TSTP Solution File: SYN116-10 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SYN116-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 12:18:48 EDT 2022
% Result : Unsatisfiable 1.03s 1.19s
% Output : Refutation 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 39 RR)
% Number of literals : 39 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(ifeq(u,u,v,w),v),
file('SYN116-10.p',unknown),
[] ).
cnf(4,axiom,
equal(n0(d,e),true__dfg),
file('SYN116-10.p',unknown),
[] ).
cnf(15,axiom,
equal(p0(b,u),true__dfg),
file('SYN116-10.p',unknown),
[] ).
cnf(27,axiom,
equal(n0(d,c),true__dfg),
file('SYN116-10.p',unknown),
[] ).
cnf(40,axiom,
equal(ifeq(n0(u,v),true__dfg,k1(v),true__dfg),true__dfg),
file('SYN116-10.p',unknown),
[] ).
cnf(41,axiom,
equal(ifeq(n0(u,v),true__dfg,l1(v,v),true__dfg),true__dfg),
file('SYN116-10.p',unknown),
[] ).
cnf(122,axiom,
equal(ifeq(p0(u,v),true__dfg,p1(v,v,v),true__dfg),true__dfg),
file('SYN116-10.p',unknown),
[] ).
cnf(173,axiom,
equal(ifeq(p1(u,v,w),true__dfg,n2(w),true__dfg),true__dfg),
file('SYN116-10.p',unknown),
[] ).
cnf(210,axiom,
equal(ifeq(n2(u),true__dfg,ifeq(k1(e),true__dfg,p2(u,u,u),true__dfg),true__dfg),true__dfg),
file('SYN116-10.p',unknown),
[] ).
cnf(278,axiom,
equal(ifeq(n2(u),true__dfg,p3(u,u,u),true__dfg),true__dfg),
file('SYN116-10.p',unknown),
[] ).
cnf(301,axiom,
equal(ifeq(p2(u,v,w),true__dfg,r3(u,w,u),true__dfg),true__dfg),
file('SYN116-10.p',unknown),
[] ).
cnf(331,axiom,
equal(ifeq(p3(u,v,w),true__dfg,ifeq(l1(x,v),true__dfg,s4(x),true__dfg),true__dfg),true__dfg),
file('SYN116-10.p',unknown),
[] ).
cnf(332,axiom,
equal(ifeq(s4(u),true__dfg,ifeq(r3(v,w,w),true__dfg,k5(w),true__dfg),true__dfg),true__dfg),
file('SYN116-10.p',unknown),
[] ).
cnf(363,axiom,
~ equal(k5(b),true__dfg),
file('SYN116-10.p',unknown),
[] ).
cnf(502,plain,
equal(ifeq(true__dfg,true__dfg,k1(e),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[4,40]),
[iquote('0:SpR:4.0,40.0')] ).
cnf(512,plain,
equal(k1(e),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,502]),
[iquote('0:Rew:1.0,502.0')] ).
cnf(513,plain,
equal(ifeq(n2(u),true__dfg,ifeq(true__dfg,true__dfg,p2(u,u,u),true__dfg),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[512,210]),
[iquote('0:Rew:512.0,210.0')] ).
cnf(523,plain,
equal(ifeq(n2(u),true__dfg,p2(u,u,u),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,513]),
[iquote('0:Rew:1.0,513.0')] ).
cnf(741,plain,
equal(ifeq(true__dfg,true__dfg,l1(c,c),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[27,41]),
[iquote('0:SpR:27.0,41.0')] ).
cnf(749,plain,
equal(l1(c,c),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,741]),
[iquote('0:Rew:1.0,741.0')] ).
cnf(1233,plain,
equal(ifeq(true__dfg,true__dfg,p1(u,u,u),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[15,122]),
[iquote('0:SpR:15.0,122.0')] ).
cnf(1235,plain,
equal(p1(u,u,u),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,1233]),
[iquote('0:Rew:1.0,1233.0')] ).
cnf(1271,plain,
equal(ifeq(true__dfg,true__dfg,n2(u),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[1235,173]),
[iquote('0:SpR:1235.0,173.0')] ).
