%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG030-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 18:02:01 EDT 2022
% Result : Unsatisfiable 0.42s 0.61s
% Output : Refutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 40 RR)
% Number of literals : 40 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(ifeq2(u,u,v,w),v),
file('ALG030-10.p',unknown),
[] ).
cnf(2,axiom,
equal(ifeq(u,u,v,w),v),
file('ALG030-10.p',unknown),
[] ).
cnf(3,axiom,
equal(ifeq(sorti1(u),true__dfg,ifeq(sorti1(v),true__dfg,sorti1(op1(v,u)),true__dfg),true__dfg),true__dfg),
file('ALG030-10.p',unknown),
[] ).
cnf(5,axiom,
~ equal(op1(sK1_ax3_V,sK2_ax3_U),op1(sK2_ax3_U,sK1_ax3_V)),
file('ALG030-10.p',unknown),
[] ).
cnf(6,axiom,
equal(sorti1(sK1_ax3_V),true__dfg),
file('ALG030-10.p',unknown),
[] ).
cnf(7,axiom,
equal(sorti1(sK2_ax3_U),true__dfg),
file('ALG030-10.p',unknown),
[] ).
cnf(8,axiom,
equal(ifeq2(sorti2(u),true__dfg,ifeq2(sorti2(v),true__dfg,op2(v,u),op2(u,v)),op2(u,v)),op2(u,v)),
file('ALG030-10.p',unknown),
[] ).
cnf(9,axiom,
equal(ifeq(sorti1(u),true__dfg,sorti2(h(u)),true__dfg),true__dfg),
file('ALG030-10.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('ALG030-10.p',unknown),
[] ).
cnf(11,axiom,
equal(ifeq2(sorti1(u),true__dfg,j(h(u)),u),u),
file('ALG030-10.p',unknown),
[] ).
cnf(21,plain,
equal(ifeq(true__dfg,true__dfg,sorti2(h(sK2_ax3_U)),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[7,9]),
[iquote('0:SpR:7.0,9.0')] ).
cnf(22,plain,
equal(ifeq(true__dfg,true__dfg,sorti2(h(sK1_ax3_V)),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[6,9]),
[iquote('0:SpR:6.0,9.0')] ).
cnf(23,plain,
equal(sorti2(h(sK2_ax3_U)),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,21]),
[iquote('0:Rew:2.0,21.0')] ).
cnf(24,plain,
equal(sorti2(h(sK1_ax3_V)),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,22]),
[iquote('0:Rew:2.0,22.0')] ).
cnf(114,plain,
equal(ifeq(sorti1(u),true__dfg,ifeq(true__dfg,true__dfg,sorti1(op1(sK2_ax3_U,u)),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.0,3.0')] ).
cnf(115,plain,
equal(ifeq(sorti1(u),true__dfg,ifeq(true__dfg,true__dfg,sorti1(op1(sK1_ax3_V,u)),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[6,3]),
[iquote('0:SpR:6.0,3.0')] ).
cnf(118,plain,
equal(ifeq(sorti1(u),true__dfg,sorti1(op1(sK2_ax3_U,u)),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,114]),
[iquote('0:Rew:2.0,114.0')] ).
cnf(119,plain,
equal(ifeq(sorti1(u),true__dfg,sorti1(op1(sK1_ax3_V,u)),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,115]),
[iquote('0:Rew:2.0,115.0')] ).
cnf(236,plain,
equal(ifeq(true__dfg,true__dfg,sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[6,118]),
[iquote('0:SpR:6.0,118.0')] ).
cnf(241,plain,
equal(sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,236]),
[iquote('0:Rew:2.0,236.0')] ).
cnf(293,plain,
equal(ifeq2(true__dfg,true__dfg,j(h(op1(sK2_ax3_U,sK1_ax3_V))),op1(sK2_ax3_U,sK1_ax3_V)),op1(sK2_ax3_U,sK1_ax3_V)),
inference(spr,[status(thm),theory(equality)],[241,11]),
[iquote('0:SpR:241.0,11.0')] ).
cnf(304,plain,
equal(j(h(op1(sK2_ax3_U,sK1_ax3_V))),op1(sK2_ax3_U,sK1_ax3_V)),
inference(rew,[status(thm),theory(equality)],[1,293]),
[iquote('0:Rew:1.0,293.0')] ).
cnf(380,plain,
equal(ifeq2(true__dfg,true__dfg,ifeq2(sorti1(u),true__dfg,op2(h(u),h(sK2_ax3_U)),h(op1(u,sK2_ax3_U))),h(op1(u,sK2_ax3_U))),h(op1(u,sK2_ax3_U))),
inference(spr,[status(thm),theory(equality)],[7,10]),
[iquote('0:SpR:7.0,10.0')] ).
cnf(381,plain,
equal(ifeq2(true__dfg,true__dfg,ifeq2(sorti1(u),true__dfg,op2(h(u),h(sK1_ax3_V)),h(op1(u,sK1_ax3_V))),h(op1(u,sK1_ax3_V))),h(op1(u,sK1_ax3_V))),
inference(spr,[status(thm),theory(equality)],[6,10]),
[iquote('0:SpR:6.0,10.0')] ).
cnf(387,plain,
equal(ifeq2(sorti1(u),true__dfg,op2(h(u),h(sK1_ax3_V)),h(op1(u,sK1_ax3_V))),h(op1(u,sK1_ax3_V))),
inference(rew,[status(thm),theory(equality)],[1,381]),
[iquote('0:Rew:1.0,381.0')] ).
