%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM003_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 01:04:15 PM UTC 2026
% Result : Theorem 1.88s 1.26s
% Output : CNFRefutation 1.88s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f65ERROR: Could not build tree for root c_949ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
bad: output ).
tff(pred_def_1,type,
decides: ( input * ( program * algorithm ) ) > $o ).
tff(pred_def_2,type,
halts2: ( input * program ) > $o ).
tff(pred_def_3,type,
halts3: ( input * ( program * program ) ) > $o ).
tff(pred_def_4,type,
outputs: ( output * program ) > $o ).
tff(func_def_5,type,
sK3: algorithm > program ).
tff(func_def_6,type,
sK4: algorithm > input ).
tff(func_def_7,type,
sK5: program > program ).
tff(func_def_8,type,
sK6: program ).
tff(func_def_9,type,
sK7: program > program ).
tff(func_def_10,type,
sK8: program ).
tff(func_def_11,type,
sK9: algorithm ).
tff(f1,axiom,
( ? [X0: algorithm] :
! [X1: program,X2: input] : decides(X0,X1,X2)
=> ? [X3: program] :
! [X1: program,X2: input] : decides(algorithm_of(X3),X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
tff(f2,axiom,
! [X0: program,X1: program,X2: input] :
( decides(algorithm_of(X0),X1,X2)
=> ! [X1: program,X2: input] :
( ( ~ halts2(X1,X2)
=> ( outputs(X0,bad)
& halts3(X0,X1,X2) ) )
& ( halts2(X1,X2)
=> ( outputs(X0,good)
& halts3(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
tff(f3,axiom,
( ? [X0: program] :
! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
=> ( outputs(X0,bad)
& halts3(X0,X1,as_input(X1)) ) )
& ( halts2(X1,as_input(X1))
=> ( outputs(X0,good)
& halts3(X0,X1,as_input(X1)) ) ) )
=> ? [X2: program] :
! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
=> ( outputs(X2,bad)
& halts2(X2,as_input(X1)) ) )
& ( halts2(X1,as_input(X1))
=> ( outputs(X2,good)
& halts2(X2,as_input(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
tff(f4,axiom,
( ? [X0: program] :
! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
=> ( outputs(X0,bad)
& halts2(X0,as_input(X1)) ) )
& ( halts2(X1,as_input(X1))
=> ( outputs(X0,good)
& halts2(X0,as_input(X1)) ) ) )
=> ? [X2: program] :
! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
=> ( outputs(X2,bad)
& halts2(X2,as_input(X1)) ) )
& ( halts2(X1,as_input(X1))
=> ~ halts2(X2,as_input(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
tff(f5,conjecture,
~ ? [X0: algorithm] :
! [X1: program,X2: input] : decides(X0,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(f6,negated_conjecture,
~ ~ ? [X0: algorithm] :
! [X1: program,X2: input] : decides(X0,X1,X2),
inference(negated_conjecture,[status(cth)],[f5]) ).
tff(f7,plain,
( ? [X0: algorithm] :
! [X1: program,X2: input] : decides(X0,X1,X2)
=> ? [X3: program] :
! [X4: program,X5: input] : decides(algorithm_of(X3),X4,X5) ),
inference(rectify,[],[f1]) ).
tff(f8,plain,
! [X0: program,X1: program,X2: input] :
( decides(algorithm_of(X0),X1,X2)
=> ! [X3: program,X4: input] :
( ( ~ halts2(X3,X4)
=> ( outputs(X0,bad)
& halts3(X0,X3,X4) ) )
& ( halts2(X3,X4)
=> ( outputs(X0,good)
& halts3(X0,X3,X4) ) ) ) ),
inference(rectify,[],[f2]) ).
tff(f9,plain,
( ? [X0: program] :
! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
=> ( outputs(X0,bad)
& halts3(X0,X1,as_input(X1)) ) )
& ( halts2(X1,as_input(X1))
=> ( outputs(X0,good)
& halts3(X0,X1,as_input(X1)) ) ) )
=> ? [X2: program] :
! [X3: program] :
( ( ~ halts2(X3,as_input(X3))
=> ( outputs(X2,bad)
& halts2(X2,as_input(X3)) ) )
& ( halts2(X3,as_input(X3))
=> ( outputs(X2,good)
& halts2(X2,as_input(X3)) ) ) ) ),
inference(rectify,[],[f3]) ).
