%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN135-1.006 : 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 : n004.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 02:30:04 PM UTC 2026
% Result : Unsatisfiable 11.71s 2.30s
% Output : CNFRefutation 11.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 74 ( 74 unt; 0 def)
% Number of atoms : 74 ( 73 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 168 ( 0 sgn 168 !; 0 ?; 143 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : minus(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule1) ).
fof(f2,axiom,
! [X0,X1] : minus(s(X0),s(X1)) = minus(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule2) ).
fof(f3,axiom,
! [X0] : '<='(zero,X0) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule3) ).
fof(f4,axiom,
! [X0] : '<='(s(X0),zero) = false,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule4) ).
fof(f5,axiom,
! [X0,X1] : '<='(s(X0),s(X1)) = '<='(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule5) ).
fof(f6,axiom,
! [X0,X1] : if(true,X0,X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule6) ).
fof(f7,axiom,
! [X0,X1] : if(false,X0,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule7) ).
fof(f10,axiom,
! [X0] : perfectp(s(X0)) = f(X0,s(zero),s(X0),s(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule9) ).
fof(f11,axiom,
! [X0,X1] : f(zero,X0,zero,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule10) ).
fof(f12,plain,
! [X0,X1] : true = f(zero,X0,zero,X1),
inference(reorient_equations,[],[f11]) ).
fof(f15,axiom,
! [X2,X0,X1] : f(s(X0),zero,X1,X2) = f(X0,X2,minus(X1,s(X0)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule12) ).
fof(f16,axiom,
! [X2,X3,X0,X1] : f(s(X0),s(X1),X2,X3) = if('<='(X0,X1),f(s(X0),minus(X1,X0),X2,X3),f(X0,X3,X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule13) ).
fof(f17,negated_conjecture,
! [X0] : perfectp(X0) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
fof(f18,plain,
! [X0] : true != perfectp(X0),
inference(reorient_equations,[],[f17]) ).
tcf(c_63,plain,
! [X0: $i] : minus(X0,zero) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : minus(s(X0),s(X1)) = minus(X0,X1),
inference(cnf_transformation,[],[f2]) ).
tcf(c_65,plain,
! [X0: $i] : '<='(zero,X0) = true,
inference(cnf_transformation,[],[f3]) ).
tcf(c_66,plain,
! [X0: $i] : '<='(s(X0),zero) = false,
inference(cnf_transformation,[],[f4]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] : '<='(s(X0),s(X1)) = '<='(X0,X1),
inference(cnf_transformation,[],[f5]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : if(true,X0,X1) = X0,
inference(cnf_transformation,[],[f6]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] : if(false,X0,X1) = X1,
inference(cnf_transformation,[],[f7]) ).
tcf(c_71,plain,
! [X0: $i] : f(X0,s(zero),s(X0),s(X0)) = perfectp(s(X0)),
inference(cnf_transformation,[],[f10]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] : f(zero,X0,zero,X1) = true,
inference(cnf_transformation,[],[f12]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] : f(X0,X1,minus(X2,s(X0)),X1) = f(s(X0),zero,X2,X1),
inference(cnf_transformation,[],[f15]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if('<='(X0,X1),f(s(X0),minus(X1,X0),X2,X3),f(X0,X3,X2,X3)) = f(s(X0),s(X1),X2,X3),
inference(cnf_transformation,[],[f16]) ).
tcf(c_76,negated_conjecture,
! [X0: $i] : perfectp(X0) != true,
inference(cnf_transformation,[],[f18]) ).
tcf(c_219,plain,
! [X0: $i,X1: $i,X2: $i] : f(X0,X1,minus(X2,X0),X1) = f(s(X0),zero,s(X2),X1),
inference(superposition,[status(thm)],[c_64,c_74]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i] : f(s(zero),zero,s(X0),X1) = f(zero,X1,X0,X1),
inference(superposition,[status(thm)],[c_63,c_219]) ).