cnf(388,plain,
equal(ifeq2(sorti1(u),true__dfg,op2(h(u),h(sK2_ax3_U)),h(op1(u,sK2_ax3_U))),h(op1(u,sK2_ax3_U))),
inference(rew,[status(thm),theory(equality)],[1,380]),
[iquote('0:Rew:1.0,380.0')] ).
cnf(473,plain,
equal(ifeq(true__dfg,true__dfg,sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[7,119]),
[iquote('0:SpR:7.0,119.0')] ).
cnf(482,plain,
equal(sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,473]),
[iquote('0:Rew:2.0,473.0')] ).
cnf(491,plain,
equal(ifeq2(true__dfg,true__dfg,j(h(op1(sK1_ax3_V,sK2_ax3_U))),op1(sK1_ax3_V,sK2_ax3_U)),op1(sK1_ax3_V,sK2_ax3_U)),
inference(spr,[status(thm),theory(equality)],[482,11]),
[iquote('0:SpR:482.0,11.0')] ).
cnf(506,plain,
equal(j(h(op1(sK1_ax3_V,sK2_ax3_U))),op1(sK1_ax3_V,sK2_ax3_U)),
inference(rew,[status(thm),theory(equality)],[1,491]),
[iquote('0:Rew:1.0,491.0')] ).
cnf(840,plain,
equal(ifeq2(true__dfg,true__dfg,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))),h(op1(sK2_ax3_U,sK1_ax3_V))),
inference(spr,[status(thm),theory(equality)],[7,387]),
[iquote('0:SpR:7.0,387.0')] ).
cnf(859,plain,
equal(op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))),
inference(rew,[status(thm),theory(equality)],[1,840]),
[iquote('0:Rew:1.0,840.0')] ).
cnf(1030,plain,
equal(ifeq2(true__dfg,true__dfg,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))),h(op1(sK1_ax3_V,sK2_ax3_U))),
inference(spr,[status(thm),theory(equality)],[6,388]),
[iquote('0:SpR:6.0,388.0')] ).
cnf(1089,plain,
equal(op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))),
inference(rew,[status(thm),theory(equality)],[1,1030]),
[iquote('0:Rew:1.0,1030.0')] ).
cnf(1538,plain,
equal(ifeq2(sorti2(h(sK2_ax3_U)),true__dfg,ifeq2(sorti2(h(sK1_ax3_V)),true__dfg,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK2_ax3_U,sK1_ax3_V))),h(op1(sK2_ax3_U,sK1_ax3_V))),h(op1(sK2_ax3_U,sK1_ax3_V))),
inference(spr,[status(thm),theory(equality)],[859,8]),
[iquote('0:SpR:859.0,8.0')] ).
cnf(1544,plain,
equal(op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK2_ax3_U,sK1_ax3_V))),
inference(rew,[status(thm),theory(equality)],[1,1538,23,24]),
[iquote('0:Rew:1.0,1538.0,23.0,1538.0,1.0,1538.0,24.0,1538.0')] ).
cnf(1545,plain,
equal(h(op1(sK1_ax3_V,sK2_ax3_U)),h(op1(sK2_ax3_U,sK1_ax3_V))),
inference(rew,[status(thm),theory(equality)],[1089,1544]),
[iquote('0:Rew:1089.0,1544.0')] ).
cnf(1547,plain,
equal(j(h(op1(sK2_ax3_U,sK1_ax3_V))),op1(sK1_ax3_V,sK2_ax3_U)),
inference(rew,[status(thm),theory(equality)],[1545,506]),
[iquote('0:Rew:1545.0,506.0')] ).
cnf(1561,plain,
equal(op1(sK1_ax3_V,sK2_ax3_U),op1(sK2_ax3_U,sK1_ax3_V)),
inference(rew,[status(thm),theory(equality)],[304,1547]),
[iquote('0:Rew:304.0,1547.0')] ).
cnf(1562,plain,
$false,
inference(mrr,[status(thm)],[1561,5]),
[iquote('0:MRR:1561.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG030-10 : TPTP v8.1.0. Released v7.3.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 8 22:54:04 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.42/0.61
% 0.42/0.61 SPASS V 3.9
% 0.42/0.61 SPASS beiseite: Proof found.
% 0.42/0.61 % SZS status Theorem
% 0.42/0.61 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.42/0.61 SPASS derived 887 clauses, backtracked 0 clauses, performed 0 splits and kept 514 clauses.
% 0.42/0.61 SPASS allocated 65380 KBytes.
% 0.42/0.61 SPASS spent 0:00:00.25 on the problem.
% 0.42/0.61 0:00:00.03 for the input.
% 0.42/0.61 0:00:00.00 for the FLOTTER CNF translation.
% 0.42/0.61 0:00:00.01 for inferences.
% 0.42/0.61 0:00:00.00 for the backtracking.
% 0.42/0.61 0:00:00.18 for the reduction.
% 0.42/0.61
% 0.42/0.61
% 0.42/0.61 Here is a proof with depth 3, length 40 :
% 0.42/0.61 % SZS output start Refutation
% See solution above
% 0.42/0.61 Formulae used in the proof : ifeq_axiom ifeq_axiom_001 ax1 ax3_2 ax3_1 ax3 ax4 co1 co1_1 co1_2
% 0.42/0.61
%------------------------------------------------------------------------------