cnf(1278,plain,
equal(n2(u),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,1271]),
[iquote('0:Rew:1.0,1271.0')] ).
cnf(1281,plain,
equal(ifeq(true__dfg,true__dfg,p3(u,u,u),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1278,278]),
[iquote('0:Rew:1278.0,278.0')] ).
cnf(1284,plain,
equal(ifeq(true__dfg,true__dfg,p2(u,u,u),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1278,523]),
[iquote('0:Rew:1278.0,523.0')] ).
cnf(1298,plain,
equal(p3(u,u,u),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,1281]),
[iquote('0:Rew:1.0,1281.0')] ).
cnf(1320,plain,
equal(p2(u,u,u),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,1284]),
[iquote('0:Rew:1.0,1284.0')] ).
cnf(1928,plain,
equal(ifeq(true__dfg,true__dfg,r3(u,u,u),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[1320,301]),
[iquote('0:SpR:1320.0,301.0')] ).
cnf(1931,plain,
equal(r3(u,u,u),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,1928]),
[iquote('0:Rew:1.0,1928.0')] ).
cnf(2188,plain,
equal(ifeq(s4(u),true__dfg,ifeq(true__dfg,true__dfg,k5(v),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[1931,332]),
[iquote('0:SpR:1931.0,332.0')] ).
cnf(2189,plain,
equal(ifeq(s4(u),true__dfg,k5(v),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,2188]),
[iquote('0:Rew:1.0,2188.0')] ).
cnf(2994,plain,
equal(ifeq(true__dfg,true__dfg,ifeq(l1(u,v),true__dfg,s4(u),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[1298,331]),
[iquote('0:SpR:1298.0,331.0')] ).
cnf(2995,plain,
equal(ifeq(l1(u,v),true__dfg,s4(u),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,2994]),
[iquote('0:Rew:1.0,2994.0')] ).
cnf(3048,plain,
equal(ifeq(true__dfg,true__dfg,s4(c),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[749,2995]),
[iquote('0:SpR:749.0,2995.0')] ).
cnf(3053,plain,
equal(s4(c),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,3048]),
[iquote('0:Rew:1.0,3048.0')] ).
cnf(3093,plain,
equal(ifeq(true__dfg,true__dfg,k5(u),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[3053,2189]),
[iquote('0:SpR:3053.0,2189.0')] ).
cnf(3097,plain,
equal(k5(u),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,3093]),
[iquote('0:Rew:1.0,3093.0')] ).
cnf(3098,plain,
$false,
inference(unc,[status(thm)],[3097,363]),
[iquote('0:UnC:3097.0,363.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN116-10 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n012.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 Jul 11 19:45:12 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.03/1.19
% 1.03/1.19 SPASS V 3.9
% 1.03/1.19 SPASS beiseite: Proof found.
% 1.03/1.19 % SZS status Theorem
% 1.03/1.19 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.03/1.19 SPASS derived 1955 clauses, backtracked 0 clauses, performed 0 splits and kept 802 clauses.
% 1.03/1.19 SPASS allocated 66116 KBytes.
% 1.03/1.19 SPASS spent 0:00:00.81 on the problem.
% 1.03/1.19 0:00:00.05 for the input.
% 1.03/1.19 0:00:00.00 for the FLOTTER CNF translation.
% 1.03/1.19 0:00:00.04 for inferences.
% 1.03/1.19 0:00:00.00 for the backtracking.
% 1.03/1.19 0:00:00.63 for the reduction.
% 1.03/1.19
% 1.03/1.19
% 1.03/1.19 Here is a proof with depth 3, length 39 :
% 1.03/1.19 % SZS output start Refutation
% See solution above
% 1.03/1.19 Formulae used in the proof : ifeq_axiom axiom_3 axiom_14 axiom_26 rule_001 rule_002 rule_085 rule_137 rule_174 rule_244 rule_267 rule_299 rule_300 prove_this
% 1.03/1.19
%------------------------------------------------------------------------------