%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : PUZ164-1 : 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 : n005.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 12.06s 2.70s
% Output : CNFRefutation 3.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 23
% Syntax : Number of formulae : 154 ( 154 unt; 9 def)
% Number of atoms : 439 ( 153 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 5 ( 5 ~; 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 : 11 ( 9 usr; 10 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-5 aty)
% Number of variables : 334 ( 0 sgn 334 !; 0 ?; 283 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
eq(zero,zero) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule1) ).
fof(f2,axiom,
! [X0] : eq(zero,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(zero,s(zero),edge(s(zero),s(s(zero)),edge(s(s(zero)),s(s(s(zero))),edge(s(s(s(zero))),zero,empty)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',graph) ).
fof(f20,negated_conjecture,
reach(zero,zero,g,empty) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
fof(f21,plain,
true != reach(zero,zero,g,empty),
inference(reorient_equations,[],[f20]) ).
tcf(c_65,plain,
eq(zero,zero) = true,
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,plain,
! [X0: $i] : eq(zero,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(zero,s(zero),edge(s(zero),s(s(zero)),edge(s(s(zero)),s(s(s(zero))),edge(s(s(s(zero))),zero,empty)))) = g,
inference(cnf_transformation,[],[f19]) ).
tcf(c_80,negated_conjecture,
reach(zero,zero,g,empty) != true,
inference(cnf_transformation,[],[f21]) ).
tcf(c_136,definition,
iPr_def_10 = reach(zero,zero,g,empty),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_137,definition,
iPr_def_11 = s(zero),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_138,definition,
iPr_def_12 = s(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_139,definition,
iPr_def_13 = s(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_140,definition,
iPr_def_14 = edge(iPr_def_13,zero,empty),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_141,definition,
iPr_def_15 = edge(iPr_def_12,iPr_def_13,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_142,definition,
iPr_def_16 = edge(iPr_def_11,iPr_def_12,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_143,definition,
iPr_def_17 = edge(zero,iPr_def_11,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_144,definition,
iPr_def_18 = eq(zero,zero),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_145,negated_conjecture,
iPr_def_10 != true,
inference(demodulation,[status(thm)],[c_80,c_136]) ).
tcf(c_146,plain,
iPr_def_17 = 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(zero,s(X0)) = false,
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_160,plain,
iPr_def_18 = true,
inference(demodulation,[status(thm)],[c_65,c_144]) ).
tcf(c_288,plain,
iPr_def_10 != iPr_def_18,
inference(demodulation,[status(thm)],[c_145,c_160]) ).
tcf(c_290,plain,
reach(zero,zero,iPr_def_17,empty) = iPr_def_10,
inference(demodulation,[status(thm)],[c_136,c_146]) ).
tcf(c_291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : if_reach_2(iPr_def_18,X0,X1,edge(X2,X3,X4),X5) = iPr_def_18,
inference(demodulation,[status(thm)],[c_149,c_160]) ).
tcf(c_292,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_18,X2,X0,edge(X3,X1,X4),X5),
inference(demodulation,[status(thm)],[c_150,c_160]) ).
tcf(c_304,plain,
eq(zero,iPr_def_11) = false,
inference(superposition,[status(thm)],[c_137,c_159]) ).
tcf(c_305,plain,
eq(zero,iPr_def_12) = false,
inference(superposition,[status(thm)],[c_138,c_159]) ).
tcf(c_306,plain,
eq(zero,iPr_def_13) = false,
inference(superposition,[status(thm)],[c_139,c_159]) ).
tcf(c_310,plain,
! [X0: $i] : eq(s(X0),iPr_def_11) = eq(X0,zero),
inference(superposition,[status(thm)],[c_137,c_157]) ).
tcf(c_311,plain,
! [X0: $i] : eq(s(X0),iPr_def_12) = eq(X0,iPr_def_11),
inference(superposition,[status(thm)],[c_138,c_157]) ).
