%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP774+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.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 01:35:23 PM UTC 2026
% Result : Theorem 8.44s 1.74s
% Output : CNFRefutation 8.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 71 ( 50 unt; 0 def)
% Number of atoms : 114 ( 81 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 80 ( 37 ~; 27 |; 13 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 114 ( 0 sgn 106 !; 8 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] : product(product(X2,X1),X0) = product(X2,product(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
fof(f2,axiom,
! [X0] : product(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
fof(f3,axiom,
! [X0,X1] :
( d(X0,X1)
<=> ( product(X1,product(X0,X1)) = X1
& product(X0,product(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
fof(f4,conjecture,
! [X0,X1,X2,X3] :
( ( d(X2,X3)
& d(X0,X1) )
=> d(product(X0,X2),product(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f5,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( d(X2,X3)
& d(X0,X1) )
=> d(product(X0,X2),product(X1,X3)) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
? [X0,X1,X2,X3] :
( d(X2,X3)
& d(X0,X1)
& ~ d(product(X0,X2),product(X1,X3)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f7,plain,
? [X0,X1,X2,X3] :
( d(X2,X3)
& d(X0,X1)
& ~ d(product(X0,X2),product(X1,X3)) ),
inference(flattening,[],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( ( ~ d(X0,X1)
| ( product(X1,product(X0,X1)) = X1
& product(X0,product(X1,X0)) = X0 ) )
& ( product(X1,product(X0,X1)) != X1
| product(X0,product(X1,X0)) != X0
| d(X0,X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f9,plain,
! [X0,X1] :
( ( ~ d(X0,X1)
| ( product(X1,product(X0,X1)) = X1
& product(X0,product(X1,X0)) = X0 ) )
& ( product(X1,product(X0,X1)) != X1
| product(X0,product(X1,X0)) != X0
| d(X0,X1) ) ),
inference(flattening,[],[f8]) ).
fof(f10,plain,
( d(sK2,sK3)
& d(sK0,sK1)
& ~ d(product(sK0,sK2),product(sK1,sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f7]) ).
fof(f11,plain,
! [X2,X0,X1] : product(product(X2,X1),X0) = product(X2,product(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f12,plain,
! [X0] : product(X0,X0) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f13,plain,
! [X0,X1] :
( ~ d(X0,X1)
| product(X1,product(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f14,plain,
! [X0,X1] :
( ~ d(X0,X1)
| product(X0,product(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f9]) ).
fof(f15,plain,
! [X0,X1] :
( product(X1,product(X0,X1)) != X1
| product(X0,product(X1,X0)) != X0
| d(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f16,plain,
d(sK2,sK3),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
d(sK0,sK1),
inference(cnf_transformation,[],[f10]) ).
fof(f18,plain,
~ d(product(sK0,sK2),product(sK1,sK3)),
inference(cnf_transformation,[],[f10]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] : product(product(X0,X1),X2) = product(X0,product(X1,X2)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_50,plain,
! [X0: $i] : product(X0,X0) = X0,
inference(cnf_transformation,[],[f12]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( d(X1,X0)
| ( product(X1,product(X0,X1)) != X1 )
| ( product(X0,product(X1,X0)) != X0 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( ( product(X0,product(X1,X0)) = X0 )
| ~ d(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( product(X1,product(X0,X1)) = X1 )
| ~ d(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_54,negated_conjecture,
~ d(product(sK0,sK2),product(sK1,sK3)),
inference(cnf_transformation,[],[f18]) ).
tcf(c_55,negated_conjecture,
d(sK0,sK1),
inference(cnf_transformation,[],[f17]) ).
tcf(c_56,negated_conjecture,
d(sK2,sK3),
inference(cnf_transformation,[],[f16]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( ( product(sK1,sK3) != X0 )
| ( product(sK0,sK2) != X1 )
| ( product(X1,product(X0,X1)) != X1 )
| ( product(X0,product(X1,X0)) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_54]) ).
