%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : PUZ164-2 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:33:05 PM UTC 2026
% Result : Unsatisfiable 8.66s 1.73s
% Output : CNFRefutation 8.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 22
% Syntax : Number of formulae : 145 ( 145 unt; 8 def)
% Number of atoms : 403 ( 144 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 9 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-5 aty)
% Number of variables : 327 ( 0 sgn 327 !; 0 ?; 274 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
eq('0','0') = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule1) ).
fof(f2,axiom,
! [X0] : eq('0',s(X0)) = false,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule2) ).
fof(f5,axiom,
! [X0,X1] : eq(s(X0),s(X1)) = eq(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule4) ).
fof(f8,axiom,
! [X0] : or(false,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule6) ).
fof(f9,axiom,
! [X0] : union(empty,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule7) ).
fof(f10,axiom,
! [X2,X3,X0,X1] : union(edge(X0,X1,X2),X3) = edge(X0,X1,union(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule8) ).
fof(f11,axiom,
! [X2,X0,X1] : reach(X0,X1,empty,X2) = false,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule9) ).
fof(f12,plain,
! [X2,X0,X1] : false = reach(X0,X1,empty,X2),
inference(reorient_equations,[],[f11]) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X4,X5] : reach(X0,X1,edge(X2,X3,X4),X5) = if_reach_1(eq(X0,X2),X0,X1,edge(X2,X3,X4),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule10) ).
fof(f14,axiom,
! [X2,X3,X0,X1,X4,X5] : if_reach_1(true,X0,X1,edge(X2,X3,X4),X5) = if_reach_2(eq(X1,X3),X0,X1,edge(X2,X3,X4),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule11) ).
fof(f15,axiom,
! [X2,X3,X0,X1,X4,X5] : if_reach_2(true,X0,X1,edge(X2,X3,X4),X5) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule12) ).
fof(f16,plain,
! [X2,X3,X0,X1,X4,X5] : true = if_reach_2(true,X0,X1,edge(X2,X3,X4),X5),
inference(reorient_equations,[],[f15]) ).
fof(f17,axiom,
! [X2,X3,X0,X1,X4,X5] : if_reach_2(false,X0,X1,edge(X2,X3,X4),X5) = or(reach(X0,X1,X4,X5),reach(X3,X1,union(X4,X5),empty)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule13) ).
fof(f18,axiom,
! [X2,X3,X0,X1,X4,X5] : if_reach_1(false,X0,X1,edge(X2,X3,X4),X5) = reach(X0,X1,X4,edge(X2,X3,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule14) ).
fof(f19,axiom,
g = edge('0',s('0'),edge(s('0'),s(s('0')),edge(s(s('0')),s(s(s('0'))),edge(s(s(s('0'))),'0',empty)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',graph) ).
fof(f20,negated_conjecture,
! [X0] : reach(X0,X0,g,empty) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
fof(f21,plain,
! [X0] : true != reach(X0,X0,g,empty),
inference(reorient_equations,[],[f20]) ).
tcf(c_65,plain,
eq('0','0') = true,
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,plain,
! [X0: $i] : eq('0',s(X0)) = false,
inference(cnf_transformation,[],[f2]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : eq(s(X0),s(X1)) = eq(X0,X1),
inference(cnf_transformation,[],[f5]) ).
tcf(c_70,plain,
! [X0: $i] : or(false,X0) = X0,
inference(cnf_transformation,[],[f8]) ).
tcf(c_71,plain,
! [X0: $i] : union(empty,X0) = X0,
inference(cnf_transformation,[],[f9]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : union(edge(X0,X1,X2),X3) = edge(X0,X1,union(X2,X3)),
inference(cnf_transformation,[],[f10]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] : reach(X0,X1,empty,X2) = false,
inference(cnf_transformation,[],[f12]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : if_reach_1(eq(X0,X1),X0,X2,edge(X1,X3,X4),X5) = reach(X0,X2,edge(X1,X3,X4),X5),
inference(cnf_transformation,[],[f13]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : if_reach_2(eq(X0,X1),X2,X0,edge(X3,X1,X4),X5) = if_reach_1(true,X2,X0,edge(X3,X1,X4),X5),
inference(cnf_transformation,[],[f14]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : if_reach_2(true,X0,X1,edge(X2,X3,X4),X5) = true,
inference(cnf_transformation,[],[f16]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : or(reach(X0,X1,X2,X3),reach(X4,X1,union(X2,X3),empty)) = if_reach_2(false,X0,X1,edge(X5,X4,X2),X3),
inference(cnf_transformation,[],[f17]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : if_reach_1(false,X0,X1,edge(X2,X3,X4),X5) = reach(X0,X1,X4,edge(X2,X3,X5)),
inference(cnf_transformation,[],[f18]) ).
