%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM926+2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.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 02:27:20 PM UTC 2026
% Result : Theorem 22.41s 3.81s
% Output : CNFRefutation 22.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 25
% Syntax : Number of formulae : 98 ( 66 unt; 0 def)
% Number of atoms : 168 ( 77 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 124 ( 54 ~; 50 |; 14 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 9 con; 0-2 aty)
% Number of variables : 150 ( 0 sgn 138 !; 12 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
is_int(one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).
fof(f18,axiom,
is_int(t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_t____) ).
fof(f19,axiom,
ord_less_eq_int(one_one_int,t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tpos) ).
fof(f20,axiom,
( t = one_one_int
=> ? [X0,X1] :
( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
& is_int(X1)
& is_int(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
fof(f21,axiom,
( ord_less_int(one_one_int,t)
=> ? [X0,X1] :
( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
& is_int(X1)
& is_int(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
fof(f57,axiom,
! [X0,X1] :
( ( is_int(X1)
& is_int(X0) )
=> ( ord_less_int(X1,X0)
| X0 = X1
| ord_less_int(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_zless__linear) ).
fof(f122,axiom,
! [X0,X1,X2] : times_times_real(times_times_real(X0,X1),X2) = times_times_real(X0,times_times_real(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(f123,axiom,
! [X0,X1,X2] : times_times_nat(times_times_nat(X0,X1),X2) = times_times_nat(X0,times_times_nat(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(f124,axiom,
! [X0,X1,X2] : times_times_int(times_times_int(X0,X1),X2) = times_times_int(X0,times_times_int(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(f131,axiom,
! [X0,X1] : times_times_real(X0,X1) = times_times_real(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f132,axiom,
! [X0,X1] : times_times_nat(X0,X1) = times_times_nat(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f133,axiom,
! [X0,X1] : times_times_int(X0,X1) = times_times_int(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f140,axiom,
! [X0,X1,X2] : plus_plus_real(plus_plus_real(X0,X1),X2) = plus_plus_real(X0,plus_plus_real(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(f141,axiom,
! [X0,X1,X2] : plus_plus_nat(plus_plus_nat(X0,X1),X2) = plus_plus_nat(X0,plus_plus_nat(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(f142,axiom,
! [X0,X1,X2] : plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(X0,plus_plus_int(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(f149,axiom,
! [X0,X1] : plus_plus_real(X0,X1) = plus_plus_real(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f150,axiom,
! [X0,X1] : plus_plus_nat(X0,X1) = plus_plus_nat(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f151,axiom,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f223,axiom,
! [X0] : bit0(X0) = plus_plus_int(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_Bit0__def) ).
fof(f270,axiom,
! [X0] : bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_Bit1__def) ).
fof(f375,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_Pls__def) ).
fof(f443,axiom,
! [X0] :
( ord_less_eq_int(one_one_int,X0)
<=> ord_less_int(zero_zero_int,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_int__one__le__iff__zero__less) ).
fof(f587,axiom,
! [X0,X1] : zcong(X0,X1,one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_zcong__1) ).
fof(f661,axiom,
! [X0,X1] :
( ord_less_int(zero_zero_int,X1)
=> ( ord_less_int(X1,X0)
=> ~ zcong(X1,zero_zero_int,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_642_zcong__not__zero) ).
fof(f717,conjecture,
? [X0,X1] : plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f718,negated_conjecture,
~ ? [X0,X1] : plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
inference(negated_conjecture,[status(cth)],[f717]) ).
fof(f731,plain,
( one_one_int != t
| ? [X0,X1] :
( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
& is_int(X1)
& is_int(X0) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f732,plain,
( ~ ord_less_int(one_one_int,t)
| ? [X0,X1] :
( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
& is_int(X1)
& is_int(X0) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f736,plain,
! [X0,X1] :
( ~ is_int(X1)
| ~ is_int(X0)
| ord_less_int(X1,X0)
| X0 = X1
| ord_less_int(X0,X1) ),
inference(ennf_transformation,[],[f57]) ).