tcf(c_95,plain,
( ( product(product(sK1,sK3),product(product(sK0,sK2),product(sK1,sK3))) != product(sK1,sK3) )
| ( product(product(sK0,sK2),product(product(sK1,sK3),product(sK0,sK2))) != product(sK0,sK2) ) ),
inference(unflattening,[status(thm)],[c_94]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i] :
( ( product(X1,product(X0,X1)) = X1 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_55]) ).
tcf(c_103,plain,
product(sK1,product(sK0,sK1)) = sK1,
inference(unflattening,[status(thm)],[c_102]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( ( product(X0,product(X1,X0)) = X0 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_55]) ).
tcf(c_108,plain,
product(sK0,product(sK1,sK0)) = sK0,
inference(unflattening,[status(thm)],[c_107]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( ( product(X1,product(X0,X1)) = X1 )
| ( X1 != sK3 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_56]) ).
tcf(c_113,plain,
product(sK3,product(sK2,sK3)) = sK3,
inference(unflattening,[status(thm)],[c_112]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] :
( ( product(X0,product(X1,X0)) = X0 )
| ( X1 != sK3 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_56]) ).
tcf(c_118,plain,
product(sK2,product(sK3,sK2)) = sK2,
inference(unflattening,[status(thm)],[c_117]) ).
tcf(c_193,plain,
! [X0: $i,X1: $i] : product(X0,product(X0,X1)) = product(X0,X1),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_194,plain,
! [X0: $i,X1: $i] : product(X0,product(X1,product(X0,X1))) = product(X0,X1),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_197,plain,
( ( product(sK1,product(sK3,product(sK0,product(sK2,product(sK1,sK3))))) != product(sK1,sK3) )
| ( product(sK0,product(sK2,product(sK1,product(sK3,product(sK0,sK2))))) != product(sK0,sK2) ) ),
inference(demodulation,[status(thm)],[c_95,c_49]) ).
tcf(c_198,plain,
! [X0: $i] : product(sK1,product(product(sK0,sK1),X0)) = product(sK1,X0),
inference(superposition,[status(thm)],[c_103,c_49]) ).
tcf(c_200,plain,
! [X0: $i] : product(sK1,product(sK0,product(sK1,X0))) = product(sK1,X0),
inference(demodulation,[status(thm)],[c_198,c_49]) ).
tcf(c_201,plain,
! [X0: $i] : product(sK0,product(product(sK1,sK0),X0)) = product(sK0,X0),
inference(superposition,[status(thm)],[c_108,c_49]) ).
tcf(c_203,plain,
! [X0: $i] : product(sK0,product(sK1,product(sK0,X0))) = product(sK0,X0),
inference(demodulation,[status(thm)],[c_201,c_49]) ).
tcf(c_205,plain,
! [X0: $i] : product(sK3,product(product(sK2,sK3),X0)) = product(sK3,X0),
inference(superposition,[status(thm)],[c_113,c_49]) ).
tcf(c_207,plain,
! [X0: $i] : product(sK3,product(sK2,product(sK3,X0))) = product(sK3,X0),
inference(demodulation,[status(thm)],[c_205,c_49]) ).
tcf(c_214,plain,
! [X0: $i] : product(sK2,product(product(sK3,sK2),X0)) = product(sK2,X0),
inference(superposition,[status(thm)],[c_118,c_49]) ).
tcf(c_216,plain,
! [X0: $i] : product(sK2,product(sK3,product(sK2,X0))) = product(sK2,X0),
inference(demodulation,[status(thm)],[c_214,c_49]) ).
tcf(c_244,plain,
! [X0: $i,X1: $i,X2: $i] : product(X0,product(X1,product(product(X0,X1),X2))) = product(product(X0,X1),X2),
inference(superposition,[status(thm)],[c_193,c_49]) ).