tff(f10,plain,
( ? [X0: program] :
! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
=> ( outputs(X0,bad)
& halts2(X0,as_input(X1)) ) )
& ( halts2(X1,as_input(X1))
=> ( outputs(X0,good)
& halts2(X0,as_input(X1)) ) ) )
=> ? [X2: program] :
! [X3: program] :
( ( ~ halts2(X3,as_input(X3))
=> ( outputs(X2,bad)
& halts2(X2,as_input(X3)) ) )
& ( halts2(X3,as_input(X3))
=> ~ halts2(X2,as_input(X3)) ) ) ),
inference(rectify,[],[f4]) ).
tff(f11,plain,
? [X0: algorithm] :
! [X1: program,X2: input] : decides(X0,X1,X2),
inference(flattening,[],[f6]) ).
tff(f12,plain,
( ! [X0: algorithm] :
? [X1: program,X2: input] : ~ decides(X0,X1,X2)
| ? [X3: program] :
! [X4: program,X5: input] : decides(algorithm_of(X3),X4,X5) ),
inference(ennf_transformation,[],[f7]) ).
tff(f13,plain,
! [X0: program,X1: program,X2: input] :
( ~ decides(algorithm_of(X0),X1,X2)
| ! [X3: program,X4: input] :
( ( halts2(X3,X4)
| ( outputs(X0,bad)
& halts3(X0,X3,X4) ) )
& ( ~ halts2(X3,X4)
| ( outputs(X0,good)
& halts3(X0,X3,X4) ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
tff(f14,plain,
( ! [X0: program] :
? [X1: program] :
( ( ~ halts2(X1,as_input(X1))
& ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,as_input(X1)) ) )
| ( halts2(X1,as_input(X1))
& ( ~ outputs(X0,good)
| ~ halts3(X0,X1,as_input(X1)) ) ) )
| ? [X2: program] :
! [X3: program] :
( ( halts2(X3,as_input(X3))
| ( outputs(X2,bad)
& halts2(X2,as_input(X3)) ) )
& ( ~ halts2(X3,as_input(X3))
| ( outputs(X2,good)
& halts2(X2,as_input(X3)) ) ) ) ),
inference(ennf_transformation,[],[f9]) ).
tff(f15,plain,
( ! [X0: program] :
? [X1: program] :
( ( ~ halts2(X1,as_input(X1))
& ( ~ outputs(X0,bad)
| ~ halts2(X0,as_input(X1)) ) )
| ( halts2(X1,as_input(X1))
& ( ~ outputs(X0,good)
| ~ halts2(X0,as_input(X1)) ) ) )
| ? [X2: program] :
! [X3: program] :
( ( halts2(X3,as_input(X3))
| ( outputs(X2,bad)
& halts2(X2,as_input(X3)) ) )
& ( ~ halts2(X3,as_input(X3))
| ~ halts2(X2,as_input(X3)) ) ) ),
inference(ennf_transformation,[],[f10]) ).
tff(f20,plain,
( ! [X3: algorithm] :
? [X4: program,X5: input] : ~ decides(X3,X4,X5)
| ? [X0: program] :
! [X1: program,X2: input] : decides(algorithm_of(X0),X1,X2) ),
inference(rectify,[],[f12]) ).
tff(f21,plain,
( ! [X3: algorithm] : ~ decides(X3,sK3(X3),sK4(X3))
| ! [X1: program,X2: input] : decides(algorithm_of(sK2),X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X4,sK3(X3)),skolemize(X5,sK4(X3))],[f20]) ).
tff(f24,plain,
( sP0
| ? [X0: program] :
! [X1: program] :
( ( halts2(X1,as_input(X1))
| ( outputs(X0,bad)
& halts2(X0,as_input(X1)) ) )
& ( ~ halts2(X1,as_input(X1))
| ( outputs(X0,good)
& halts2(X0,as_input(X1)) ) ) ) ),
inference(rectify,[],[f17]) ).
tff(f25,plain,
( sP0
| ! [X1: program] :
( ( halts2(X1,as_input(X1))
| ( outputs(sK6,bad)
& halts2(sK6,as_input(X1)) ) )
& ( ~ halts2(X1,as_input(X1))
| ( outputs(sK6,good)
& halts2(sK6,as_input(X1)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f24]) ).