tcf(c_312,plain,
! [X0: $i] : eq(s(X0),iPr_def_13) = eq(X0,iPr_def_12),
inference(superposition,[status(thm)],[c_139,c_157]) ).
tcf(c_317,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_320,plain,
! [X0: $i,X1: $i,X2: $i] : reach(X0,X1,empty,edge(iPr_def_13,zero,X2)) = if_reach_1(false,X0,X1,iPr_def_14,X2),
inference(superposition,[status(thm)],[c_140,c_147]) ).
tcf(c_321,plain,
! [X0: $i,X1: $i,X2: $i] : reach(X0,X1,iPr_def_14,edge(iPr_def_12,iPr_def_13,X2)) = if_reach_1(false,X0,X1,iPr_def_15,X2),
inference(superposition,[status(thm)],[c_141,c_147]) ).
tcf(c_324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_1(iPr_def_18,zero,X0,edge(zero,X1,X2),X3) = reach(zero,X0,edge(zero,X1,X2),X3),
inference(superposition,[status(thm)],[c_144,c_151]) ).
tcf(c_325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : if_reach_1(false,zero,X0,edge(s(X1),X2,X3),X4) = reach(zero,X0,edge(s(X1),X2,X3),X4),
inference(superposition,[status(thm)],[c_159,c_151]) ).
tcf(c_329,plain,
! [X0: $i,X1: $i,X2: $i] : if_reach_1(eq(X0,iPr_def_13),X0,X1,iPr_def_14,X2) = reach(X0,X1,iPr_def_14,X2),
inference(superposition,[status(thm)],[c_140,c_151]) ).
tcf(c_330,plain,
! [X0: $i,X1: $i,X2: $i] : if_reach_1(eq(X0,iPr_def_12),X0,X1,iPr_def_15,X2) = reach(X0,X1,iPr_def_15,X2),
inference(superposition,[status(thm)],[c_141,c_151]) ).
tcf(c_331,plain,
! [X0: $i,X1: $i,X2: $i] : if_reach_1(eq(X0,iPr_def_11),X0,X1,iPr_def_16,X2) = reach(X0,X1,iPr_def_16,X2),
inference(superposition,[status(thm)],[c_142,c_151]) ).
tcf(c_339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_1(iPr_def_18,X0,zero,edge(X1,zero,X2),X3) = if_reach_2(iPr_def_18,X0,zero,edge(X1,zero,X2),X3),
inference(superposition,[status(thm)],[c_144,c_292]) ).
tcf(c_345,plain,
! [X0: $i,X1: $i,X2: $i] : if_reach_2(eq(X0,iPr_def_13),X1,X0,iPr_def_15,X2) = if_reach_1(iPr_def_18,X1,X0,iPr_def_15,X2),
inference(superposition,[status(thm)],[c_141,c_292]) ).
tcf(c_346,plain,
! [X0: $i,X1: $i,X2: $i] : if_reach_2(eq(X0,iPr_def_12),X1,X0,iPr_def_16,X2) = if_reach_1(iPr_def_18,X1,X0,iPr_def_16,X2),
inference(superposition,[status(thm)],[c_142,c_292]) ).
tcf(c_347,plain,
! [X0: $i,X1: $i,X2: $i] : if_reach_2(eq(X0,iPr_def_11),X1,X0,iPr_def_17,X2) = if_reach_1(iPr_def_18,X1,X0,iPr_def_17,X2),
inference(superposition,[status(thm)],[c_143,c_292]) ).
tcf(c_353,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_354,plain,
! [X0: $i,X1: $i,X2: $i] : if_reach_1(false,X0,X1,iPr_def_14,X2) = false,
inference(demodulation,[status(thm)],[c_320,c_152]) ).
tcf(c_356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_1(iPr_def_18,X0,zero,edge(X1,zero,X2),X3) = iPr_def_18,
inference(demodulation,[status(thm)],[c_339,c_291]) ).
