TSTP Solution File: HAL004+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HAL004+1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 255.85s 256.02s
% Output : Refutation 255.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of clauses : 56 ( 14 unt; 0 nHn; 56 RR)
% Number of literals : 144 ( 0 equ; 97 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 22 ( 22 usr; 18 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
surjection(beta),
file('HAL004+1.p',unknown),
[] ).
cnf(6,axiom,
surjection(h),
file('HAL004+1.p',unknown),
[] ).
cnf(7,axiom,
element(skc1,e),
file('HAL004+1.p',unknown),
[] ).
cnf(11,axiom,
morphism(beta,b,c),
file('HAL004+1.p',unknown),
[] ).
cnf(13,axiom,
morphism(delta,e,r),
file('HAL004+1.p',unknown),
[] ).
cnf(15,axiom,
morphism(g,b,e),
file('HAL004+1.p',unknown),
[] ).
cnf(16,axiom,
morphism(h,c,r),
file('HAL004+1.p',unknown),
[] ).
cnf(18,axiom,
commute(beta,h,g,delta),
file('HAL004+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ element(u,v)
| equal(subtract(v,u,u),zero(v)) ),
file('HAL004+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ element(u,v)
| ~ morphism(w,v,x)
| element(apply(w,u),x) ),
file('HAL004+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ element(u,v)
| ~ element(w,v)
| element(subtract(v,w,u),v) ),
file('HAL004+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ element(u,v)
| ~ element(w,v)
| equal(subtract(v,w,subtract(v,w,u)),u) ),
file('HAL004+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ surjection(u)
| ~ element(v,w)
| ~ morphism(u,x,w)
| element(skf10(x,y,z),x) ),
file('HAL004+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ surjection(u)
| ~ element(v,w)
| ~ morphism(u,x,w)
| equal(apply(u,skf10(x,v,u)),v) ),
file('HAL004+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ element(u,v)
| ~ element(w,v)
| ~ morphism(x,v,y)
| equal(apply(x,subtract(v,w,u)),subtract(y,apply(x,w),apply(x,u))) ),
file('HAL004+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ element(u,b)
| ~ element(apply(delta,skc1),r)
| ~ equal(apply(delta,apply(g,u)),apply(delta,skc1))
| ~ equal(apply(h,apply(beta,u)),apply(delta,skc1)) ),
file('HAL004+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ element(u,v)
| ~ morphism(w,x,y)
| ~ morphism(z,v,x)
| ~ morphism(x1,x2,y)
| ~ morphism(x3,v,x2)
| ~ commute(x3,x1,z,w)
| equal(apply(x1,apply(x3,u)),apply(w,apply(z,u))) ),
file('HAL004+1.p',unknown),
[] ).
cnf(56,plain,
( ~ element(u,e)
| equal(subtract(e,u,subtract(e,u,skc1)),skc1) ),
inference(res,[status(thm),theory(equality)],[7,27]),
[iquote('0:Res:7.0,27.1')] ).
cnf(57,plain,
( ~ element(u,e)
| element(subtract(e,u,skc1),e) ),
inference(res,[status(thm),theory(equality)],[7,25]),
[iquote('0:Res:7.0,25.1')] ).
cnf(126,plain,
( ~ element(u,v)
| ~ element(u,v)
| ~ element(u,v)
| element(zero(v),v) ),
inference(spr,[status(thm),theory(equality)],[19,25]),
[iquote('0:SpR:19.1,25.2')] ).
cnf(130,plain,
( ~ element(u,v)
| element(zero(v),v) ),
inference(obv,[status(thm),theory(equality)],[126]),
[iquote('0:Obv:126.1')] ).
cnf(150,plain,
( ~ element(u,e)
| element(apply(delta,u),r) ),
inference(res,[status(thm),theory(equality)],[13,24]),
[iquote('0:Res:13.0,24.1')] ).
cnf(220,plain,
( ~ surjection(h)
| ~ element(u,r)
| element(skf10(c,v,w),c) ),
inference(res,[status(thm),theory(equality)],[16,29]),
[iquote('0:Res:16.0,29.2')] ).
cnf(226,plain,
( ~ surjection(beta)
| ~ element(u,c)
| element(skf10(b,v,w),b) ),
inference(res,[status(thm),theory(equality)],[11,29]),
[iquote('0:Res:11.0,29.2')] ).
cnf(230,plain,
( ~ element(u,c)
| element(skf10(b,v,w),b) ),
inference(ssi,[status(thm)],[226,3]),
[iquote('0:SSi:226.0,3.0')] ).
cnf(236,plain,
( ~ surjection(h)
| ~ element(u,r)
| equal(apply(h,skf10(c,u,h)),u) ),
inference(res,[status(thm),theory(equality)],[16,31]),
[iquote('0:Res:16.0,31.2')] ).