tff(f28,plain,
( sP1
| ? [X0: program] :
! [X1: program] :
( ( halts2(X1,as_input(X1))
| ( outputs(X0,bad)
& halts2(X0,as_input(X1)) ) )
& ( ~ halts2(X1,as_input(X1))
| ~ halts2(X0,as_input(X1)) ) ) ),
inference(rectify,[],[f19]) ).
tff(f29,plain,
( sP1
| ! [X1: program] :
( ( halts2(X1,as_input(X1))
| ( outputs(sK8,bad)
& halts2(sK8,as_input(X1)) ) )
& ( ~ halts2(X1,as_input(X1))
| ~ halts2(sK8,as_input(X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X0,sK8)],[f28]) ).
tff(f30,plain,
! [X1: program,X2: input] : decides(sK9,X1,X2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f11]) ).
tff(f31,plain,
! [X2: input,X3: algorithm,X1: program] :
( ~ decides(X3,sK3(X3),sK4(X3))
| decides(algorithm_of(sK2),X1,X2) ),
inference(cnf_transformation,[],[f21]) ).
tff(f32,plain,
! [X2: input,X3: program,X0: program,X1: program,X4: input] :
( ~ decides(algorithm_of(X0),X1,X2)
| halts2(X3,X4)
| outputs(X0,bad) ),
inference(cnf_transformation,[],[f13]) ).
tff(f33,plain,
! [X2: input,X3: program,X0: program,X1: program,X4: input] :
( ~ decides(algorithm_of(X0),X1,X2)
| halts2(X3,X4)
| halts3(X0,X3,X4) ),
inference(cnf_transformation,[],[f13]) ).
tff(f34,plain,
! [X2: input,X3: program,X0: program,X1: program,X4: input] :
( ~ decides(algorithm_of(X0),X1,X2)
| ~ halts2(X3,X4)
| outputs(X0,good) ),
inference(cnf_transformation,[],[f13]) ).
tff(f35,plain,
! [X2: input,X3: program,X0: program,X1: program,X4: input] :
( ~ decides(algorithm_of(X0),X1,X2)
| ~ halts2(X3,X4)
| halts3(X0,X3,X4) ),
inference(cnf_transformation,[],[f13]) ).
tff(f40,plain,
! [X1: program] :
( sP0
| halts2(X1,as_input(X1))
| outputs(sK6,bad) ),
inference(cnf_transformation,[],[f25]) ).
tff(f41,plain,
! [X1: program] :
( sP0
| halts2(X1,as_input(X1))
| halts2(sK6,as_input(X1)) ),
inference(cnf_transformation,[],[f25]) ).
tff(f42,plain,
! [X1: program] :
( sP0
| ~ halts2(X1,as_input(X1))
| outputs(sK6,good) ),
inference(cnf_transformation,[],[f25]) ).
tff(f43,plain,
! [X1: program] :
( sP0
| ~ halts2(X1,as_input(X1))
| halts2(sK6,as_input(X1)) ),
inference(cnf_transformation,[],[f25]) ).
tff(f48,plain,
! [X1: program] :
( sP1
| halts2(X1,as_input(X1))
| outputs(sK8,bad) ),
inference(cnf_transformation,[],[f29]) ).
tff(f49,plain,
! [X1: program] :
( sP1
| halts2(X1,as_input(X1))
| halts2(sK8,as_input(X1)) ),
inference(cnf_transformation,[],[f29]) ).
tff(f50,plain,
! [X1: program] :
( sP1
| ~ halts2(X1,as_input(X1))
| ~ halts2(sK8,as_input(X1)) ),
inference(cnf_transformation,[],[f29]) ).
tff(f51,plain,
! [X2: input,X1: program] : decides(sK9,X1,X2),
inference(cnf_transformation,[],[f30]) ).