tcf(c_358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : reach(zero,X0,edge(s(X1),X2,X3),X4) = reach(zero,X0,X3,edge(s(X1),X2,X4)),
inference(demodulation,[status(thm)],[c_325,c_147]) ).
tcf(c_475,plain,
eq(zero,zero) = eq(iPr_def_11,iPr_def_11),
inference(superposition,[status(thm)],[c_137,c_310]) ).
tcf(c_480,plain,
eq(zero,iPr_def_11) = eq(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_137,c_311]) ).
tcf(c_481,plain,
eq(iPr_def_11,iPr_def_11) = eq(iPr_def_12,iPr_def_12),
inference(superposition,[status(thm)],[c_138,c_311]) ).
tcf(c_485,plain,
eq(zero,iPr_def_12) = eq(iPr_def_11,iPr_def_13),
inference(superposition,[status(thm)],[c_137,c_312]) ).
tcf(c_486,plain,
eq(iPr_def_11,iPr_def_12) = eq(iPr_def_12,iPr_def_13),
inference(superposition,[status(thm)],[c_138,c_312]) ).
tcf(c_487,plain,
eq(iPr_def_12,iPr_def_12) = eq(iPr_def_13,iPr_def_13),
inference(superposition,[status(thm)],[c_139,c_312]) ).
tcf(c_490,plain,
! [X0: $i] : edge(iPr_def_13,zero,X0) = union(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_140,c_317]) ).
tcf(c_501,plain,
! [X0: $i,X1: $i] : if_reach_1(false,zero,X0,iPr_def_14,X1) = reach(zero,X0,iPr_def_14,X1),
inference(superposition,[status(thm)],[c_306,c_329]) ).
tcf(c_526,plain,
! [X0: $i,X1: $i] : if_reach_1(iPr_def_18,X0,zero,iPr_def_15,X1) = if_reach_2(false,X0,zero,iPr_def_15,X1),
inference(superposition,[status(thm)],[c_306,c_345]) ).
tcf(c_528,plain,
! [X0: $i,X1: $i] : if_reach_1(iPr_def_18,X0,zero,iPr_def_16,X1) = if_reach_2(false,X0,zero,iPr_def_16,X1),
inference(superposition,[status(thm)],[c_305,c_346]) ).
tcf(c_530,plain,
! [X0: $i,X1: $i] : if_reach_1(iPr_def_18,X0,zero,iPr_def_17,X1) = if_reach_2(false,X0,zero,iPr_def_17,X1),
inference(superposition,[status(thm)],[c_304,c_347]) ).
tcf(c_537,plain,
! [X0: $i,X1: $i] : if_reach_1(iPr_def_18,zero,X0,iPr_def_17,X1) = reach(zero,X0,iPr_def_17,X1),
inference(superposition,[status(thm)],[c_143,c_324]) ).
tcf(c_573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_2(false,X0,X1,edge(X2,iPr_def_13,iPr_def_14),X3) = if_reach_2(false,X0,X1,iPr_def_15,X3),
inference(superposition,[status(thm)],[c_141,c_353]) ).
tcf(c_574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_2(false,X0,X1,edge(X2,iPr_def_12,iPr_def_15),X3) = if_reach_2(false,X0,X1,iPr_def_16,X3),
inference(superposition,[status(thm)],[c_142,c_353]) ).
tcf(c_575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_2(false,X0,X1,edge(X2,iPr_def_11,iPr_def_16),X3) = if_reach_2(false,X0,X1,iPr_def_17,X3),
inference(superposition,[status(thm)],[c_143,c_353]) ).
tcf(c_618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : reach(zero,X0,edge(iPr_def_11,X1,X2),X3) = reach(zero,X0,X2,edge(iPr_def_11,X1,X3)),
inference(superposition,[status(thm)],[c_137,c_358]) ).
tcf(c_619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : reach(zero,X0,edge(iPr_def_12,X1,X2),X3) = reach(zero,X0,X2,edge(iPr_def_12,X1,X3)),
inference(superposition,[status(thm)],[c_138,c_358]) ).