tcf(c_254,plain,
! [X0: $i,X1: $i,X2: $i] : product(X0,product(X1,product(X0,product(X1,X2)))) = product(X0,product(X1,X2)),
inference(demodulation,[status(thm)],[c_244,c_49]) ).
tcf(c_274,plain,
! [X0: $i,X1: $i,X2: $i] : product(X0,product(X1,product(X2,product(product(X0,X1),X2)))) = product(product(X0,X1),X2),
inference(superposition,[status(thm)],[c_194,c_49]) ).
tcf(c_289,plain,
! [X0: $i,X1: $i,X2: $i] : product(X0,product(X1,product(X2,product(X0,product(X1,X2))))) = product(X0,product(X1,X2)),
inference(demodulation,[status(thm)],[c_274,c_49]) ).
tcf(c_321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : product(X0,product(X1,product(X2,product(product(X0,X1),product(X2,X3))))) = product(product(X0,X1),product(X2,X3)),
inference(superposition,[status(thm)],[c_254,c_49]) ).
tcf(c_345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : product(X0,product(X1,product(X2,product(X0,product(X1,product(X2,X3)))))) = product(X0,product(X1,product(X2,X3))),
inference(demodulation,[status(thm)],[c_321,c_49]) ).
tcf(c_407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : product(X0,product(X1,product(X2,product(X3,product(product(X0,X1),product(X2,X3)))))) = product(product(X0,X1),product(X2,X3)),
inference(superposition,[status(thm)],[c_289,c_49]) ).
tcf(c_465,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : product(X0,product(X1,product(X2,product(X3,product(X0,product(X1,product(X2,X3))))))) = product(X0,product(X1,product(X2,X3))),
inference(demodulation,[status(thm)],[c_407,c_49]) ).
tcf(c_1690,plain,
! [X0: $i] : product(X0,product(sK3,product(sK2,product(X0,sK3)))) = product(X0,sK3),
inference(superposition,[status(thm)],[c_113,c_345]) ).
tcf(c_1691,plain,
! [X0: $i] : product(X0,product(sK2,product(sK3,product(X0,sK2)))) = product(X0,sK2),
inference(superposition,[status(thm)],[c_118,c_345]) ).
tcf(c_1694,plain,
! [X0: $i,X1: $i] : product(X0,product(sK1,product(sK0,product(X0,product(sK1,X1))))) = product(X0,product(sK1,X1)),
inference(superposition,[status(thm)],[c_200,c_345]) ).
tcf(c_1695,plain,
! [X0: $i,X1: $i] : product(X0,product(sK0,product(sK1,product(X0,product(sK0,X1))))) = product(X0,product(sK0,X1)),
inference(superposition,[status(thm)],[c_203,c_345]) ).
tcf(c_1696,plain,
! [X0: $i,X1: $i] : product(X0,product(sK3,product(sK2,product(X0,product(sK3,X1))))) = product(X0,product(sK3,X1)),
inference(superposition,[status(thm)],[c_207,c_345]) ).
tcf(c_1697,plain,
! [X0: $i,X1: $i] : product(X0,product(sK2,product(sK3,product(X0,product(sK2,X1))))) = product(X0,product(sK2,X1)),
inference(superposition,[status(thm)],[c_216,c_345]) ).
tcf(c_2798,plain,
! [X0: $i,X1: $i] : product(X0,product(sK1,product(X1,product(sK0,product(X0,product(sK1,X1)))))) = product(X0,product(sK1,product(sK0,product(X0,product(sK1,X1))))),
inference(superposition,[status(thm)],[c_465,c_1694]) ).
tcf(c_2922,plain,
! [X0: $i,X1: $i] : product(X0,product(sK1,product(X1,product(sK0,product(X0,product(sK1,X1)))))) = product(X0,product(sK1,X1)),
inference(demodulation,[status(thm)],[c_2798,c_1694]) ).