tcf(c_79,plain,
edge('0',s('0'),edge(s('0'),s(s('0')),edge(s(s('0')),s(s(s('0'))),edge(s(s(s('0'))),'0',empty)))) = g,
inference(cnf_transformation,[],[f19]) ).
tcf(c_80,negated_conjecture,
! [X0: $i] : reach(X0,X0,g,empty) != true,
inference(cnf_transformation,[],[f21]) ).
tcf(c_137,definition,
iPr_def_10 = s('0'),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_138,definition,
iPr_def_11 = s(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_139,definition,
iPr_def_12 = s(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_140,definition,
iPr_def_13 = edge(iPr_def_12,'0',empty),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_141,definition,
iPr_def_14 = edge(iPr_def_11,iPr_def_12,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_142,definition,
iPr_def_15 = edge(iPr_def_10,iPr_def_11,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_143,definition,
iPr_def_16 = edge('0',iPr_def_10,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_144,definition,
iPr_def_17 = eq('0','0'),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_145,negated_conjecture,
! [X0: $i] : reach(X0,X0,g,empty) != true,
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_146,plain,
iPr_def_16 = g,
inference(demodulation,[status(thm)],[c_79,c_140,c_139,c_141,c_138,c_142,c_137,c_143]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : if_reach_1(false,X0,X1,edge(X2,X3,X4),X5) = reach(X0,X1,X4,edge(X2,X3,X5)),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : or(reach(X0,X1,X2,X3),reach(X4,X1,union(X2,X3),empty)) = if_reach_2(false,X0,X1,edge(X5,X4,X2),X3),
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : if_reach_2(true,X0,X1,edge(X2,X3,X4),X5) = true,
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : if_reach_2(eq(X0,X1),X2,X0,edge(X3,X1,X4),X5) = if_reach_1(true,X2,X0,edge(X3,X1,X4),X5),
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : if_reach_1(eq(X0,X1),X0,X2,edge(X1,X3,X4),X5) = reach(X0,X2,edge(X1,X3,X4),X5),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i,X2: $i] : reach(X0,X1,empty,X2) = false,
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : union(edge(X0,X1,X2),X3) = edge(X0,X1,union(X2,X3)),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_154,plain,
! [X0: $i] : union(empty,X0) = X0,
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_155,plain,
! [X0: $i] : or(false,X0) = X0,
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i] : eq(s(X0),s(X1)) = eq(X0,X1),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_159,plain,
! [X0: $i] : eq('0',s(X0)) = false,
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_160,plain,
iPr_def_17 = true,
inference(demodulation,[status(thm)],[c_65,c_144]) ).
tcf(c_283,plain,
! [X0: $i] : reach(X0,X0,iPr_def_16,empty) != iPr_def_17,
inference(demodulation,[status(thm)],[c_145,c_146,c_160]) ).
tcf(c_284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : if_reach_2(iPr_def_17,X0,X1,edge(X2,X3,X4),X5) = iPr_def_17,
inference(demodulation,[status(thm)],[c_149,c_160]) ).
tcf(c_285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : if_reach_2(eq(X0,X1),X2,X0,edge(X3,X1,X4),X5) = if_reach_1(iPr_def_17,X2,X0,edge(X3,X1,X4),X5),
inference(demodulation,[status(thm)],[c_150,c_160]) ).
tcf(c_297,plain,
eq('0',iPr_def_10) = false,
inference(superposition,[status(thm)],[c_137,c_159]) ).
tcf(c_298,plain,
eq('0',iPr_def_11) = false,
inference(superposition,[status(thm)],[c_138,c_159]) ).
tcf(c_299,plain,
eq('0',iPr_def_12) = false,
inference(superposition,[status(thm)],[c_139,c_159]) ).
tcf(c_303,plain,
! [X0: $i] : eq(s(X0),iPr_def_10) = eq(X0,'0'),
inference(superposition,[status(thm)],[c_137,c_157]) ).
tcf(c_304,plain,
! [X0: $i] : eq(s(X0),iPr_def_11) = eq(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_138,c_157]) ).