tcf(c_762,plain,
eq(iPr_def_11,iPr_def_13) = false,
inference(demodulation,[status(thm)],[c_485,c_305]) ).
tcf(c_763,plain,
eq(zero,iPr_def_11) = eq(iPr_def_12,iPr_def_13),
inference(demodulation,[status(thm)],[c_480,c_486]) ).
tcf(c_764,plain,
eq(iPr_def_12,iPr_def_13) = false,
inference(demodulation,[status(thm)],[c_763,c_304]) ).
tcf(c_767,plain,
eq(zero,zero) = eq(iPr_def_12,iPr_def_12),
inference(demodulation,[status(thm)],[c_475,c_481]) ).
tcf(c_768,plain,
eq(iPr_def_12,iPr_def_12) = iPr_def_18,
inference(demodulation,[status(thm)],[c_767,c_144]) ).
tcf(c_771,plain,
! [X0: $i,X1: $i] : reach(zero,X0,iPr_def_14,X1) = false,
inference(demodulation,[status(thm)],[c_501,c_354]) ).
tcf(c_1215,plain,
! [X0: $i,X1: $i] : if_reach_1(false,iPr_def_11,X0,iPr_def_14,X1) = reach(iPr_def_11,X0,iPr_def_14,X1),
inference(superposition,[status(thm)],[c_762,c_329]) ).
tcf(c_1223,plain,
! [X0: $i,X1: $i] : if_reach_1(false,iPr_def_12,X0,iPr_def_14,X1) = reach(iPr_def_12,X0,iPr_def_14,X1),
inference(superposition,[status(thm)],[c_764,c_329]) ).
tcf(c_1247,plain,
! [X0: $i,X1: $i] : if_reach_1(iPr_def_18,iPr_def_12,X0,iPr_def_15,X1) = reach(iPr_def_12,X0,iPr_def_15,X1),
inference(superposition,[status(thm)],[c_768,c_330]) ).
tcf(c_1256,plain,
eq(iPr_def_11,iPr_def_11) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_481,c_768]) ).
tcf(c_1264,plain,
! [X0: $i,X1: $i] : if_reach_1(iPr_def_18,iPr_def_11,X0,iPr_def_16,X1) = reach(iPr_def_11,X0,iPr_def_16,X1),
inference(superposition,[status(thm)],[c_1256,c_331]) ).
tcf(c_1274,plain,
eq(iPr_def_11,iPr_def_12) = false,
inference(light_normalisation,[status(thm)],[c_486,c_764]) ).
tcf(c_1282,plain,
! [X0: $i,X1: $i] : if_reach_1(false,iPr_def_11,X0,iPr_def_15,X1) = reach(iPr_def_11,X0,iPr_def_15,X1),
inference(superposition,[status(thm)],[c_1274,c_330]) ).
tcf(c_1283,plain,
eq(iPr_def_13,iPr_def_13) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_487,c_768]) ).
tcf(c_1289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_1(iPr_def_18,iPr_def_13,X0,edge(iPr_def_13,X1,X2),X3) = reach(iPr_def_13,X0,edge(iPr_def_13,X1,X2),X3),
inference(superposition,[status(thm)],[c_1283,c_151]) ).
tcf(c_1307,plain,
union(iPr_def_14,empty) = iPr_def_14,
inference(superposition,[status(thm)],[c_490,c_140]) ).
tcf(c_1349,plain,
! [X0: $i] : if_reach_2(false,zero,zero,iPr_def_17,X0) = reach(zero,zero,iPr_def_17,X0),
inference(superposition,[status(thm)],[c_537,c_530]) ).
tcf(c_1431,plain,
! [X0: $i,X1: $i] : reach(zero,X0,iPr_def_15,edge(iPr_def_11,iPr_def_12,X1)) = reach(zero,X0,iPr_def_16,X1),
inference(superposition,[status(thm)],[c_142,c_618]) ).