tcf(c_49,plain,
! [X0_program: program,X0_algorithm: algorithm,X0_input: input] :
( decides(algorithm_of(sK2),X0_program,X0_input)
| ~ decides(X0_algorithm,sK3(X0_algorithm),sK4(X0_algorithm)) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_50,plain,
! [X0_program: program,X0_input: input,X1_program: program,X1_input: input,X2_program: program] :
( halts3(X0_program,X2_program,X1_input)
| ~ halts2(X2_program,X1_input)
| ~ decides(algorithm_of(X0_program),X1_program,X0_input) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_51,plain,
! [X0_program: program,X0_input: input,X1_program: program,X1_input: input,X2_program: program] :
( outputs(X0_program,good)
| ~ halts2(X2_program,X1_input)
| ~ decides(algorithm_of(X0_program),X1_program,X0_input) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_52,plain,
! [X0_program: program,X0_input: input,X1_program: program,X1_input: input,X2_program: program] :
( halts2(X2_program,X1_input)
| halts3(X0_program,X2_program,X1_input)
| ~ decides(algorithm_of(X0_program),X1_program,X0_input) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_53,plain,
! [X0_program: program,X0_input: input,X1_program: program,X1_input: input,X2_program: program] :
( outputs(X0_program,bad)
| halts2(X2_program,X1_input)
| ~ decides(algorithm_of(X0_program),X1_program,X0_input) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_57,plain,
! [X0_program: program] :
( sP0
| halts2(sK6,as_input(X0_program))
| ~ halts2(X0_program,as_input(X0_program)) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_58,plain,
! [X0_program: program] :
( sP0
| outputs(sK6,good)
| ~ halts2(X0_program,as_input(X0_program)) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_59,plain,
! [X0_program: program] :
( sP0
| halts2(sK6,as_input(X0_program))
| halts2(X0_program,as_input(X0_program)) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_60,plain,
! [X0_program: program] :
( sP0
| outputs(sK6,bad)
| halts2(X0_program,as_input(X0_program)) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_61,plain,
! [X0_program: program] :
( ~ sP1
| ~ outputs(X0_program,good)
| ~ outputs(X0_program,bad)
| ~ halts2(X0_program,as_input(sK7(X0_program))) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_64,plain,
! [X0_program: program] :
( sP1
| ~ halts2(sK8,as_input(X0_program))
| ~ halts2(X0_program,as_input(X0_program)) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_65,plain,
! [X0_program: program] :
( sP1
| halts2(sK8,as_input(X0_program))
| halts2(X0_program,as_input(X0_program)) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_66,plain,
! [X0_program: program] :
( sP1
| outputs(sK8,bad)
| halts2(X0_program,as_input(X0_program)) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_67,negated_conjecture,
! [X0_program: program,X0_input: input] : decides(sK9,X0_program,X0_input),
inference(cnf_transformation,[],[f51]) ).
tcf(c_72,plain,
( sP0
| halts2(sK6,as_input(sK6)) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_73,plain,
( sP0
| outputs(sK6,good)
| ~ halts2(sK6,as_input(sK6)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_76,plain,
( decides(algorithm_of(sK2),sK6,iProver_bot)
| ~ decides(sK9,sK3(sK9),sK4(sK9)) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_80,plain,
( ~ sP1
| ~ outputs(sK6,good)
| ~ outputs(sK6,bad)
| ~ halts2(sK6,as_input(sK7(sK6))) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_86,plain,
! [X0_program: program] :
( sP0
| halts2(sK6,as_input(X0_program)) ),
inference(global_subsumption_just,[status(thm)],[c_59,c_59,c_57]) ).
tcf(c_88,plain,
( sP0
| outputs(sK6,good) ),
inference(global_subsumption_just,[status(thm)],[c_58,c_72,c_73]) ).
tcf(c_90,plain,
! [X0_program: program] :
( sP0
| halts2(sK6,as_input(X0_program)) ),
inference(global_subsumption_just,[status(thm)],[c_57,c_86]) ).
tcf(c_92,plain,
! [X0_program: program,X0_input: input,X1_program: program,X1_input: input,X2_program: program] :
( ~ decides(algorithm_of(X0_program),X1_program,X0_input)
| halts3(X0_program,X2_program,X1_input) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_52,c_50]) ).
tcf(c_93,plain,
! [X0_program: program,X0_input: input,X1_program: program,X1_input: input,X2_program: program] :
( halts3(X0_program,X2_program,X1_input)
| ~ decides(algorithm_of(X0_program),X1_program,X0_input) ),
inference(renaming,[status(thm)],[c_92]) ).
tcf(c_95,plain,
! [X0_program: program,X0_input: input,X1_program: program,X1_input: input,X2_program: program] :
( halts3(X0_program,X2_program,X1_input)
| ~ decides(algorithm_of(X0_program),X1_program,X0_input) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_93]) ).
tcf(c_887,plain,
! [X0_program: program] :
( ~ iPr_def_10
| halts2(X0_program,as_input(X0_program)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_66]) ).