fof(f737,plain,
! [X0,X1] :
( ~ is_int(X1)
| ~ is_int(X0)
| ord_less_int(X1,X0)
| X0 = X1
| ord_less_int(X0,X1) ),
inference(flattening,[],[f736]) ).
fof(f1083,plain,
! [X0,X1] :
( ~ ord_less_int(zero_zero_int,X1)
| ~ ord_less_int(X1,X0)
| ~ zcong(X1,zero_zero_int,X0) ),
inference(ennf_transformation,[],[f661]) ).
fof(f1084,plain,
! [X0,X1] :
( ~ ord_less_int(zero_zero_int,X1)
| ~ ord_less_int(X1,X0)
| ~ zcong(X1,zero_zero_int,X0) ),
inference(flattening,[],[f1083]) ).
fof(f1146,plain,
! [X0,X1] : plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
inference(ennf_transformation,[],[f718]) ).
fof(f1147,plain,
( one_one_int != t
| ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK1,number_number_of_nat(bit0(bit1(pls)))))
& is_int(sK1)
& is_int(sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f731]) ).
fof(f1148,plain,
( ~ ord_less_int(one_one_int,t)
| ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK2,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK3,number_number_of_nat(bit0(bit1(pls)))))
& is_int(sK3)
& is_int(sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f732]) ).
fof(f1256,plain,
! [X0] :
( ( ~ ord_less_eq_int(one_one_int,X0)
| ord_less_int(zero_zero_int,X0) )
& ( ~ ord_less_int(zero_zero_int,X0)
| ord_less_eq_int(one_one_int,X0) ) ),
inference(nnf_transformation,[],[f443]) ).
fof(f1365,plain,
is_int(one_one_int),
inference(cnf_transformation,[],[f2]) ).
fof(f1381,plain,
is_int(t),
inference(cnf_transformation,[],[f18]) ).
fof(f1382,plain,
ord_less_eq_int(one_one_int,t),
inference(cnf_transformation,[],[f19]) ).
fof(f1383,plain,
( one_one_int != t
| plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK1,number_number_of_nat(bit0(bit1(pls))))) ),
inference(cnf_transformation,[],[f1147]) ).
fof(f1386,plain,
( ~ ord_less_int(one_one_int,t)
| plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK2,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK3,number_number_of_nat(bit0(bit1(pls))))) ),
inference(cnf_transformation,[],[f1148]) ).
fof(f1427,plain,
! [X0,X1] :
( ~ is_int(X1)
| ~ is_int(X0)
| ord_less_int(X1,X0)
| X0 = X1
| ord_less_int(X0,X1) ),
inference(cnf_transformation,[],[f737]) ).
fof(f1519,plain,
! [X2,X0,X1] : times_times_real(times_times_real(X0,X1),X2) = times_times_real(X0,times_times_real(X1,X2)),
inference(cnf_transformation,[],[f122]) ).
fof(f1520,plain,
! [X2,X0,X1] : times_times_nat(times_times_nat(X0,X1),X2) = times_times_nat(X0,times_times_nat(X1,X2)),
inference(cnf_transformation,[],[f123]) ).
fof(f1521,plain,
! [X2,X0,X1] : times_times_int(times_times_int(X0,X1),X2) = times_times_int(X0,times_times_int(X1,X2)),
inference(cnf_transformation,[],[f124]) ).
fof(f1528,plain,
! [X0,X1] : times_times_real(X0,X1) = times_times_real(X1,X0),
inference(cnf_transformation,[],[f131]) ).
fof(f1529,plain,
! [X0,X1] : times_times_nat(X0,X1) = times_times_nat(X1,X0),
inference(cnf_transformation,[],[f132]) ).
fof(f1530,plain,
! [X0,X1] : times_times_int(X0,X1) = times_times_int(X1,X0),
inference(cnf_transformation,[],[f133]) ).
fof(f1537,plain,
! [X2,X0,X1] : plus_plus_real(plus_plus_real(X0,X1),X2) = plus_plus_real(X0,plus_plus_real(X1,X2)),
inference(cnf_transformation,[],[f140]) ).
fof(f1538,plain,
! [X2,X0,X1] : plus_plus_nat(plus_plus_nat(X0,X1),X2) = plus_plus_nat(X0,plus_plus_nat(X1,X2)),
inference(cnf_transformation,[],[f141]) ).