tcf(c_1443,plain,
! [X0: $i,X1: $i] : reach(zero,X0,iPr_def_14,edge(iPr_def_12,iPr_def_13,X1)) = reach(zero,X0,iPr_def_15,X1),
inference(superposition,[status(thm)],[c_141,c_619]) ).
tcf(c_1456,plain,
! [X0: $i,X1: $i] : reach(iPr_def_12,X0,iPr_def_14,X1) = false,
inference(demodulation,[status(thm)],[c_1223,c_354]) ).
tcf(c_1457,plain,
! [X0: $i,X1: $i] : reach(iPr_def_11,X0,iPr_def_14,X1) = false,
inference(demodulation,[status(thm)],[c_1215,c_354]) ).
tcf(c_1462,plain,
! [X0: $i,X1: $i] : reach(zero,X0,iPr_def_15,X1) = false,
inference(demodulation,[status(thm)],[c_1443,c_771]) ).
tcf(c_1463,plain,
! [X0: $i,X1: $i] : reach(zero,X0,iPr_def_16,X1) = false,
inference(demodulation,[status(thm)],[c_1431,c_1462]) ).
tcf(c_1873,plain,
! [X0: $i,X1: $i] : union(edge(X0,X1,iPr_def_14),empty) = edge(X0,X1,iPr_def_14),
inference(superposition,[status(thm)],[c_1307,c_153]) ).
tcf(c_1887,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_2(false,iPr_def_12,X0,edge(X1,X2,iPr_def_14),X3) = or(false,reach(X2,X0,union(iPr_def_14,X3),empty)),
inference(superposition,[status(thm)],[c_1456,c_148]) ).
tcf(c_1890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_2(false,iPr_def_11,X0,edge(X1,X2,iPr_def_14),X3) = or(false,reach(X2,X0,union(iPr_def_14,X3),empty)),
inference(superposition,[status(thm)],[c_1457,c_148]) ).
tcf(c_1891,plain,
! [X0: $i,X1: $i] : if_reach_1(false,iPr_def_11,X0,iPr_def_15,X1) = false,
inference(superposition,[status(thm)],[c_1457,c_321]) ).
tcf(c_1896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_2(false,zero,X0,edge(X1,X2,iPr_def_16),X3) = or(false,reach(X2,X0,union(iPr_def_16,X3),empty)),
inference(superposition,[status(thm)],[c_1463,c_148]) ).
tcf(c_2070,plain,
! [X0: $i] : if_reach_2(false,iPr_def_12,zero,iPr_def_15,X0) = reach(iPr_def_12,zero,iPr_def_15,X0),
inference(superposition,[status(thm)],[c_1247,c_526]) ).
tcf(c_2074,plain,
! [X0: $i] : if_reach_2(false,iPr_def_11,zero,iPr_def_16,X0) = reach(iPr_def_11,zero,iPr_def_16,X0),
inference(superposition,[status(thm)],[c_1264,c_528]) ).
tcf(c_2182,plain,
! [X0: $i,X1: $i] : reach(iPr_def_13,zero,edge(iPr_def_13,zero,X0),X1) = iPr_def_18,
inference(superposition,[status(thm)],[c_1289,c_356]) ).
tcf(c_2225,plain,
! [X0: $i,X1: $i] : reach(iPr_def_13,zero,union(iPr_def_14,X0),X1) = iPr_def_18,
inference(demodulation,[status(thm)],[c_2182,c_490]) ).
tcf(c_2232,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_2(false,zero,X0,edge(X1,X2,iPr_def_16),X3) = reach(X2,X0,union(iPr_def_16,X3),empty),
inference(demodulation,[status(thm)],[c_1896,c_155]) ).
tcf(c_2234,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_2(false,iPr_def_11,X0,edge(X1,X2,iPr_def_14),X3) = reach(X2,X0,union(iPr_def_14,X3),empty),
inference(demodulation,[status(thm)],[c_1890,c_155]) ).