tcf(c_2949,plain,
! [X0: $i,X1: $i] : product(X0,product(sK0,product(X1,product(sK1,product(X0,product(sK0,X1)))))) = product(X0,product(sK0,product(sK1,product(X0,product(sK0,X1))))),
inference(superposition,[status(thm)],[c_465,c_1695]) ).
tcf(c_3058,plain,
! [X0: $i,X1: $i] : product(X0,product(sK0,product(X1,product(sK1,product(X0,product(sK0,X1)))))) = product(X0,product(sK0,X1)),
inference(demodulation,[status(thm)],[c_2949,c_1695]) ).
tcf(c_4756,plain,
product(sK1,product(sK3,product(sK0,product(sK2,product(sK1,sK3))))) = product(sK1,product(sK3,product(sK2,product(sK1,sK3)))),
inference(superposition,[status(thm)],[c_2922,c_1696]) ).
tcf(c_4774,plain,
product(sK1,product(sK3,product(sK0,product(sK2,product(sK1,sK3))))) = product(sK1,sK3),
inference(demodulation,[status(thm)],[c_4756,c_1690]) ).
tcf(c_4866,plain,
product(sK0,product(sK2,product(sK1,product(sK3,product(sK0,sK2))))) != product(sK0,sK2),
inference(backward_subsumption_resolution,[status(thm)],[c_197,c_4774]) ).
tcf(c_6524,plain,
product(sK0,product(sK2,product(sK1,product(sK3,product(sK0,sK2))))) = product(sK0,product(sK2,product(sK3,product(sK0,sK2)))),
inference(superposition,[status(thm)],[c_3058,c_1697]) ).
tcf(c_6538,plain,
product(sK0,product(sK2,product(sK1,product(sK3,product(sK0,sK2))))) = product(sK0,sK2),
inference(demodulation,[status(thm)],[c_6524,c_1691]) ).
tcf(c_6589,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_4866,c_6538]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP774+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.34 % Computer : n011.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Wed Sep 23 16:00:59 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 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
% 0.12/0.39
% 0.12/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.39
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 8.44/1.74 % SZS status Started for theBenchmark.p
% 8.44/1.74 % SZS status Theorem for theBenchmark.p
% 8.44/1.74
% 8.44/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.44/1.74
% 8.44/1.74 % ------ iProver source info
% 8.44/1.74
% 8.44/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 8.44/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.44/1.74 % git: non_committed_changes: false
% 8.44/1.74
% 8.44/1.74 % ------ Parsing...
% 8.44/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.44/1.74
% 8.44/1.74 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e %
% 8.44/1.74
% 8.44/1.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.44/1.74
% 8.44/1.74 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 8.44/1.74 % ------ Proving...
% 8.44/1.74 % ------ Problem Properties
% 8.44/1.74
% 8.44/1.74 %
% 8.44/1.74 % clauses 9
% 8.44/1.74 % conjectures 0
% 8.44/1.74 % EPR 0
% 8.44/1.74 % Horn 9
% 8.44/1.74 % unary 6
% 8.44/1.74 % binary 3
% 8.44/1.74 % lits 12
% 8.44/1.74 % lits eq 12
% 8.44/1.74 % fd_pure 0
% 8.44/1.74 % fd_pseudo 0
% 8.44/1.74 % fd_cond 0
% 8.44/1.74 % fd_pseudo_cond 0
% 8.44/1.74 % AC symbols 0
% 8.44/1.74
% 8.44/1.74 % ------ Input Options Time Limit: Unbounded
% 8.44/1.74
% 8.44/1.74
% 8.44/1.74 % ------
% 8.44/1.74 % Current options:
% 8.44/1.74 % ------
% 8.44/1.74
% 8.44/1.74
% 8.44/1.74 %
% 8.44/1.74
% 8.44/1.74 % ------ Proving...
% 8.44/1.74 %
% 8.44/1.74
% 8.44/1.74 % SZS status Theorem for theBenchmark.p
% 8.44/1.74
% 8.44/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.44/1.74
% 8.44/1.74
%------------------------------------------------------------------------------