fof(f1539,plain,
! [X2,X0,X1] : plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(X0,plus_plus_int(X1,X2)),
inference(cnf_transformation,[],[f142]) ).
fof(f1546,plain,
! [X0,X1] : plus_plus_real(X0,X1) = plus_plus_real(X1,X0),
inference(cnf_transformation,[],[f149]) ).
fof(f1547,plain,
! [X0,X1] : plus_plus_nat(X0,X1) = plus_plus_nat(X1,X0),
inference(cnf_transformation,[],[f150]) ).
fof(f1548,plain,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
inference(cnf_transformation,[],[f151]) ).
fof(f1661,plain,
! [X0] : bit0(X0) = plus_plus_int(X0,X0),
inference(cnf_transformation,[],[f223]) ).
fof(f1708,plain,
! [X0] : bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0),
inference(cnf_transformation,[],[f270]) ).
fof(f1839,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f375]) ).
fof(f1930,plain,
! [X0] :
( ~ ord_less_eq_int(one_one_int,X0)
| ord_less_int(zero_zero_int,X0) ),
inference(cnf_transformation,[],[f1256]) ).
fof(f2147,plain,
! [X0,X1] : zcong(X0,X1,one_one_int),
inference(cnf_transformation,[],[f587]) ).
fof(f2250,plain,
! [X0,X1] :
( ~ ord_less_int(zero_zero_int,X1)
| ~ ord_less_int(X1,X0)
| ~ zcong(X1,zero_zero_int,X0) ),
inference(cnf_transformation,[],[f1084]) ).
fof(f2327,plain,
! [X0,X1] : plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
inference(cnf_transformation,[],[f1146]) ).
fof(f2331,plain,
( one_one_int != t
| plus_plus_int(times_times_int(number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)),plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK0,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),power_power_int(sK1,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls))))) ),
inference(definition_unfolding,[],[f1383,f1661,f1661,f1708,f1661,f1708,f1661,f1708]) ).
fof(f2332,plain,
( ~ ord_less_int(one_one_int,t)
| plus_plus_int(times_times_int(number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)),plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK2,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),power_power_int(sK3,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls))))) ),
inference(definition_unfolding,[],[f1386,f1661,f1661,f1708,f1661,f1708,f1661,f1708]) ).
fof(f2568,plain,
! [X0] :
( ~ ord_less_eq_int(one_one_int,X0)
| ord_less_int(pls,X0) ),
inference(definition_unfolding,[],[f1930,f1839]) ).
fof(f2707,plain,
! [X0,X1] :
( ~ ord_less_int(pls,X1)
| ~ ord_less_int(X1,X0)
| ~ zcong(X1,pls,X0) ),
inference(definition_unfolding,[],[f2250,f1839,f1839]) ).
fof(f2739,plain,
! [X0,X1] : plus_plus_int(times_times_int(number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)),plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),m),one_one_int) != plus_plus_int(power_power_int(X0,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),power_power_int(X1,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls))))),
inference(definition_unfolding,[],[f2327,f1661,f1708,f1661,f1708,f1661,f1661,f1708]) ).
tcf(c_50,plain,
is_int(one_one_int),
inference(cnf_transformation,[],[f1365]) ).
tcf(c_66,plain,
is_int(t),
inference(cnf_transformation,[],[f1381]) ).
tcf(c_67,plain,
ord_less_eq_int(one_one_int,t),
inference(cnf_transformation,[],[f1382]) ).
tcf(c_70,plain,
( ( plus_plus_int(power_power_int(sK0,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),power_power_int(sK1,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls))))) = plus_plus_int(times_times_int(number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)),plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),m),one_one_int) )
| ( one_one_int != t ) ),
inference(cnf_transformation,[],[f2331]) ).
tcf(c_73,plain,
( ( plus_plus_int(power_power_int(sK2,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),power_power_int(sK3,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls))))) = plus_plus_int(times_times_int(number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)),plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),m),one_one_int) )
| ~ ord_less_int(one_one_int,t) ),
inference(cnf_transformation,[],[f2332]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( ord_less_int(X1,X0)
| ord_less_int(X0,X1)
| ( X0 = X1 )
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f1427]) ).