tcf(c_222,plain,
! [X0: $i,X1: $i,X2: $i] : f(s(s(X0)),zero,s(s(X1)),X2) = f(s(X0),X2,minus(X1,X0),X2),
inference(superposition,[status(thm)],[c_64,c_219]) ).
tcf(c_231,plain,
! [X0: $i] : f(s(zero),zero,s(zero),X0) = true,
inference(superposition,[status(thm)],[c_221,c_72]) ).
tcf(c_256,plain,
! [X0: $i,X1: $i] : f(s(s(zero)),zero,s(s(X0)),X1) = f(s(zero),X1,X0,X1),
inference(superposition,[status(thm)],[c_63,c_222]) ).
tcf(c_257,plain,
! [X0: $i,X1: $i,X2: $i] : f(s(s(s(X0))),zero,s(s(s(X1))),X2) = f(s(s(X0)),X2,minus(X1,X0),X2),
inference(superposition,[status(thm)],[c_64,c_222]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i,X2: $i] : if(false,f(s(s(X0)),minus(zero,s(X0)),X1,X2),f(s(X0),X2,X1,X2)) = f(s(s(X0)),s(zero),X1,X2),
inference(superposition,[status(thm)],[c_66,c_75]) ).
tcf(c_279,plain,
! [X0: $i,X1: $i,X2: $i] : if('<='(zero,X0),f(s(zero),X0,X1,X2),f(zero,X2,X1,X2)) = f(s(zero),s(X0),X1,X2),
inference(superposition,[status(thm)],[c_63,c_75]) ).
tcf(c_280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if('<='(s(X0),s(X1)),f(s(s(X0)),minus(X1,X0),X2,X3),f(s(X0),X3,X2,X3)) = f(s(s(X0)),s(s(X1)),X2,X3),
inference(superposition,[status(thm)],[c_64,c_75]) ).
tcf(c_298,plain,
! [X0: $i,X1: $i,X2: $i] : if(true,f(s(zero),X0,X1,X2),f(zero,X2,X1,X2)) = f(s(zero),s(X0),X1,X2),
inference(light_normalisation,[status(thm)],[c_279,c_65]) ).
tcf(c_302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if('<='(X0,X1),f(s(s(X0)),minus(X1,X0),X2,X3),f(s(X0),X3,X2,X3)) = f(s(s(X0)),s(s(X1)),X2,X3),
inference(light_normalisation,[status(thm)],[c_280,c_67]) ).
tcf(c_410,plain,
! [X0: $i,X1: $i] : f(s(s(s(zero))),zero,s(s(s(X0))),X1) = f(s(s(zero)),X1,X0,X1),
inference(superposition,[status(thm)],[c_63,c_257]) ).
tcf(c_493,plain,
! [X0: $i,X1: $i,X2: $i] : f(s(zero),s(X0),X1,X2) = f(s(zero),X0,X1,X2),
inference(demodulation,[status(thm)],[c_298,c_68]) ).
tcf(c_509,plain,
! [X0: $i,X1: $i] : f(s(s(zero)),zero,s(s(X0)),s(X1)) = f(s(zero),X1,X0,s(X1)),
inference(superposition,[status(thm)],[c_493,c_256]) ).
tcf(c_537,plain,
! [X0: $i,X1: $i] : f(s(s(zero)),zero,s(s(X0)),s(s(X1))) = f(s(zero),X1,X0,s(s(X1))),
inference(superposition,[status(thm)],[c_509,c_493]) ).
tcf(c_562,plain,
! [X0: $i,X1: $i] : f(s(s(zero)),zero,s(s(X0)),s(s(s(X1)))) = f(s(zero),X1,X0,s(s(s(X1)))),
inference(superposition,[status(thm)],[c_537,c_493]) ).
tcf(c_741,plain,
! [X0: $i,X1: $i,X2: $i] : f(s(s(X0)),s(zero),X1,X2) = f(s(X0),X2,X1,X2),
inference(demodulation,[status(thm)],[c_273,c_69]) ).