cnf(242,plain,
( ~ surjection(beta)
| ~ element(u,c)
| equal(apply(beta,skf10(b,u,beta)),u) ),
inference(res,[status(thm),theory(equality)],[11,31]),
[iquote('0:Res:11.0,31.2')] ).
cnf(246,plain,
( ~ element(u,c)
| equal(apply(beta,skf10(b,u,beta)),u) ),
inference(ssi,[status(thm)],[242,3]),
[iquote('0:SSi:242.0,3.0')] ).
cnf(332,plain,
( ~ element(u,e)
| ~ element(v,e)
| equal(subtract(r,apply(delta,v),apply(delta,u)),apply(delta,subtract(e,v,u))) ),
inference(res,[status(thm),theory(equality)],[13,34]),
[iquote('0:Res:13.0,34.2')] ).
cnf(569,plain,
( ~ element(u,v)
| ~ morphism(delta,w,x)
| ~ morphism(g,v,w)
| ~ morphism(h,y,x)
| ~ morphism(beta,v,y)
| equal(apply(h,apply(beta,u)),apply(delta,apply(g,u))) ),
inference(res,[status(thm),theory(equality)],[18,44]),
[iquote('0:Res:18.0,44.5')] ).
cnf(790,plain,
( ~ element(u,e)
| ~ element(v,e)
| ~ element(apply(delta,u),r)
| ~ element(apply(delta,v),r)
| element(apply(delta,subtract(e,v,u)),r) ),
inference(spr,[status(thm),theory(equality)],[332,25]),
[iquote('0:SpR:332.2,25.2')] ).
cnf(809,plain,
( ~ element(u,e)
| ~ element(v,e)
| element(apply(delta,subtract(e,v,u)),r) ),
inference(mrr,[status(thm)],[790,150]),
[iquote('0:MRR:790.2,790.3,150.1,150.1')] ).
cnf(967,plain,
( ~ element(u,e)
| ~ element(subtract(e,u,skc1),e)
| ~ element(u,e)
| element(apply(delta,skc1),r) ),
inference(spr,[status(thm),theory(equality)],[56,809]),
[iquote('0:SpR:56.1,809.2')] ).
cnf(982,plain,
( ~ element(subtract(e,u,skc1),e)
| ~ element(u,e)
| element(apply(delta,skc1),r) ),
inference(obv,[status(thm),theory(equality)],[967]),
[iquote('0:Obv:967.0')] ).
cnf(983,plain,
( ~ element(u,e)
| element(apply(delta,skc1),r) ),
inference(mrr,[status(thm)],[982,57]),
[iquote('0:MRR:982.0,57.1')] ).
cnf(989,plain,
element(apply(delta,skc1),r),
inference(res,[status(thm),theory(equality)],[7,983]),
[iquote('0:Res:7.0,983.0')] ).
cnf(2840,plain,
( ~ element(u,v)
| ~ morphism(g,v,e)
| ~ morphism(h,w,r)
| ~ morphism(beta,v,w)
| equal(apply(h,apply(beta,u)),apply(delta,apply(g,u))) ),
inference(res,[status(thm),theory(equality)],[13,569]),
[iquote('0:Res:13.0,569.1')] ).
cnf(19925,plain,
( ~ element(u,b)
| ~ morphism(h,v,r)
| ~ morphism(beta,b,v)
| equal(apply(h,apply(beta,u)),apply(delta,apply(g,u))) ),
inference(res,[status(thm),theory(equality)],[15,2840]),
[iquote('0:Res:15.0,2840.1')] ).
cnf(96984,plain,
( ~ element(u,b)
| ~ morphism(beta,b,c)
| equal(apply(h,apply(beta,u)),apply(delta,apply(g,u))) ),
inference(res,[status(thm),theory(equality)],[16,19925]),
[iquote('0:Res:16.0,19925.1')] ).
cnf(96985,plain,
( ~ element(u,b)
| equal(apply(h,apply(beta,u)),apply(delta,apply(g,u))) ),
inference(mrr,[status(thm)],[96984,11]),
[iquote('0:MRR:96984.1,11.0')] ).
cnf(97216,plain,
( ~ element(u,c)
| ~ element(skf10(b,u,beta),b)
| equal(apply(delta,apply(g,skf10(b,u,beta))),apply(h,u)) ),
inference(spr,[status(thm),theory(equality)],[246,96985]),
[iquote('0:SpR:246.1,96985.1')] ).
cnf(98285,plain,
( ~ element(u,r)
| element(skf10(c,v,w),c) ),
inference(ssi,[status(thm)],[220,6]),
[iquote('0:SSi:220.0,6.0')] ).
cnf(98287,plain,
( ~ element(u,r)
| equal(apply(h,skf10(c,u,h)),u) ),
inference(ssi,[status(thm)],[236,6]),
[iquote('0:SSi:236.0,6.0')] ).
