%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP012+5 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.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 01:29:54 PM UTC 2026
% Result : Theorem 3.07s 0.98s
% Output : CNFRefutation 3.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 1
% Syntax : Number of formulae : 49 ( 24 unt; 0 def)
% Number of atoms : 187 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 215 ( 77 ~; 57 |; 69 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 236 ( 0 sgn 215 !; 21 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ! [X1] : product(inverse(X1),X1,X0)
& ! [X1] : product(X1,inverse(X1),X0)
& ! [X1] : product(X0,X1,X1)
& ! [X1] : product(X1,X0,X1)
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X1,X5,X6)
& product(X2,X3,X5)
& product(X1,X2,X4) )
=> product(X4,X3,X6) )
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X4,X3,X6)
& product(X2,X3,X5)
& product(X1,X2,X4) )
=> product(X1,X5,X6) )
& ! [X1,X2] :
? [X3] : product(X1,X2,X3) )
=> ! [X4,X5,X6,X1] :
( ( product(X5,X4,X1)
& product(inverse(X4),inverse(X5),X6) )
=> product(inverse(X6),inverse(X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distribution) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ! [X1] : product(inverse(X1),X1,X0)
& ! [X1] : product(X1,inverse(X1),X0)
& ! [X1] : product(X0,X1,X1)
& ! [X1] : product(X1,X0,X1)
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X1,X5,X6)
& product(X2,X3,X5)
& product(X1,X2,X4) )
=> product(X4,X3,X6) )
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X4,X3,X6)
& product(X2,X3,X5)
& product(X1,X2,X4) )
=> product(X1,X5,X6) )
& ! [X1,X2] :
? [X3] : product(X1,X2,X3) )
=> ! [X4,X5,X6,X1] :
( ( product(X5,X4,X1)
& product(inverse(X4),inverse(X5),X6) )
=> product(inverse(X6),inverse(X1),X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ! [X0] :
( ( ! [X19] : product(inverse(X19),X19,X0)
& ! [X18] : product(X18,inverse(X18),X0)
& ! [X17] : product(X0,X17,X17)
& ! [X16] : product(X16,X0,X16)
& ! [X10,X11,X12,X13,X14,X15] :
( ( product(X10,X14,X15)
& product(X11,X12,X14)
& product(X10,X11,X13) )
=> product(X13,X12,X15) )
& ! [X4,X5,X6,X7,X8,X9] :
( ( product(X7,X6,X9)
& product(X5,X6,X8)
& product(X4,X5,X7) )
=> product(X4,X8,X9) )
& ! [X1,X2] :
? [X3] : product(X1,X2,X3) )
=> ! [X20,X21,X22,X23] :
( ( product(X21,X20,X23)
& product(inverse(X20),inverse(X21),X22) )
=> product(inverse(X22),inverse(X23),X0) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
? [X0] :
( ! [X19] : product(inverse(X19),X19,X0)
& ! [X18] : product(X18,inverse(X18),X0)
& ! [X17] : product(X0,X17,X17)
& ! [X16] : product(X16,X0,X16)
& ! [X10,X11,X12,X13,X14,X15] :
( ~ product(X10,X14,X15)
| ~ product(X11,X12,X14)
| ~ product(X10,X11,X13)
| product(X13,X12,X15) )
& ! [X4,X5,X6,X7,X8,X9] :
( ~ product(X7,X6,X9)
| ~ product(X5,X6,X8)
| ~ product(X4,X5,X7)
| product(X4,X8,X9) )
& ! [X1,X2] :
? [X3] : product(X1,X2,X3)
& ? [X20,X21,X22,X23] :
( product(X21,X20,X23)
& product(inverse(X20),inverse(X21),X22)
& ~ product(inverse(X22),inverse(X23),X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
? [X0] :
( ! [X19] : product(inverse(X19),X19,X0)
& ! [X18] : product(X18,inverse(X18),X0)
& ! [X17] : product(X0,X17,X17)
& ! [X16] : product(X16,X0,X16)
& ! [X10,X11,X12,X13,X14,X15] :
( ~ product(X10,X14,X15)
| ~ product(X11,X12,X14)
| ~ product(X10,X11,X13)
| product(X13,X12,X15) )
& ! [X4,X5,X6,X7,X8,X9] :
( ~ product(X7,X6,X9)
| ~ product(X5,X6,X8)
| ~ product(X4,X5,X7)
| product(X4,X8,X9) )
& ! [X1,X2] :
? [X3] : product(X1,X2,X3)
& ? [X20,X21,X22,X23] :
( product(X21,X20,X23)
& product(inverse(X20),inverse(X21),X22)
& ~ product(inverse(X22),inverse(X23),X0) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
? [X0] :
( ! [X23] : product(inverse(X23),X23,X0)
& ! [X22] : product(X22,inverse(X22),X0)
& ! [X21] : product(X0,X21,X21)
& ! [X20] : product(X20,X0,X20)
& ! [X14,X15,X16,X17,X18,X19] :
( ~ product(X14,X18,X19)
| ~ product(X15,X16,X18)
| ~ product(X14,X15,X17)
| product(X17,X16,X19) )
& ! [X8,X9,X10,X11,X12,X13] :
( ~ product(X11,X10,X13)