tcf(c_204,plain,
! [X0: $i,X1: $i,X2: $i] : times_times_real(times_times_real(X0,X1),X2) = times_times_real(X0,times_times_real(X1,X2)),
inference(cnf_transformation,[],[f1519]) ).
tcf(c_205,plain,
! [X0: $i,X1: $i,X2: $i] : times_times_nat(times_times_nat(X0,X1),X2) = times_times_nat(X0,times_times_nat(X1,X2)),
inference(cnf_transformation,[],[f1520]) ).
tcf(c_206,plain,
! [X0: $i,X1: $i,X2: $i] : times_times_int(times_times_int(X0,X1),X2) = times_times_int(X0,times_times_int(X1,X2)),
inference(cnf_transformation,[],[f1521]) ).
tcf(c_213,plain,
! [X0: $i,X1: $i] : times_times_real(X0,X1) = times_times_real(X1,X0),
inference(cnf_transformation,[],[f1528]) ).
tcf(c_214,plain,
! [X0: $i,X1: $i] : times_times_nat(X0,X1) = times_times_nat(X1,X0),
inference(cnf_transformation,[],[f1529]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i] : times_times_int(X0,X1) = times_times_int(X1,X0),
inference(cnf_transformation,[],[f1530]) ).
tcf(c_222,plain,
! [X0: $i,X1: $i,X2: $i] : plus_plus_real(plus_plus_real(X0,X1),X2) = plus_plus_real(X0,plus_plus_real(X1,X2)),
inference(cnf_transformation,[],[f1537]) ).
tcf(c_223,plain,
! [X0: $i,X1: $i,X2: $i] : plus_plus_nat(plus_plus_nat(X0,X1),X2) = plus_plus_nat(X0,plus_plus_nat(X1,X2)),
inference(cnf_transformation,[],[f1538]) ).
tcf(c_224,plain,
! [X0: $i,X1: $i,X2: $i] : plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(X0,plus_plus_int(X1,X2)),
inference(cnf_transformation,[],[f1539]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i] : plus_plus_real(X0,X1) = plus_plus_real(X1,X0),
inference(cnf_transformation,[],[f1546]) ).
tcf(c_232,plain,
! [X0: $i,X1: $i] : plus_plus_nat(X0,X1) = plus_plus_nat(X1,X0),
inference(cnf_transformation,[],[f1547]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
inference(cnf_transformation,[],[f1548]) ).
tcf(c_602,plain,
! [X0: $i] :
( ord_less_int(pls,X0)
| ~ ord_less_eq_int(one_one_int,X0) ),
inference(cnf_transformation,[],[f2568]) ).
tcf(c_815,plain,
! [X0: $i,X1: $i] : zcong(X0,X1,one_one_int),
inference(cnf_transformation,[],[f2147]) ).
tcf(c_918,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ ord_less_int(pls,X0)
| ~ ord_less_int(X0,X1)
| ~ zcong(X0,pls,X1) ),
inference(cnf_transformation,[],[f2707]) ).
tcf(c_993,negated_conjecture,
! [X0: $i,X1: $i] : plus_plus_int(power_power_int(X0,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),power_power_int(X1,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls))))) != plus_plus_int(times_times_int(number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)),plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),m),one_one_int),
inference(cnf_transformation,[],[f2739]) ).
tcf(c_1525,plain,
( ( plus_plus_int(power_power_int(sK0,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int))))))),power_power_int(sK1,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int)))))))) = plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int)))))))))))))) )
| ( one_one_int != t ) ),
inference(theory_normalisation,[status(thm)],[c_70,c_205,c_214,c_223,c_232,c_204,c_213,c_222,c_231,c_206,c_215,c_224,c_233]) ).
tcf(c_1526,plain,
( ( plus_plus_int(power_power_int(sK2,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int))))))),power_power_int(sK3,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int)))))))) = plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int)))))))))))))) )
| ~ ord_less_int(one_one_int,t) ),
inference(theory_normalisation,[status(thm)],[c_73,c_205,c_214,c_223,c_232,c_204,c_213,c_222,c_231,c_206,c_215,c_224,c_233]) ).