tcf(c_305,plain,
! [X0: $i] : eq(s(X0),iPr_def_12) = eq(X0,iPr_def_11),
inference(superposition,[status(thm)],[c_139,c_157]) ).
tcf(c_310,plain,
! [X0: $i,X1: $i,X2: $i] : union(edge(X0,X1,empty),X2) = edge(X0,X1,X2),
inference(superposition,[status(thm)],[c_154,c_153]) ).
tcf(c_313,plain,
! [X0: $i,X1: $i,X2: $i] : reach(X0,X1,empty,edge(iPr_def_12,'0',X2)) = if_reach_1(false,X0,X1,iPr_def_13,X2),
inference(superposition,[status(thm)],[c_140,c_147]) ).
tcf(c_317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_1(iPr_def_17,'0',X0,edge('0',X1,X2),X3) = reach('0',X0,edge('0',X1,X2),X3),
inference(superposition,[status(thm)],[c_144,c_151]) ).
tcf(c_318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : if_reach_1(false,'0',X0,edge(s(X1),X2,X3),X4) = reach('0',X0,edge(s(X1),X2,X3),X4),
inference(superposition,[status(thm)],[c_159,c_151]) ).
tcf(c_320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : if_reach_1(eq(X0,X1),s(X0),X2,edge(s(X1),X3,X4),X5) = reach(s(X0),X2,edge(s(X1),X3,X4),X5),
inference(superposition,[status(thm)],[c_157,c_151]) ).
tcf(c_322,plain,
! [X0: $i,X1: $i,X2: $i] : if_reach_1(eq(X0,iPr_def_12),X0,X1,iPr_def_13,X2) = reach(X0,X1,iPr_def_13,X2),
inference(superposition,[status(thm)],[c_140,c_151]) ).
tcf(c_323,plain,
! [X0: $i,X1: $i,X2: $i] : if_reach_1(eq(X0,iPr_def_11),X0,X1,iPr_def_14,X2) = reach(X0,X1,iPr_def_14,X2),
inference(superposition,[status(thm)],[c_141,c_151]) ).
tcf(c_324,plain,
! [X0: $i,X1: $i,X2: $i] : if_reach_1(eq(X0,iPr_def_10),X0,X1,iPr_def_15,X2) = reach(X0,X1,iPr_def_15,X2),
inference(superposition,[status(thm)],[c_142,c_151]) ).
tcf(c_326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_1(iPr_def_17,X0,'0',edge(X1,'0',X2),X3) = if_reach_2(iPr_def_17,X0,'0',edge(X1,'0',X2),X3),
inference(superposition,[status(thm)],[c_144,c_285]) ).
tcf(c_332,plain,
! [X0: $i,X1: $i,X2: $i] : if_reach_2(eq(X0,iPr_def_12),X1,X0,iPr_def_14,X2) = if_reach_1(iPr_def_17,X1,X0,iPr_def_14,X2),
inference(superposition,[status(thm)],[c_141,c_285]) ).
tcf(c_333,plain,
! [X0: $i,X1: $i,X2: $i] : if_reach_2(eq(X0,iPr_def_11),X1,X0,iPr_def_15,X2) = if_reach_1(iPr_def_17,X1,X0,iPr_def_15,X2),
inference(superposition,[status(thm)],[c_142,c_285]) ).
tcf(c_334,plain,
! [X0: $i,X1: $i,X2: $i] : if_reach_2(eq(X0,iPr_def_10),X1,X0,iPr_def_16,X2) = if_reach_1(iPr_def_17,X1,X0,iPr_def_16,X2),
inference(superposition,[status(thm)],[c_143,c_285]) ).
tcf(c_339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : if_reach_2(false,X0,X1,edge(X2,X3,X4),X5) = if_reach_2(false,X0,X1,edge(X6,X3,X4),X5),
inference(superposition,[status(thm)],[c_148,c_148]) ).
tcf(c_340,plain,
! [X0: $i,X1: $i,X2: $i] : if_reach_1(false,X0,X1,iPr_def_13,X2) = false,
inference(demodulation,[status(thm)],[c_313,c_152]) ).
tcf(c_342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_1(iPr_def_17,X0,'0',edge(X1,'0',X2),X3) = iPr_def_17,
inference(demodulation,[status(thm)],[c_326,c_284]) ).