| ~ product(X9,X10,X12)
| ~ product(X8,X9,X11)
| product(X8,X12,X13) )
& ! [X5,X6] :
? [X7] : product(X5,X6,X7)
& ? [X1,X2,X3,X4] :
( product(X2,X1,X4)
& product(inverse(X1),inverse(X2),X3)
& ~ product(inverse(X3),inverse(X4),X0) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ! [X23] : product(inverse(X23),X23,sK0)
& ! [X22] : product(X22,inverse(X22),sK0)
& ! [X21] : product(sK0,X21,X21)
& ! [X20] : product(X20,sK0,X20)
& ! [X14,X15,X16,X17,X18,X19] :
( ~ product(X14,X18,X19)
| ~ product(X15,X16,X18)
| ~ product(X14,X15,X17)
| product(X17,X16,X19) )
& ! [X8,X9,X10,X11,X12,X13] :
( ~ product(X11,X10,X13)
| ~ product(X9,X10,X12)
| ~ product(X8,X9,X11)
| product(X8,X12,X13) )
& ! [X5,X6] : product(X5,X6,sK5(X5,X6))
& product(sK2,sK1,sK4)
& product(inverse(sK1),inverse(sK2),sK3)
& ~ product(inverse(sK3),inverse(sK4),sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X7,sK5(X5,X6))],[f6]) ).
fof(f8,plain,
! [X23] : product(inverse(X23),X23,sK0),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X22] : product(X22,inverse(X22),sK0),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X21] : product(sK0,X21,X21),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X20] : product(X20,sK0,X20),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X18,X19,X16,X14,X17,X15] :
( ~ product(X14,X18,X19)
| ~ product(X15,X16,X18)
| ~ product(X14,X15,X17)
| product(X17,X16,X19) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X10,X11,X8,X9,X12,X13] :
( ~ product(X11,X10,X13)
| ~ product(X9,X10,X12)
| ~ product(X8,X9,X11)
| product(X8,X12,X13) ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
! [X6,X5] : product(X5,X6,sK5(X5,X6)),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
product(sK2,sK1,sK4),
inference(cnf_transformation,[],[f7]) ).
fof(f16,plain,
product(inverse(sK1),inverse(sK2),sK3),
inference(cnf_transformation,[],[f7]) ).
fof(f17,plain,
~ product(inverse(sK3),inverse(sK4),sK0),
inference(cnf_transformation,[],[f7]) ).
tcf(c_49,negated_conjecture,
~ product(inverse(sK3),inverse(sK4),sK0),
inference(cnf_transformation,[],[f17]) ).
tcf(c_50,negated_conjecture,
product(inverse(sK1),inverse(sK2),sK3),
inference(cnf_transformation,[],[f16]) ).
tcf(c_51,negated_conjecture,
product(sK2,sK1,sK4),
inference(cnf_transformation,[],[f15]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i] : product(X0,X1,sK5(X0,X1)),
inference(cnf_transformation,[],[f14]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_54,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X2,X5,X4)
| ~ product(X1,X5,X3)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_55,negated_conjecture,
! [X0: $i] : product(X0,sK0,X0),
inference(cnf_transformation,[],[f11]) ).
tcf(c_56,negated_conjecture,
! [X0: $i] : product(sK0,X0,X0),
inference(cnf_transformation,[],[f10]) ).
tcf(c_57,negated_conjecture,
! [X0: $i] : product(X0,inverse(X0),sK0),
inference(cnf_transformation,[],[f9]) ).
tcf(c_58,negated_conjecture,
! [X0: $i] : product(inverse(X0),X0,sK0),
inference(cnf_transformation,[],[f8]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ product(X1,X2,sK0)
| ~ product(X0,X2,inverse(sK4))
| ~ product(inverse(sK3),X0,X1) ),
inference(resolution,[status(thm)],[c_53,c_49]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,X1,inverse(sK4))
| ~ product(inverse(sK3),X0,inverse(X1)) ),
inference(resolution,[status(thm)],[c_107,c_58]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X0,X3,X2)
| ~ product(sK0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_55,c_53]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(sK0,X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_56,c_53]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(sK4,X0,X2)
| ~ product(sK2,X1,X2)
| ~ product(sK1,X0,X1) ),
inference(superposition,[status(thm)],[c_51,c_54]) ).
tcf(c_227,plain,
~ product(sK0,sK3,inverse(sK4)),
inference(resolution,[status(thm)],[c_119,c_55]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ product(sK0,X2,X0)
| ~ product(X2,X1,sK3)
| ~ product(X0,X1,inverse(sK4)) ),
inference(resolution,[status(thm)],[c_227,c_53]) ).