tcf(c_768,plain,
! [X0: $i,X1: $i] : f(s(s(zero)),zero,s(s(X0)),X1) = f(s(s(zero)),s(zero),X0,X1),
inference(superposition,[status(thm)],[c_741,c_256]) ).
tcf(c_771,plain,
! [X0: $i,X1: $i] : f(s(s(s(zero))),zero,s(s(s(X0))),X1) = f(s(s(s(zero))),s(zero),X0,X1),
inference(superposition,[status(thm)],[c_741,c_410]) ).
tcf(c_777,plain,
! [X0: $i,X1: $i] : f(s(s(zero)),s(zero),X0,s(s(s(X1)))) = f(s(zero),X1,X0,s(s(s(X1)))),
inference(demodulation,[status(thm)],[c_562,c_768]) ).
tcf(c_1015,plain,
! [X0: $i,X1: $i] : f(s(s(zero)),s(zero),X0,s(s(s(s(X1))))) = f(s(zero),X1,X0,s(s(s(s(X1))))),
inference(superposition,[status(thm)],[c_777,c_493]) ).
tcf(c_1137,plain,
! [X0: $i,X1: $i] : f(s(s(zero)),s(zero),X0,s(s(s(s(s(X1)))))) = f(s(zero),X1,X0,s(s(s(s(s(X1)))))),
inference(superposition,[status(thm)],[c_1015,c_493]) ).
tcf(c_1164,plain,
! [X0: $i,X1: $i,X2: $i] : if(false,f(s(s(s(X0))),minus(zero,s(X0)),X1,X2),f(s(s(X0)),X2,X1,X2)) = f(s(s(s(X0))),s(s(zero)),X1,X2),
inference(superposition,[status(thm)],[c_66,c_302]) ).
tcf(c_1174,plain,
! [X0: $i,X1: $i,X2: $i] : if('<='(zero,X0),f(s(s(zero)),X0,X1,X2),f(s(zero),X2,X1,X2)) = f(s(s(zero)),s(s(X0)),X1,X2),
inference(superposition,[status(thm)],[c_63,c_302]) ).
tcf(c_1175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if('<='(s(X0),s(X1)),f(s(s(s(X0))),minus(X1,X0),X2,X3),f(s(s(X0)),X3,X2,X3)) = f(s(s(s(X0))),s(s(s(X1))),X2,X3),
inference(superposition,[status(thm)],[c_64,c_302]) ).
tcf(c_1208,plain,
! [X0: $i,X1: $i,X2: $i] : if(true,f(s(s(zero)),X0,X1,X2),f(s(zero),X2,X1,X2)) = f(s(s(zero)),s(s(X0)),X1,X2),
inference(light_normalisation,[status(thm)],[c_1174,c_65]) ).
tcf(c_1214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if('<='(X0,X1),f(s(s(s(X0))),minus(X1,X0),X2,X3),f(s(s(X0)),X3,X2,X3)) = f(s(s(s(X0))),s(s(s(X1))),X2,X3),
inference(light_normalisation,[status(thm)],[c_1175,c_67]) ).
tcf(c_1342,plain,
! [X0: $i,X1: $i,X2: $i] : f(s(s(zero)),s(s(X0)),X1,X2) = f(s(s(zero)),X0,X1,X2),
inference(demodulation,[status(thm)],[c_1208,c_68]) ).
tcf(c_1356,plain,
! [X0: $i,X1: $i] : f(s(s(s(zero))),s(zero),X0,s(s(X1))) = f(s(s(zero)),X1,X0,s(s(X1))),
inference(superposition,[status(thm)],[c_1342,c_741]) ).
tcf(c_1391,plain,
! [X0: $i,X1: $i] : f(s(s(s(zero))),s(zero),X0,s(s(s(s(X1))))) = f(s(s(zero)),X1,X0,s(s(s(s(X1))))),
inference(superposition,[status(thm)],[c_1356,c_1342]) ).