cnf(98371,plain,
( ~ element(u,b)
| ~ element(apply(delta,skc1),r)
| ~ equal(apply(delta,apply(g,u)),apply(delta,skc1))
| ~ equal(apply(delta,apply(g,u)),apply(delta,skc1)) ),
inference(rew,[status(thm),theory(equality)],[96985,37]),
[iquote('0:Rew:96985.1,37.3')] ).
cnf(98372,plain,
( ~ element(u,b)
| ~ element(apply(delta,skc1),r)
| ~ equal(apply(delta,apply(g,u)),apply(delta,skc1)) ),
inference(obv,[status(thm),theory(equality)],[98371]),
[iquote('0:Obv:98371.2')] ).
cnf(98373,plain,
( ~ element(u,b)
| ~ equal(apply(delta,apply(g,u)),apply(delta,skc1)) ),
inference(mrr,[status(thm)],[98372,989]),
[iquote('0:MRR:98372.1,989.0')] ).
cnf(98970,plain,
element(skf10(c,u,v),c),
inference(res,[status(thm),theory(equality)],[989,98285]),
[iquote('0:Res:989.0,98285.0')] ).
cnf(99086,plain,
element(zero(c),c),
inference(res,[status(thm),theory(equality)],[98970,130]),
[iquote('0:Res:98970.0,130.0')] ).
cnf(103627,plain,
( ~ element(u,c)
| equal(apply(delta,apply(g,skf10(b,u,beta))),apply(h,u)) ),
inference(mrr,[status(thm)],[97216,230]),
[iquote('0:MRR:97216.1,230.1')] ).
cnf(104377,plain,
element(skf10(b,u,v),b),
inference(res,[status(thm),theory(equality)],[99086,230]),
[iquote('0:Res:99086.0,230.0')] ).
cnf(112699,plain,
( ~ element(u,c)
| ~ element(skf10(b,u,beta),b)
| ~ equal(apply(h,u),apply(delta,skc1)) ),
inference(spl,[status(thm),theory(equality)],[103627,98373]),
[iquote('0:SpL:103627.1,98373.1')] ).
cnf(112702,plain,
( ~ element(u,c)
| ~ equal(apply(h,u),apply(delta,skc1)) ),
inference(mrr,[status(thm)],[112699,104377]),
[iquote('0:MRR:112699.1,104377.0')] ).
cnf(112742,plain,
( ~ element(u,r)
| ~ element(skf10(c,u,h),c)
| ~ equal(u,apply(delta,skc1)) ),
inference(spl,[status(thm),theory(equality)],[98287,112702]),
[iquote('0:SpL:98287.1,112702.1')] ).
cnf(112744,plain,
( ~ element(u,r)
| ~ equal(u,apply(delta,skc1)) ),
inference(mrr,[status(thm)],[112742,98970]),
[iquote('0:MRR:112742.1,98970.0')] ).
cnf(112749,plain,
~ element(apply(delta,skc1),r),
inference(eqr,[status(thm),theory(equality)],[112744]),
[iquote('0:EqR:112744.1')] ).
cnf(112750,plain,
$false,
inference(mrr,[status(thm)],[112749,989]),
[iquote('0:MRR:112749.0,989.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : HAL004+1 : TPTP v8.1.0. Released v2.6.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 7 21:29:06 EDT 2022
% 0.13/0.35 % CPUTime :
% 255.85/256.02
% 255.85/256.02 SPASS V 3.9
% 255.85/256.02 SPASS beiseite: Proof found.
% 255.85/256.02 % SZS status Theorem
% 255.85/256.02 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 255.85/256.02 SPASS derived 75764 clauses, backtracked 8667 clauses, performed 196 splits and kept 37897 clauses.
% 255.85/256.02 SPASS allocated 212357 KBytes.
% 255.85/256.02 SPASS spent 0:04:00.72 on the problem.
% 255.85/256.02 0:00:00.04 for the input.
% 255.85/256.02 0:00:00.16 for the FLOTTER CNF translation.
% 255.85/256.02 0:00:01.82 for inferences.
% 255.85/256.02 0:0:14.45 for the backtracking.
% 255.85/256.02 0:3:42.59 for the reduction.
% 255.85/256.02
% 255.85/256.02
% 255.85/256.02 Here is a proof with depth 8, length 56 :
% 255.85/256.02 % SZS output start Refutation
% See solution above
% 255.85/256.02 Formulae used in the proof : beta_surjection h_surjection lemma3 beta_morphism delta_morphism g_morphism h_morphism beta_h_g_delta_commute subtract_to_0 morphism subtract_in_domain subtract_cancellation surjection_properties subtract_distribution commute_properties
% 255.85/256.02
%------------------------------------------------------------------------------