tcf(c_344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : reach('0',X0,edge(s(X1),X2,X3),X4) = reach('0',X0,X3,edge(s(X1),X2,X4)),
inference(demodulation,[status(thm)],[c_318,c_147]) ).
tcf(c_465,plain,
eq('0','0') = eq(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_137,c_303]) ).
tcf(c_470,plain,
eq('0',iPr_def_10) = eq(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_137,c_304]) ).
tcf(c_471,plain,
eq(iPr_def_10,iPr_def_10) = eq(iPr_def_11,iPr_def_11),
inference(superposition,[status(thm)],[c_138,c_304]) ).
tcf(c_475,plain,
eq('0',iPr_def_11) = eq(iPr_def_10,iPr_def_12),
inference(superposition,[status(thm)],[c_137,c_305]) ).
tcf(c_476,plain,
eq(iPr_def_10,iPr_def_11) = eq(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_138,c_305]) ).
tcf(c_477,plain,
eq(iPr_def_11,iPr_def_11) = eq(iPr_def_12,iPr_def_12),
inference(superposition,[status(thm)],[c_139,c_305]) ).
tcf(c_480,plain,
! [X0: $i] : edge(iPr_def_12,'0',X0) = union(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_140,c_310]) ).
tcf(c_491,plain,
! [X0: $i,X1: $i] : if_reach_1(false,'0',X0,iPr_def_13,X1) = reach('0',X0,iPr_def_13,X1),
inference(superposition,[status(thm)],[c_299,c_322]) ).
tcf(c_516,plain,
! [X0: $i,X1: $i] : if_reach_1(iPr_def_17,X0,'0',iPr_def_14,X1) = if_reach_2(false,X0,'0',iPr_def_14,X1),
inference(superposition,[status(thm)],[c_299,c_332]) ).
tcf(c_518,plain,
! [X0: $i,X1: $i] : if_reach_1(iPr_def_17,X0,'0',iPr_def_15,X1) = if_reach_2(false,X0,'0',iPr_def_15,X1),
inference(superposition,[status(thm)],[c_298,c_333]) ).
tcf(c_520,plain,
! [X0: $i,X1: $i] : if_reach_1(iPr_def_17,X0,'0',iPr_def_16,X1) = if_reach_2(false,X0,'0',iPr_def_16,X1),
inference(superposition,[status(thm)],[c_297,c_334]) ).
tcf(c_527,plain,
! [X0: $i,X1: $i] : if_reach_1(iPr_def_17,'0',X0,iPr_def_16,X1) = reach('0',X0,iPr_def_16,X1),
inference(superposition,[status(thm)],[c_143,c_317]) ).
tcf(c_544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_2(false,X0,X1,edge(X2,iPr_def_12,iPr_def_13),X3) = if_reach_2(false,X0,X1,iPr_def_14,X3),
inference(superposition,[status(thm)],[c_141,c_339]) ).
tcf(c_545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_2(false,X0,X1,edge(X2,iPr_def_11,iPr_def_14),X3) = if_reach_2(false,X0,X1,iPr_def_15,X3),
inference(superposition,[status(thm)],[c_142,c_339]) ).
tcf(c_546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_2(false,X0,X1,edge(X2,iPr_def_10,iPr_def_15),X3) = if_reach_2(false,X0,X1,iPr_def_16,X3),
inference(superposition,[status(thm)],[c_143,c_339]) ).
tcf(c_577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : reach('0',X0,edge(iPr_def_10,X1,X2),X3) = reach('0',X0,X2,edge(iPr_def_10,X1,X3)),
inference(superposition,[status(thm)],[c_137,c_344]) ).
tcf(c_578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : reach('0',X0,edge(iPr_def_11,X1,X2),X3) = reach('0',X0,X2,edge(iPr_def_11,X1,X3)),
inference(superposition,[status(thm)],[c_138,c_344]) ).
tcf(c_672,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_1(false,s('0'),X0,edge(s(iPr_def_10),X1,X2),X3) = reach(s('0'),X0,edge(s(iPr_def_10),X1,X2),X3),
inference(superposition,[status(thm)],[c_297,c_320]) ).
tcf(c_764,plain,
eq(iPr_def_10,iPr_def_12) = false,
inference(demodulation,[status(thm)],[c_475,c_298]) ).
tcf(c_765,plain,
eq(iPr_def_10,iPr_def_11) = false,
inference(demodulation,[status(thm)],[c_470,c_297]) ).