tcf(c_2235,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_2(false,iPr_def_12,X0,edge(X1,X2,iPr_def_14),X3) = reach(X2,X0,union(iPr_def_14,X3),empty),
inference(demodulation,[status(thm)],[c_1887,c_155]) ).
tcf(c_2360,plain,
union(iPr_def_15,empty) = iPr_def_15,
inference(superposition,[status(thm)],[c_141,c_1873]) ).
tcf(c_2392,plain,
! [X0: $i,X1: $i] : reach(iPr_def_11,X0,iPr_def_15,X1) = false,
inference(superposition,[status(thm)],[c_1891,c_1282]) ).
tcf(c_2416,plain,
! [X0: $i,X1: $i,X2: $i] : if_reach_2(false,X0,zero,edge(X1,iPr_def_13,iPr_def_14),X2) = or(reach(X0,zero,iPr_def_14,X2),iPr_def_18),
inference(superposition,[status(thm)],[c_2225,c_148]) ).
tcf(c_2525,plain,
! [X0: $i,X1: $i] : reach(iPr_def_11,X0,union(iPr_def_16,X1),empty) = if_reach_2(false,zero,X0,iPr_def_17,X1),
inference(superposition,[status(thm)],[c_2232,c_575]) ).
tcf(c_2554,plain,
! [X0: $i,X1: $i] : reach(iPr_def_13,X0,union(iPr_def_14,X1),empty) = if_reach_2(false,iPr_def_11,X0,iPr_def_15,X1),
inference(superposition,[status(thm)],[c_2234,c_573]) ).
tcf(c_2564,plain,
! [X0: $i,X1: $i] : reach(iPr_def_13,X0,union(iPr_def_14,X1),empty) = if_reach_2(false,iPr_def_12,X0,iPr_def_15,X1),
inference(superposition,[status(thm)],[c_2235,c_573]) ).
tcf(c_2618,plain,
! [X0: $i,X1: $i] : if_reach_2(false,iPr_def_11,X0,iPr_def_15,X1) = if_reach_2(false,iPr_def_12,X0,iPr_def_15,X1),
inference(demodulation,[status(thm)],[c_2554,c_2564]) ).
tcf(c_2626,plain,
! [X0: $i,X1: $i] : or(reach(X0,zero,iPr_def_14,X1),iPr_def_18) = if_reach_2(false,X0,zero,iPr_def_15,X1),
inference(demodulation,[status(thm)],[c_2416,c_573]) ).
tcf(c_2753,plain,
! [X0: $i,X1: $i] : union(edge(X0,X1,iPr_def_15),empty) = edge(X0,X1,iPr_def_15),
inference(superposition,[status(thm)],[c_2360,c_153]) ).
tcf(c_2762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_2(false,iPr_def_11,X0,edge(X1,X2,iPr_def_15),X3) = or(false,reach(X2,X0,union(iPr_def_15,X3),empty)),
inference(superposition,[status(thm)],[c_2392,c_148]) ).
tcf(c_3013,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if_reach_2(false,iPr_def_11,X0,edge(X1,X2,iPr_def_15),X3) = reach(X2,X0,union(iPr_def_15,X3),empty),
inference(demodulation,[status(thm)],[c_2762,c_155]) ).
tcf(c_3171,plain,
union(iPr_def_16,empty) = iPr_def_16,
inference(superposition,[status(thm)],[c_142,c_2753]) ).
tcf(c_3281,plain,
! [X0: $i] : if_reach_2(false,iPr_def_11,zero,iPr_def_15,X0) = or(false,iPr_def_18),
inference(superposition,[status(thm)],[c_1457,c_2626]) ).
tcf(c_3415,plain,
! [X0: $i] : reach(iPr_def_12,zero,iPr_def_15,X0) = iPr_def_18,
inference(demodulation,[status(thm)],[c_3281,c_155,c_2070,c_2618]) ).