tcf(c_889,plain,
( iPr_def_10
| sP0
| outputs(sK6,bad) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_60]) ).
tcf(c_893,plain,
! [X0_program: program,X0_input: input] :
( ~ iPr_def_13
| ~ halts2(X0_program,X0_input) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_51]) ).
tcf(c_894,plain,
! [X0_program: program,X0_input: input,X1_program: program] :
( ~ iPr_def_14
| outputs(X0_program,good)
| ~ decides(algorithm_of(X0_program),X1_program,X0_input) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_14])],[c_51]) ).
tcf(c_895,plain,
( iPr_def_14
| iPr_def_13 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_51]) ).
tcf(c_896,plain,
! [X0_program: program,X0_input: input] :
( ~ iPr_def_15
| decides(algorithm_of(sK2),X0_program,X0_input) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_15])],[c_49]) ).
tcf(c_897,plain,
! [X0_algorithm: algorithm] :
( ~ iPr_def_16
| ~ decides(X0_algorithm,sK3(X0_algorithm),sK4(X0_algorithm)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_16])],[c_49]) ).
tcf(c_898,plain,
( iPr_def_16
| iPr_def_15 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_49]) ).
tcf(c_899,negated_conjecture,
! [X0_program: program,X0_input: input] : decides(sK9,X0_program,X0_input),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_904,plain,
( ~ iPr_def_16
| ~ decides(sK9,sK3(sK9),sK4(sK9)) ),
inference(instantiation,[status(thm)],[c_897]) ).
tcf(c_908,plain,
decides(sK9,sK3(sK9),sK4(sK9)),
inference(instantiation,[status(thm)],[c_899]) ).
tcf(c_909,plain,
! [X0_program: program] :
( ~ iPr_def_13
| ~ halts2(X0_program,as_input(X0_program)) ),
inference(instantiation,[status(thm)],[c_893]) ).
tcf(c_911,plain,
( sP1
| ~ halts2(sK8,as_input(sK8)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_921,plain,
! [X0_program: program,X0_input: input] :
( outputs(sK2,good)
| ~ iPr_def_14
| ~ decides(algorithm_of(sK2),X0_program,X0_input) ),
inference(instantiation,[status(thm)],[c_894]) ).
tcf(c_929,plain,
( ~ iPr_def_13
| ~ halts2(sK5(sK2),as_input(sK5(sK2))) ),
inference(instantiation,[status(thm)],[c_909]) ).
tcf(c_930,plain,
( sP0
| halts2(sK6,as_input(sK7(sK6))) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_932,plain,
! [X0_program: program] :
( ~ iPr_def_13
| ~ halts2(sK6,as_input(X0_program)) ),
inference(instantiation,[status(thm)],[c_893]) ).
tcf(c_941,plain,
( sP1
| halts2(sK8,as_input(sK8)) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_948,plain,
( halts2(sK7(sK6),as_input(sK7(sK6)))
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_887]) ).
tff(f16,definition,
( ~ sP0
| ! [X0: program] :
? [X1: program] :
( ( ~ halts2(X1,as_input(X1))
& ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,as_input(X1)) ) )
| ( halts2(X1,as_input(X1))
& ( ~ outputs(X0,good)
| ~ halts3(X0,X1,as_input(X1)) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
tff(f17,plain,
( sP0
| ? [X2: program] :
! [X3: program] :
( ( halts2(X3,as_input(X3))
| ( outputs(X2,bad)
& halts2(X2,as_input(X3)) ) )
& ( ~ halts2(X3,as_input(X3))
| ( outputs(X2,good)
& halts2(X2,as_input(X3)) ) ) ) ),
inference(definition_folding,[],[f14,f16]) ).
tff(f18,definition,
( ~ sP1
| ! [X0: program] :
? [X1: program] :
( ( ~ halts2(X1,as_input(X1))
& ( ~ outputs(X0,bad)
| ~ halts2(X0,as_input(X1)) ) )
| ( halts2(X1,as_input(X1))
& ( ~ outputs(X0,good)
| ~ halts2(X0,as_input(X1)) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
tff(f19,plain,
( sP1
| ? [X2: program] :
! [X3: program] :
( ( halts2(X3,as_input(X3))
| ( outputs(X2,bad)
& halts2(X2,as_input(X3)) ) )
& ( ~ halts2(X3,as_input(X3))
| ~ halts2(X2,as_input(X3)) ) ) ),
inference(definition_folding,[],[f15,f18]) ).