tcf(c_768,plain,
eq(iPr_def_10,iPr_def_10) = iPr_def_17,
inference(demodulation,[status(thm)],[c_465,c_144]) ).
tcf(c_769,plain,
! [X0: $i,X1: $i] : reach('0',X0,iPr_def_13,X1) = false,
inference(demodulation,[status(thm)],[c_491,c_340]) ).
tcf(c_794,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : reach(iPr_def_10,X0,edge(iPr_def_11,X1,X2),X3) = reach(iPr_def_10,X0,X2,edge(iPr_def_11,X1,X3)),
inference(demodulation,[status(thm)],[c_672,c_147,c_137,c_138]) ).
tcf(c_1185,plain,
! [X0: $i,X1: $i] : if_reach_1(false,iPr_def_10,X0,iPr_def_13,X1) = reach(iPr_def_10,X0,iPr_def_13,X1),
inference(superposition,[status(thm)],[c_764,c_322]) ).
tcf(c_1217,plain,
! [X0: $i,X1: $i] : if_reach_1(iPr_def_17,iPr_def_10,X0,iPr_def_15,X1) = reach(iPr_def_10,X0,iPr_def_15,X1),
inference(superposition,[status(thm)],[c_768,c_324]) ).
tcf(c_1218,plain,
eq(iPr_def_11,iPr_def_11) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_471,c_768]) ).
tcf(c_1226,plain,
! [X0: $i,X1: $i] : if_reach_1(iPr_def_17,iPr_def_11,X0,iPr_def_14,X1) = reach(iPr_def_11,X0,iPr_def_14,X1),
inference(superposition,[status(thm)],[c_1218,c_323]) ).
tcf(c_1236,plain,
eq(iPr_def_11,iPr_def_12) = false,
inference(light_normalisation,[status(thm)],[c_476,c_765]) ).
tcf(c_1244,plain,
! [X0: $i,X1: $i] : if_reach_1(false,iPr_def_11,X0,iPr_def_13,X1) = reach(iPr_def_11,X0,iPr_def_13,X1),
inference(superposition,[status(thm)],[c_1236,c_322]) ).
tcf(c_1245,plain,
eq(iPr_def_12,iPr_def_12) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_477,c_1218]) ).
tcf(c_1251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_1(iPr_def_17,iPr_def_12,X0,edge(iPr_def_12,X1,X2),X3) = reach(iPr_def_12,X0,edge(iPr_def_12,X1,X2),X3),
inference(superposition,[status(thm)],[c_1245,c_151]) ).
tcf(c_1266,plain,
union(iPr_def_13,empty) = iPr_def_13,
inference(superposition,[status(thm)],[c_480,c_140]) ).
tcf(c_1316,plain,
! [X0: $i] : if_reach_2(false,'0','0',iPr_def_16,X0) = reach('0','0',iPr_def_16,X0),
inference(superposition,[status(thm)],[c_527,c_520]) ).
tcf(c_1399,plain,
! [X0: $i,X1: $i] : reach('0',X0,iPr_def_14,edge(iPr_def_10,iPr_def_11,X1)) = reach('0',X0,iPr_def_15,X1),
inference(superposition,[status(thm)],[c_142,c_577]) ).
tcf(c_1402,plain,
! [X0: $i,X1: $i] : reach('0',X0,iPr_def_13,edge(iPr_def_11,iPr_def_12,X1)) = reach('0',X0,iPr_def_14,X1),
inference(superposition,[status(thm)],[c_141,c_578]) ).
tcf(c_1413,plain,
! [X0: $i,X1: $i] : reach(iPr_def_10,X0,iPr_def_13,edge(iPr_def_11,iPr_def_12,X1)) = reach(iPr_def_10,X0,iPr_def_14,X1),
inference(superposition,[status(thm)],[c_141,c_794]) ).
tcf(c_1421,plain,
! [X0: $i,X1: $i] : reach(iPr_def_11,X0,iPr_def_13,X1) = false,
inference(demodulation,[status(thm)],[c_1244,c_340]) ).
tcf(c_1422,plain,
! [X0: $i,X1: $i] : reach(iPr_def_10,X0,iPr_def_13,X1) = false,
inference(demodulation,[status(thm)],[c_1185,c_340]) ).
tcf(c_1427,plain,
! [X0: $i,X1: $i] : reach(iPr_def_10,X0,iPr_def_14,X1) = false,
inference(demodulation,[status(thm)],[c_1413,c_1422]) ).