tcf(c_327,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,X1)
| ~ product(sK0,sK0,X0) ),
inference(superposition,[status(thm)],[c_55,c_145]) ).
tcf(c_399,plain,
! [X0: $i,X1: $i] :
( product(sK0,sK0,X1)
| ~ product(X0,inverse(X0),X1) ),
inference(superposition,[status(thm)],[c_57,c_146]) ).
tcf(c_1131,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,X1,sK3)
| ~ product(X0,X1,inverse(sK4)) ),
inference(resolution,[status(thm)],[c_229,c_56]) ).
tcf(c_1217,plain,
~ product(inverse(sK4),sK0,sK3),
inference(resolution,[status(thm)],[c_1131,c_55]) ).
tcf(c_1231,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ product(X1,X2,sK3)
| ~ product(X0,X2,sK0)
| ~ product(inverse(sK4),X0,X1) ),
inference(resolution,[status(thm)],[c_1217,c_53]) ).
tcf(c_1376,plain,
! [X0: $i] : product(sK0,sK0,sK5(X0,inverse(X0))),
inference(superposition,[status(thm)],[c_52,c_399]) ).
tcf(c_1389,plain,
! [X0: $i,X1: $i] : product(X0,sK5(X1,inverse(X1)),X0),
inference(superposition,[status(thm)],[c_1376,c_327]) ).
tcf(c_2880,plain,
! [X0: $i,X1: $i] :
( product(sK4,X0,X1)
| ~ product(sK2,sK5(sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_52,c_190]) ).
tcf(c_3199,plain,
product(sK4,inverse(sK1),sK2),
inference(superposition,[status(thm)],[c_1389,c_2880]) ).
tcf(c_3261,plain,
! [X0: $i] :
( ~ product(sK0,X0,sK3)
| ~ product(sK4,X0,sK0) ),
inference(resolution,[status(thm)],[c_1231,c_58]) ).
tcf(c_3313,plain,
~ product(sK4,sK3,sK0),
inference(resolution,[status(thm)],[c_3261,c_56]) ).
tcf(c_3359,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ product(sK4,X2,X0)
| ~ product(X2,X1,sK3)
| ~ product(X0,X1,sK0) ),
inference(resolution,[status(thm)],[c_3313,c_53]) ).
tcf(c_3714,plain,
! [X0: $i] :
( ~ product(sK4,inverse(sK1),X0)
| ~ product(X0,inverse(sK2),sK0) ),
inference(resolution,[status(thm)],[c_3359,c_50]) ).
tcf(c_4104,plain,
~ product(sK4,inverse(sK1),sK2),
inference(resolution,[status(thm)],[c_3714,c_57]) ).
tcf(c_4105,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4104,c_3199]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP012+5 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Wed Sep 23 13:13:51 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.05/0.33 Running first-order theorem proving
% 0.05/0.33 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
% 0.07/0.33
% 0.07/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.33
% 0.07/0.33 % Detected problem language: tptp
% 0.07/0.34 % Proving...
% 3.07/0.98 % SZS status Started for theBenchmark.p
% 3.07/0.98 % SZS status Theorem for theBenchmark.p
% 3.07/0.98
% 3.07/0.98 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.07/0.98
% 3.07/0.98 % ------ iProver source info
% 3.07/0.98
% 3.07/0.98 % git: date: 2026-07-19 20:42:38 +0200
% 3.07/0.98 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.07/0.98 % git: non_committed_changes: false
% 3.07/0.98
% 3.07/0.98 % ------ Parsing...
% 3.07/0.98 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.07/0.98
% 3.07/0.98 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.07/0.98
% 3.07/0.98 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.07/0.98 % ------ Proving...
% 3.07/0.98 % ------ Problem Properties
% 3.07/0.98
% 3.07/0.98 %
% 3.07/0.98 % clauses 10
% 3.07/0.98 % conjectures 10
% 3.07/0.98 % EPR 5
% 3.07/0.98 % Horn 10
% 3.07/0.98 % unary 8
% 3.07/0.98 % binary 0
% 3.07/0.98 % lits 16
% 3.07/0.98 % lits eq 0
% 3.07/0.98 % fd_pure 0
% 3.07/0.98 % fd_pseudo 0
% 3.07/0.98 % fd_cond 0
% 3.07/0.98 % fd_pseudo_cond 0
% 3.07/0.98 % AC symbols 0
% 3.07/0.98
% 3.07/0.98 % ------ Input Options Time Limit: Unbounded
% 3.07/0.98
% 3.07/0.98
% 3.07/0.98 % ------
% 3.07/0.98 % Current options:
% 3.07/0.98 % ------
% 3.07/0.98
% 3.07/0.98
% 3.07/0.98 %
% 3.07/0.98
% 3.07/0.98 % ------ Proving...
% 3.07/0.98 %
% 3.07/0.98
% 3.07/0.98 % SZS status Theorem for theBenchmark.p
% 3.07/0.98
% 3.07/0.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.07/0.98
% 3.07/0.98
%------------------------------------------------------------------------------