tcf(c_1518,plain,
! [X0: $i,X1: $i] : f(s(s(zero)),s(zero),X0,s(s(s(s(s(s(X1))))))) = f(s(zero),X1,X0,s(s(s(s(s(s(X1))))))),
inference(superposition,[status(thm)],[c_1137,c_493]) ).
tcf(c_1724,plain,
! [X0: $i,X1: $i] : f(s(s(s(zero))),s(zero),X0,s(s(s(s(s(s(X1))))))) = f(s(s(zero)),X1,X0,s(s(s(s(s(s(X1))))))),
inference(superposition,[status(thm)],[c_1391,c_1342]) ).
tcf(c_1972,plain,
! [X0: $i,X1: $i,X2: $i] : f(s(s(s(X0))),s(s(zero)),X1,X2) = f(s(s(X0)),X2,X1,X2),
inference(demodulation,[status(thm)],[c_1164,c_69]) ).
tcf(c_2005,plain,
! [X0: $i,X1: $i,X2: $i] : f(s(s(s(X0))),s(s(zero)),X1,X2) = f(s(s(s(X0))),s(zero),X1,X2),
inference(superposition,[status(thm)],[c_1972,c_741]) ).
tcf(c_3360,plain,
! [X0: $i,X1: $i,X2: $i] : if('<='(zero,X0),f(s(s(s(zero))),X0,X1,X2),f(s(s(zero)),X2,X1,X2)) = f(s(s(s(zero))),s(s(s(X0))),X1,X2),
inference(superposition,[status(thm)],[c_63,c_1214]) ).
tcf(c_3361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if('<='(s(X0),s(X1)),f(s(s(s(s(X0)))),minus(X1,X0),X2,X3),f(s(s(s(X0))),X3,X2,X3)) = f(s(s(s(s(X0)))),s(s(s(s(X1)))),X2,X3),
inference(superposition,[status(thm)],[c_64,c_1214]) ).
tcf(c_3400,plain,
! [X0: $i,X1: $i,X2: $i] : if(true,f(s(s(s(zero))),X0,X1,X2),f(s(s(zero)),X2,X1,X2)) = f(s(s(s(zero))),s(s(s(X0))),X1,X2),
inference(light_normalisation,[status(thm)],[c_3360,c_65]) ).
tcf(c_3407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : if('<='(X0,X1),f(s(s(s(s(X0)))),minus(X1,X0),X2,X3),f(s(s(s(X0))),X3,X2,X3)) = f(s(s(s(s(X0)))),s(s(s(s(X1)))),X2,X3),
inference(light_normalisation,[status(thm)],[c_3361,c_67]) ).
tcf(c_3572,plain,
! [X0: $i,X1: $i,X2: $i] : f(s(s(s(zero))),s(s(s(X0))),X1,X2) = f(s(s(s(zero))),X0,X1,X2),
inference(demodulation,[status(thm)],[c_3400,c_68]) ).
tcf(c_3585,plain,
! [X0: $i,X1: $i] : f(s(s(s(s(zero)))),s(zero),X0,s(s(s(X1)))) = f(s(s(s(zero))),X1,X0,s(s(s(X1)))),
inference(superposition,[status(thm)],[c_3572,c_741]) ).
tcf(c_3719,plain,
! [X0: $i,X1: $i] : f(s(s(s(s(zero)))),s(zero),X0,s(s(s(s(s(s(X1))))))) = f(s(s(s(zero))),X1,X0,s(s(s(s(s(s(X1))))))),
inference(superposition,[status(thm)],[c_3585,c_3572]) ).
tcf(c_5924,plain,
! [X0: $i,X1: $i,X2: $i] : if('<='(zero,X0),f(s(s(s(s(zero)))),X0,X1,X2),f(s(s(s(zero))),X2,X1,X2)) = f(s(s(s(s(zero)))),s(s(s(s(X0)))),X1,X2),
inference(superposition,[status(thm)],[c_63,c_3407]) ).
