| ~ morphism(g,v,w)
| surjection(g) ),
inference(spl,[status(thm),theory(equality)],[33,42]),
[iquote('0:SpL:33.1,42.1')] ).
cnf(275,plain,
( ~ element(u,e)
| ~ element(subtract(b,skf17(u),skf16(u)),v)
| ~ equal(u,skf22(w,g,v))
| ~ morphism(g,v,w) ),
inference(mrr,[status(thm)],[273,7]),
[iquote('0:MRR:273.4,7.0')] ).
cnf(1321,plain,
( ~ element(skf16(u),b)
| ~ element(skf17(u),b)
| ~ element(u,e)
| ~ equal(u,skf22(v,g,b))
| ~ morphism(g,b,v) ),
inference(res,[status(thm),theory(equality)],[35,275]),
[iquote('0:Res:35.2,275.1')] ).
cnf(1322,plain,
( ~ element(u,e)
| ~ equal(u,skf22(v,g,b))
| ~ morphism(g,b,v) ),
inference(mrr,[status(thm)],[1321,69,68]),
[iquote('0:MRR:1321.0,1321.1,69.0,68.0')] ).
cnf(1323,plain,
( ~ element(skf22(u,g,b),e)
| ~ morphism(g,b,u) ),
inference(eqr,[status(thm),theory(equality)],[1322]),
[iquote('0:EqR:1322.1')] ).
cnf(1324,plain,
~ morphism(g,b,e),
inference(res,[status(thm),theory(equality)],[65,1323]),
[iquote('0:Res:65.0,1323.0')] ).
cnf(1325,plain,
$false,
inference(mrr,[status(thm)],[1324,15]),
[iquote('0:MRR:1324.0,15.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HAL003+3 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 7 21:27:21 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.69/0.86
% 0.69/0.86 SPASS V 3.9
% 0.69/0.86 SPASS beiseite: Proof found.
% 0.69/0.86 % SZS status Theorem
% 0.69/0.86 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.69/0.86 SPASS derived 916 clauses, backtracked 0 clauses, performed 6 splits and kept 488 clauses.
% 0.69/0.86 SPASS allocated 99318 KBytes.
% 0.69/0.86 SPASS spent 0:00:00.50 on the problem.
% 0.69/0.86 0:00:00.03 for the input.
% 0.69/0.86 0:00:00.23 for the FLOTTER CNF translation.
% 0.69/0.86 0:00:00.03 for inferences.
% 0.69/0.86 0:00:00.00 for the backtracking.
% 0.69/0.86 0:00:00.17 for the reduction.
% 0.69/0.86
% 0.69/0.86
% 0.69/0.86 Here is a proof with depth 4, length 19 :
% 0.69/0.86 % SZS output start Refutation
% See solution above
% 0.69/0.86 Formulae used in the proof : g_surjection g_morphism lemma12 properties_for_surjection subtract_in_domain
% 0.69/0.86
%------------------------------------------------------------------------------