tff(f22,plain,
( ~ sP0
| ! [X0: program] :
? [X1: program] :
( ( ~ halts2(X1,as_input(X1))
& ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,as_input(X1)) ) )
| ( halts2(X1,as_input(X1))
& ( ~ outputs(X0,good)
| ~ halts3(X0,X1,as_input(X1)) ) ) ) ),
inference(nnf_transformation,[],[f16]) ).
tff(f23,plain,
( ~ sP0
| ! [X0: program] :
( ( ~ halts2(sK5(X0),as_input(sK5(X0)))
& ( ~ outputs(X0,bad)
| ~ halts3(X0,sK5(X0),as_input(sK5(X0))) ) )
| ( halts2(sK5(X0),as_input(sK5(X0)))
& ( ~ outputs(X0,good)
| ~ halts3(X0,sK5(X0),as_input(sK5(X0))) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X1,sK5(X0))],[f22]) ).
tff(f26,plain,
( ~ sP1
| ! [X0: program] :
? [X1: program] :
( ( ~ halts2(X1,as_input(X1))
& ( ~ outputs(X0,bad)
| ~ halts2(X0,as_input(X1)) ) )
| ( halts2(X1,as_input(X1))
& ( ~ outputs(X0,good)
| ~ halts2(X0,as_input(X1)) ) ) ) ),
inference(nnf_transformation,[],[f18]) ).
tff(f27,plain,
( ~ sP1
| ! [X0: program] :
( ( ~ halts2(sK7(X0),as_input(sK7(X0)))
& ( ~ outputs(X0,bad)
| ~ halts2(X0,as_input(sK7(X0))) ) )
| ( halts2(sK7(X0),as_input(sK7(X0)))
& ( ~ outputs(X0,good)
| ~ halts2(X0,as_input(sK7(X0))) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f26]) ).
tff(f37,plain,
! [X0: program] :
( ~ sP0
| ~ outputs(X0,bad)
| ~ halts3(X0,sK5(X0),as_input(sK5(X0)))
| halts2(sK5(X0),as_input(sK5(X0))) ),
inference(cnf_transformation,[],[f23]) ).
tff(f38,plain,
! [X0: program] :
( ~ sP0
| ~ halts2(sK5(X0),as_input(sK5(X0)))
| ~ outputs(X0,good)
| ~ halts3(X0,sK5(X0),as_input(sK5(X0))) ),
inference(cnf_transformation,[],[f23]) ).
tff(f46,plain,
! [X0: program] :
( ~ sP1
| ~ halts2(sK7(X0),as_input(sK7(X0)))
| ~ outputs(X0,good)
| ~ halts2(X0,as_input(sK7(X0))) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_55,plain,
! [X0_program: program] :
( ~ sP0
| ~ outputs(X0_program,good)
| ~ halts2(sK5(X0_program),as_input(sK5(X0_program)))
| ~ halts3(X0_program,sK5(X0_program),as_input(sK5(X0_program))) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_56,plain,
! [X0_program: program] :
( halts2(sK5(X0_program),as_input(sK5(X0_program)))
| ~ sP0
| ~ outputs(X0_program,bad)
| ~ halts3(X0_program,sK5(X0_program),as_input(sK5(X0_program))) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_62,plain,
! [X0_program: program] :
( ~ sP1
| ~ outputs(X0_program,good)
| ~ halts2(X0_program,as_input(sK7(X0_program)))
| ~ halts2(sK7(X0_program),as_input(sK7(X0_program))) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_83,plain,
( ~ sP1
| ~ outputs(sK6,good)
| ~ halts2(sK6,as_input(sK7(sK6)))
| ~ halts2(sK7(sK6),as_input(sK7(sK6))) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_199,plain,
! [X0_program: program,X0_input: input,X1_program: program] :
( halts2(sK5(X0_program),as_input(sK5(X0_program)))
| ~ sP0
| ~ outputs(X0_program,bad)
| ~ decides(algorithm_of(X0_program),X1_program,X0_input) ),
inference(resolution,[status(thm)],[c_95,c_56]) ).
tcf(c_209,plain,
! [X0_program: program,X0_input: input,X1_program: program] :
( halts2(sK5(X0_program),as_input(sK5(X0_program)))
| ~ sP0
| ~ decides(algorithm_of(X0_program),X1_program,X0_input) ),
inference(forward_subsumption_resolution,[status(thm)],[c_199,c_53]) ).