tcf(c_5969,plain,
! [X0: $i,X1: $i,X2: $i] : if(true,f(s(s(s(s(zero)))),X0,X1,X2),f(s(s(s(zero))),X2,X1,X2)) = f(s(s(s(s(zero)))),s(s(s(s(X0)))),X1,X2),
inference(light_normalisation,[status(thm)],[c_5924,c_65]) ).
tcf(c_6272,plain,
! [X0: $i,X1: $i,X2: $i] : f(s(s(s(s(zero)))),s(s(s(s(X0)))),X1,X2) = f(s(s(s(s(zero)))),X0,X1,X2),
inference(demodulation,[status(thm)],[c_5969,c_68]) ).
tcf(c_6287,plain,
! [X0: $i,X1: $i] : f(s(s(s(s(s(zero))))),s(zero),X0,s(s(s(s(X1))))) = f(s(s(s(s(zero)))),X1,X0,s(s(s(s(X1))))),
inference(superposition,[status(thm)],[c_6272,c_741]) ).
tcf(c_6475,plain,
f(s(s(s(s(zero)))),s(s(zero)),s(s(s(s(s(s(zero)))))),s(s(s(s(s(s(zero))))))) = perfectp(s(s(s(s(s(s(zero))))))),
inference(superposition,[status(thm)],[c_6287,c_71]) ).
tcf(c_6595,plain,
perfectp(s(s(s(s(s(s(zero))))))) = true,
inference(demodulation,[status(thm)],[c_6475,c_231,c_768,c_771,c_1518,c_1724,c_2005,c_3719]) ).
tcf(c_6596,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6595,c_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN135-1.006 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.34 % Computer : n004.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Thu Sep 24 06:04:51 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.38 Running UEQ theorem proving
% 0.07/0.38 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
% 0.07/0.39
% 0.07/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.39
% 0.07/0.39 % Detected problem language: tptp
% 0.07/0.40 % Proving...
% 11.71/2.30 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 11.71/2.30 % SZS status Started for theBenchmark.p
% 11.71/2.30 % SZS status Unsatisfiable for theBenchmark.p
% 11.71/2.30
% 11.71/2.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 11.71/2.30
% 11.71/2.30 % ------ iProver source info
% 11.71/2.30
% 11.71/2.30 % git: date: 2026-07-19 20:42:38 +0200
% 11.71/2.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 11.71/2.30 % git: non_committed_changes: false
% 11.71/2.30
% 11.71/2.30 % ------ Parsing...% successful
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% 11.71/2.30
% 11.71/2.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 11.71/2.30
% 11.71/2.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 11.71/2.30
% 11.71/2.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 11.71/2.30
% 11.71/2.30 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 11.71/2.30 % ------ Proving...
% 11.71/2.30 % ------ Problem Properties
% 11.71/2.30
% 11.71/2.30 %
% 11.71/2.30 % clauses 14
% 11.71/2.30 % conjectures 1
% 11.71/2.30 % EPR 0
% 11.71/2.30 % Horn 14
% 11.71/2.30 % unary 14
% 11.71/2.30 % binary 0
% 11.71/2.30 % lits 14
% 11.71/2.30 % lits eq 14
% 11.71/2.30 % fd_pure 0
% 11.71/2.30 % fd_pseudo 0
% 11.71/2.30 % fd_cond 0
% 11.71/2.30 % fd_pseudo_cond 0
% 11.71/2.30 % AC symbols 0
% 11.71/2.30
% 11.71/2.30 % ------ Input Options Time Limit: Unbounded
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% 11.71/2.30
% 11.71/2.30 % ------
% 11.71/2.30 % Current options:
% 11.71/2.30 % ------
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% 11.71/2.30 %
% 11.71/2.30
% 11.71/2.30 % ------ Proving...
% 11.71/2.30 %
% 11.71/2.30
% 11.71/2.30 % SZS status Unsatisfiable for theBenchmark.p
% 11.71/2.30
% 11.71/2.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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%------------------------------------------------------------------------------