%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG069-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 14 18:02:12 EDT 2022
% Result : Unsatisfiable 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 25 RR)
% Number of literals : 25 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(ifeq2(u,u,v,w),v),
file('ALG069-10.p',unknown),
[] ).
cnf(2,axiom,
equal(ifeq(u,u,v,w),v),
file('ALG069-10.p',unknown),
[] ).
cnf(5,axiom,
equal(ifeq(sorti1(u),true__dfg,sorti1(sK2_ax3_V(u)),true__dfg),true__dfg),
file('ALG069-10.p',unknown),
[] ).
cnf(6,axiom,
equal(ifeq2(sorti1(u),true__dfg,op1(sK2_ax3_V(u),sK2_ax3_V(u)),u),u),
file('ALG069-10.p',unknown),
[] ).
cnf(7,axiom,
~ equal(tuple(op2(u,u),sorti2(u)),tuple(sK1_ax4_U,true__dfg)),
file('ALG069-10.p',unknown),
[] ).
cnf(8,axiom,
equal(sorti2(sK1_ax4_U),true__dfg),
file('ALG069-10.p',unknown),
[] ).
cnf(9,axiom,
equal(ifeq(sorti1(u),true__dfg,sorti2(h(u)),true__dfg),true__dfg),
file('ALG069-10.p',unknown),
[] ).
cnf(10,axiom,
equal(ifeq2(sorti1(u),true__dfg,ifeq2(sorti1(v),true__dfg,op2(h(v),h(u)),h(op1(v,u))),h(op1(v,u))),h(op1(v,u))),
file('ALG069-10.p',unknown),
[] ).
cnf(12,axiom,
equal(ifeq(sorti2(u),true__dfg,sorti1(j(u)),true__dfg),true__dfg),
file('ALG069-10.p',unknown),
[] ).
cnf(14,axiom,
equal(ifeq2(sorti2(u),true__dfg,h(j(u)),u),u),
file('ALG069-10.p',unknown),
[] ).
cnf(19,plain,
equal(ifeq(true__dfg,true__dfg,sorti1(j(sK1_ax4_U)),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[8,12]),
[iquote('0:SpR:8.0,12.0')] ).
cnf(20,plain,
equal(sorti1(j(sK1_ax4_U)),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,19]),
[iquote('0:Rew:2.0,19.0')] ).
cnf(43,plain,
equal(ifeq(true__dfg,true__dfg,sorti1(sK2_ax3_V(j(sK1_ax4_U))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[20,5]),
[iquote('0:SpR:20.0,5.0')] ).
cnf(45,plain,
equal(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,43]),
[iquote('0:Rew:2.0,43.0')] ).
cnf(47,plain,
equal(ifeq(true__dfg,true__dfg,sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[45,9]),
[iquote('0:SpR:45.0,9.0')] ).
cnf(52,plain,
equal(sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,47]),
[iquote('0:Rew:2.0,47.0')] ).
cnf(74,plain,
equal(ifeq2(true__dfg,true__dfg,h(j(sK1_ax4_U)),sK1_ax4_U),sK1_ax4_U),
inference(spr,[status(thm),theory(equality)],[8,14]),
[iquote('0:SpR:8.0,14.0')] ).
cnf(78,plain,
equal(h(j(sK1_ax4_U)),sK1_ax4_U),
inference(rew,[status(thm),theory(equality)],[1,74]),
[iquote('0:Rew:1.0,74.0')] ).
cnf(174,plain,
~ equal(tuple(op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),true__dfg),tuple(sK1_ax4_U,true__dfg)),
inference(spl,[status(thm),theory(equality)],[52,7]),
[iquote('0:SpL:52.0,7.0')] ).
cnf(205,plain,
equal(ifeq2(true__dfg,true__dfg,op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))),j(sK1_ax4_U)),j(sK1_ax4_U)),
inference(spr,[status(thm),theory(equality)],[20,6]),
[iquote('0:SpR:20.0,6.0')] ).
cnf(211,plain,
equal(op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))),j(sK1_ax4_U)),
inference(rew,[status(thm),theory(equality)],[1,205]),
[iquote('0:Rew:1.0,205.0')] ).
cnf(573,plain,
equal(ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true__dfg,ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true__dfg,op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),h(j(sK1_ax4_U))),h(j(sK1_ax4_U))),h(j(sK1_ax4_U))),
inference(spr,[status(thm),theory(equality)],[211,10]),
[iquote('0:SpR:211.0,10.0')] ).
cnf(606,plain,
equal(op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),sK1_ax4_U),
inference(rew,[status(thm),theory(equality)],[1,573,45,78]),
[iquote('0:Rew:1.0,573.0,1.0,573.0,45.0,573.0,78.0,573.0')] ).
cnf(607,plain,
~ equal(tuple(sK1_ax4_U,true__dfg),tuple(sK1_ax4_U,true__dfg)),
inference(rew,[status(thm),theory(equality)],[606,174]),
[iquote('0:Rew:606.0,174.0')] ).
cnf(608,plain,
$false,
inference(obv,[status(thm),theory(equality)],[607]),
[iquote('0:Obv:607.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG069-10 : TPTP v8.1.0. Released v7.3.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jun 8 08:17:46 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.20/0.49
% 0.20/0.49 SPASS V 3.9
% 0.20/0.49 SPASS beiseite: Proof found.
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.49 SPASS derived 331 clauses, backtracked 0 clauses, performed 0 splits and kept 208 clauses.
% 0.20/0.49 SPASS allocated 64246 KBytes.
% 0.20/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.20/0.49 0:00:00.03 for the input.
% 0.20/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.49 0:00:00.01 for inferences.
% 0.20/0.49 0:00:00.00 for the backtracking.
% 0.20/0.49 0:00:00.08 for the reduction.
% 0.20/0.49
% 0.20/0.49
% 0.20/0.49 Here is a proof with depth 4, length 25 :
% 0.20/0.49 % SZS output start Refutation
% See solution above
% 0.20/0.49 Formulae used in the proof : ifeq_axiom ifeq_axiom_001 ax3_1 ax3 ax4_1 ax4 co1 co1_1 co1_3 co1_5
% 0.20/0.49
%------------------------------------------------------------------------------