tcf(c_3711,plain,
! [X0: $i] : if_reach_2(false,zero,X0,iPr_def_17,empty) = reach(iPr_def_11,X0,iPr_def_16,empty),
inference(superposition,[status(thm)],[c_3171,c_2525]) ).
tcf(c_3997,plain,
reach(zero,zero,iPr_def_17,empty) = reach(iPr_def_11,zero,iPr_def_16,empty),
inference(superposition,[status(thm)],[c_3711,c_1349]) ).
tcf(c_4137,plain,
reach(iPr_def_11,zero,iPr_def_16,empty) = iPr_def_10,
inference(demodulation,[status(thm)],[c_3997,c_290]) ).
tcf(c_6620,plain,
! [X0: $i,X1: $i] : reach(iPr_def_12,X0,union(iPr_def_15,X1),empty) = if_reach_2(false,iPr_def_11,X0,iPr_def_16,X1),
inference(superposition,[status(thm)],[c_3013,c_574]) ).
tcf(c_8449,plain,
! [X0: $i] : if_reach_2(false,iPr_def_11,X0,iPr_def_16,empty) = reach(iPr_def_12,X0,iPr_def_15,empty),
inference(superposition,[status(thm)],[c_2360,c_6620]) ).
tcf(c_8941,plain,
reach(iPr_def_11,zero,iPr_def_16,empty) = reach(iPr_def_12,zero,iPr_def_15,empty),
inference(superposition,[status(thm)],[c_8449,c_2074]) ).
tcf(c_9030,plain,
iPr_def_10 = iPr_def_18,
inference(demodulation,[status(thm)],[c_8941,c_3415,c_4137]) ).
tcf(c_9031,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9030,c_288]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ164-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 07:02:02 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running UEQ theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 12.06/2.70 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 12.06/2.70 % SZS status Started for theBenchmark.p
% 12.06/2.70 % SZS status Unsatisfiable for theBenchmark.p
% 12.06/2.70
% 12.06/2.70 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 12.06/2.70
% 12.06/2.70 % ------ iProver source info
% 12.06/2.70
% 12.06/2.70 % git: date: 2026-07-19 20:42:38 +0200
% 12.06/2.70 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 12.06/2.70 % git: non_committed_changes: false
% 12.06/2.70
% 12.06/2.70 % ------ Parsing...% successful
% 12.06/2.70
% 12.06/2.70
% 12.06/2.70 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 12.06/2.70
% 12.06/2.70 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 12.06/2.70
% 12.06/2.70 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 12.06/2.70
% 12.06/2.70 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 12.06/2.70 % ------ Proving...
% 12.06/2.70 % ------ Problem Properties
% 12.06/2.70
% 12.06/2.70 %
% 12.06/2.70 % clauses 25
% 12.06/2.70 % conjectures 1
% 12.06/2.70 % EPR 3
% 12.06/2.70 % Horn 25
% 12.06/2.70 % unary 25
% 12.06/2.70 % binary 0
% 12.06/2.70 % lits 25
% 12.06/2.70 % lits eq 25
% 12.06/2.70 % fd_pure 0
% 12.06/2.70 % fd_pseudo 0
% 12.06/2.70 % fd_cond 0
% 12.06/2.70 % fd_pseudo_cond 0
% 12.06/2.70 % AC symbols 0
% 12.06/2.70
% 12.06/2.70 % ------ Input Options Time Limit: Unbounded
% 12.06/2.70
% 12.06/2.70
% 12.06/2.70 % ------
% 12.06/2.70 % Current options:
% 12.06/2.70 % ------
% 12.06/2.70
% 12.06/2.70
% 12.06/2.70 %
% 12.06/2.70
% 12.06/2.70 % ------ Proving...
% 12.06/2.70 %
% 12.06/2.70
% 12.06/2.70 % SZS status Unsatisfiable for theBenchmark.p
% 12.06/2.70
% 12.06/2.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.33/2.71
% 3.33/2.71
%------------------------------------------------------------------------------