tcf(c_214,plain,
! [X0_program: program,X0_input: input,X1_program: program] :
( ~ sP0
| ~ outputs(X0_program,good)
| ~ decides(algorithm_of(X0_program),X1_program,X0_input)
| ~ halts2(sK5(X0_program),as_input(sK5(X0_program))) ),
inference(resolution,[status(thm)],[c_95,c_55]) ).
tcf(c_216,plain,
! [X0_program: program,X0_input: input,X1_program: program] :
( ~ sP0
| ~ outputs(X0_program,good)
| ~ decides(algorithm_of(X0_program),X1_program,X0_input) ),
inference(global_subsumption_just,[status(thm)],[c_214,c_209,c_214]) ).
tcf(c_917,plain,
! [X0_program: program,X0_input: input] :
( halts2(sK5(sK2),as_input(sK5(sK2)))
| ~ sP0
| ~ decides(algorithm_of(sK2),X0_program,X0_input) ),
inference(instantiation,[status(thm)],[c_209]) ).
tcf(c_920,plain,
( halts2(sK5(sK2),as_input(sK5(sK2)))
| ~ sP0
| ~ decides(algorithm_of(sK2),sK6,iProver_bot) ),
inference(instantiation,[status(thm)],[c_917]) ).
tcf(c_927,plain,
! [X0_program: program,X0_input: input] :
( ~ sP0
| ~ outputs(sK2,good)
| ~ decides(algorithm_of(sK2),X0_program,X0_input) ),
inference(instantiation,[status(thm)],[c_216]) ).
tcf(c_928,plain,
( ~ sP0
| ~ outputs(sK2,good)
| ~ decides(algorithm_of(sK2),sK6,iProver_bot) ),
inference(instantiation,[status(thm)],[c_927]) ).
tcf(c_949,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_948,c_941,c_932,c_930,c_929,c_928,c_921,c_920,c_911,c_909,c_908,c_904,c_896,c_889,c_898,c_895,c_88,c_83,c_80,c_76,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM003_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 07:45:54 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 1.88/1.26 % SZS status Started for theBenchmark.p
% 1.88/1.26 % SZS status Theorem for theBenchmark.p
% 1.88/1.26
% 1.88/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.88/1.26
% 1.88/1.26 % ------ iProver source info
% 1.88/1.26
% 1.88/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 1.88/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.88/1.26 % git: non_committed_changes: false
% 1.88/1.26
% 1.88/1.26 % ------ Parsing...
% 1.88/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.88/1.26 %
% 1.88/1.26
% 1.88/1.26 % ------ Preprocessing... pe_s pe:1:0s pe_e pe_s pe_e %
% 1.88/1.26
% 1.88/1.26 % ------ Preprocessing...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.88/1.26 gs_s sp: 8 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.88/1.26 % ------ Proving...
% 1.88/1.26 % ------ Problem Properties
% 1.88/1.26
% 1.88/1.26 %
% 1.88/1.26 % clauses 22
% 1.88/1.26 % conjectures 1
% 1.88/1.26 % EPR 9
% 1.88/1.26 % Horn 14
% 1.88/1.26 % unary 1
% 1.88/1.26 % binary 10
% 1.88/1.26 % lits 57
% 1.88/1.26 % lits eq 0
% 1.88/1.26 % fd_pure 0
% 1.88/1.26 % fd_pseudo 0
% 1.88/1.26 % fd_cond 0
% 1.88/1.26 % fd_pseudo_cond 0
% 1.88/1.26 % AC symbols 0
% 1.88/1.26
% 1.88/1.26 % ------ Schedule dynamic 5 is on
% 1.88/1.26
% 1.88/1.26 % ------ no equalities: superposition off
% 1.88/1.26
% 1.88/1.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.88/1.26
% 1.88/1.26
% 1.88/1.26 % ------
% 1.88/1.26 % Current options:
% 1.88/1.26 % ------
% 1.88/1.26
% 1.88/1.26
% 1.88/1.26 %
% 1.88/1.26
% 1.88/1.26 % ------ Proving...
% 1.88/1.26 %
% 1.88/1.26
% 1.88/1.26 % SZS status Theorem for theBenchmark.p
% 1.88/1.26
% 1.88/1.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.88/1.26
% 1.88/1.26
%------------------------------------------------------------------------------