tcf(c_1727,negated_conjecture,
! [X0: $i,X1: $i] : plus_plus_int(power_power_int(X0,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int))))))),power_power_int(X1,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int)))))))) != plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int)))))))))))))),
inference(theory_normalisation,[status(thm)],[c_993,c_205,c_214,c_223,c_232,c_204,c_213,c_222,c_231,c_206,c_215,c_224,c_233]) ).
tcf(c_2931,plain,
! [X0: $i] :
( ~ ord_less_int(pls,X0)
| ~ ord_less_int(X0,one_one_int) ),
inference(superposition,[status(thm)],[c_815,c_918]) ).
tcf(c_3409,plain,
ord_less_int(pls,t),
inference(superposition,[status(thm)],[c_67,c_602]) ).
tcf(c_3417,plain,
~ ord_less_int(t,one_one_int),
inference(superposition,[status(thm)],[c_3409,c_2931]) ).
tcf(c_4612,plain,
( ord_less_int(t,one_one_int)
| ord_less_int(one_one_int,t)
| ( one_one_int = t )
| ~ is_int(t)
| ~ is_int(one_one_int) ),
inference(instantiation,[status(thm)],[c_112]) ).
tcf(c_9389,plain,
~ ord_less_int(one_one_int,t),
inference(backward_subsumption_resolution,[status(thm)],[c_1526,c_1727]) ).
tcf(c_9390,plain,
one_one_int != t,
inference(backward_subsumption_resolution,[status(thm)],[c_1525,c_1727]) ).
tcf(c_9391,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9389,c_9390,c_4612,c_3417,c_50,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n001.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 05:50:22 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_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
% 0.10/0.43 % Proving...
% 22.41/3.81 % SZS status Started for theBenchmark.p
% 22.41/3.81 % SZS status Theorem for theBenchmark.p
% 22.41/3.81
% 22.41/3.81 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 22.41/3.81
% 22.41/3.81 % ------ iProver source info
% 22.41/3.81
% 22.41/3.81 % git: date: 2026-07-19 20:42:38 +0200
% 22.41/3.81 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 22.41/3.81 % git: non_committed_changes: false
% 22.41/3.81
% 22.41/3.81 % ------ Parsing...
% 22.41/3.81 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 22.41/3.81
% 22.41/3.81 % ------ Preprocessing... sup_sim: 4 sf_s rm: 11 0s sf_e sup_sim: 0 sf_s rm: 3 0s sf_e %
% 22.41/3.81
% 22.41/3.81 % ------ Preprocessing...%
% 22.41/3.81
% 22.41/3.81 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 22.41/3.81 % ------ Proving...
% 22.41/3.81 % ------ Problem Properties
% 22.41/3.81
% 22.41/3.81 %
% 22.41/3.81 % clauses 703
% 22.41/3.81 % conjectures 42
% 22.41/3.81 % EPR 74
% 22.41/3.81 % Horn 630
% 22.41/3.81 % unary 259
% 22.41/3.81 % binary 238
% 22.41/3.81 % lits 1486
% 22.41/3.81 % lits eq 421
% 22.41/3.81 % fd_pure 0
% 22.41/3.81 % fd_pseudo 0
% 22.41/3.81 % fd_cond 67
% 22.41/3.81 % fd_pseudo_cond 37
% 22.41/3.81 % AC symbols 6
% 22.41/3.81
% 22.41/3.81 % ------ Input Options Time Limit: Unbounded
% 22.41/3.81
% 22.41/3.81
% 22.41/3.81 % ------
% 22.41/3.81 % Current options:
% 22.41/3.81 % ------
% 22.41/3.81
% 22.41/3.81
% 22.41/3.81 %
% 22.41/3.81
% 22.41/3.81 % ------ Proving...
% 22.41/3.81 %
% 22.41/3.81
% 22.41/3.81 % SZS status Theorem for theBenchmark.p
% 22.41/3.81
% 22.41/3.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 22.41/3.82
% 22.41/3.82
%------------------------------------------------------------------------------