tcf(c_1429,plain,
! [X0: $i,X1: $i] : reach('0',X0,iPr_def_14,X1) = false,
inference(demodulation,[status(thm)],[c_1402,c_769]) ).
tcf(c_1430,plain,
! [X0: $i,X1: $i] : reach('0',X0,iPr_def_15,X1) = false,
inference(demodulation,[status(thm)],[c_1399,c_1429]) ).
tcf(c_1834,plain,
! [X0: $i,X1: $i] : union(edge(X0,X1,iPr_def_13),empty) = edge(X0,X1,iPr_def_13),
inference(superposition,[status(thm)],[c_1266,c_153]) ).
tcf(c_1866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_2(false,iPr_def_10,X0,edge(X1,X2,iPr_def_14),X3) = or(false,reach(X2,X0,union(iPr_def_14,X3),empty)),
inference(superposition,[status(thm)],[c_1427,c_148]) ).
tcf(c_1872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_2(false,'0',X0,edge(X1,X2,iPr_def_15),X3) = or(false,reach(X2,X0,union(iPr_def_15,X3),empty)),
inference(superposition,[status(thm)],[c_1430,c_148]) ).
tcf(c_2046,plain,
! [X0: $i] : if_reach_2(false,iPr_def_10,'0',iPr_def_15,X0) = reach(iPr_def_10,'0',iPr_def_15,X0),
inference(superposition,[status(thm)],[c_1217,c_518]) ).
tcf(c_2050,plain,
! [X0: $i] : if_reach_2(false,iPr_def_11,'0',iPr_def_14,X0) = reach(iPr_def_11,'0',iPr_def_14,X0),
inference(superposition,[status(thm)],[c_1226,c_516]) ).
tcf(c_2151,plain,
! [X0: $i,X1: $i] : reach(iPr_def_12,'0',edge(iPr_def_12,'0',X0),X1) = iPr_def_17,
inference(superposition,[status(thm)],[c_1251,c_342]) ).
tcf(c_2192,plain,
! [X0: $i,X1: $i] : reach(iPr_def_12,'0',union(iPr_def_13,X0),X1) = iPr_def_17,
inference(demodulation,[status(thm)],[c_2151,c_480]) ).
tcf(c_2198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_2(false,'0',X0,edge(X1,X2,iPr_def_15),X3) = reach(X2,X0,union(iPr_def_15,X3),empty),
inference(demodulation,[status(thm)],[c_1872,c_155]) ).
tcf(c_2200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_2(false,iPr_def_10,X0,edge(X1,X2,iPr_def_14),X3) = reach(X2,X0,union(iPr_def_14,X3),empty),
inference(demodulation,[status(thm)],[c_1866,c_155]) ).
tcf(c_2332,plain,
union(iPr_def_14,empty) = iPr_def_14,
inference(superposition,[status(thm)],[c_141,c_1834]) ).
tcf(c_2389,plain,
! [X0: $i,X1: $i,X2: $i] : if_reach_2(false,X0,'0',edge(X1,iPr_def_12,iPr_def_13),X2) = or(reach(X0,'0',iPr_def_13,X2),iPr_def_17),
inference(superposition,[status(thm)],[c_2192,c_148]) ).
tcf(c_2483,plain,
! [X0: $i,X1: $i] : reach(iPr_def_10,X0,union(iPr_def_15,X1),empty) = if_reach_2(false,'0',X0,iPr_def_16,X1),
inference(superposition,[status(thm)],[c_2198,c_546]) ).
tcf(c_2503,plain,
! [X0: $i,X1: $i] : reach(iPr_def_11,X0,union(iPr_def_14,X1),empty) = if_reach_2(false,iPr_def_10,X0,iPr_def_15,X1),
inference(superposition,[status(thm)],[c_2200,c_545]) ).
tcf(c_2584,plain,
! [X0: $i,X1: $i] : or(reach(X0,'0',iPr_def_13,X1),iPr_def_17) = if_reach_2(false,X0,'0',iPr_def_14,X1),
inference(demodulation,[status(thm)],[c_2389,c_544]) ).
tcf(c_2702,plain,
! [X0: $i,X1: $i] : union(edge(X0,X1,iPr_def_14),empty) = edge(X0,X1,iPr_def_14),
inference(superposition,[status(thm)],[c_2332,c_153]) ).
tcf(c_2912,plain,
! [X0: $i] : if_reach_2(false,iPr_def_11,'0',iPr_def_14,X0) = or(false,iPr_def_17),
inference(superposition,[status(thm)],[c_1421,c_2584]) ).
tcf(c_2945,plain,
! [X0: $i] : if_reach_2(false,iPr_def_11,'0',iPr_def_14,X0) = iPr_def_17,
inference(demodulation,[status(thm)],[c_2912,c_155]) ).
tcf(c_3121,plain,
union(iPr_def_15,empty) = iPr_def_15,
inference(superposition,[status(thm)],[c_142,c_2702]) ).
tcf(c_3169,plain,
! [X0: $i] : reach(iPr_def_11,'0',iPr_def_14,X0) = iPr_def_17,
inference(superposition,[status(thm)],[c_2050,c_2945]) ).
tcf(c_3666,plain,
! [X0: $i] : if_reach_2(false,'0',X0,iPr_def_16,empty) = reach(iPr_def_10,X0,iPr_def_15,empty),
inference(superposition,[status(thm)],[c_3121,c_2483]) ).
tcf(c_3962,plain,
reach('0','0',iPr_def_16,empty) = reach(iPr_def_10,'0',iPr_def_15,empty),
inference(superposition,[status(thm)],[c_3666,c_1316]) ).
tcf(c_4007,plain,
! [X0: $i] : if_reach_2(false,iPr_def_10,X0,iPr_def_15,empty) = reach(iPr_def_11,X0,iPr_def_14,empty),
inference(superposition,[status(thm)],[c_2332,c_2503]) ).
tcf(c_4283,plain,
reach(iPr_def_10,'0',iPr_def_15,empty) != iPr_def_17,
inference(superposition,[status(thm)],[c_3962,c_283]) ).
tcf(c_4311,plain,
reach(iPr_def_10,'0',iPr_def_15,empty) = reach(iPr_def_11,'0',iPr_def_14,empty),
inference(superposition,[status(thm)],[c_4007,c_2046]) ).
tcf(c_4404,plain,
reach(iPr_def_10,'0',iPr_def_15,empty) = iPr_def_17,
inference(demodulation,[status(thm)],[c_4311,c_3169]) ).
tcf(c_4424,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4283,c_4404]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ164-2 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n002.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 07:05:19 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 Running UEQ theorem proving
% 0.12/0.38 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.39
% 0.12/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.39
% 0.12/0.39 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 8.66/1.73 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 8.66/1.73 % SZS status Started for theBenchmark.p
% 8.66/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 8.66/1.73
% 8.66/1.73 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.66/1.73
% 8.66/1.73 % ------ iProver source info
% 8.66/1.73
% 8.66/1.73 % git: date: 2026-07-19 20:42:38 +0200
% 8.66/1.73 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.66/1.73 % git: non_committed_changes: false
% 8.66/1.73
% 8.66/1.73 % ------ Parsing...% successful
% 8.66/1.73
% 8.66/1.73
% 8.66/1.73 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.66/1.73
% 8.66/1.73 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 8.66/1.73
% 8.66/1.73 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.66/1.73
% 8.66/1.73 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 8.66/1.73 % ------ Proving...
% 8.66/1.73 % ------ Problem Properties
% 8.66/1.73
% 8.66/1.73 %
% 8.66/1.73 % clauses 24
% 8.66/1.73 % conjectures 1
% 8.66/1.73 % EPR 2
% 8.66/1.73 % Horn 24
% 8.66/1.73 % unary 24
% 8.66/1.73 % binary 0
% 8.66/1.73 % lits 24
% 8.66/1.73 % lits eq 24
% 8.66/1.73 % fd_pure 0
% 8.66/1.73 % fd_pseudo 0
% 8.66/1.73 % fd_cond 0
% 8.66/1.73 % fd_pseudo_cond 0
% 8.66/1.73 % AC symbols 0
% 8.66/1.73
% 8.66/1.73 % ------ Input Options Time Limit: Unbounded
% 8.66/1.73
% 8.66/1.73
% 8.66/1.73 % ------
% 8.66/1.73 % Current options:
% 8.66/1.73 % ------
% 8.66/1.73
% 8.66/1.73
% 8.66/1.73 %
% 8.66/1.73
% 8.66/1.73 % ------ Proving...
% 8.66/1.73 %
% 8.66/1.73
% 8.66/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 8.66/1.73
% 8.66/1.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.66/1.73
% 8.66/1.73
%------------------------------------------------------------------------------