%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG006-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n005.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 02:38:08 PM UTC 2026
% Result : Unsatisfiable 3.62s 1.18s
% Output : CNFRefutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 11 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 58 ( 30 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-1 aty)
% Number of variables : 28 ( 0 sgn 28 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
fof(f29,axiom,
! [X2,X0,X1] :
( product(X0,additive_inverse(X1),additive_inverse(X2))
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_lemma1) ).
fof(f32,axiom,
sum(b,additive_inverse(c),bS_Ic),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_plus_inverse_c) ).
fof(f33,axiom,
product(a,b,aPb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
fof(f34,axiom,
product(a,c,aPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c) ).
fof(f35,axiom,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aPb_plus_IaPc) ).
fof(f36,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_times_bS_Ic_is_aPb_S__IaPc) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X6,X2,X5)
| ~ product(X6,X1,X4)
| ~ product(X6,X0,X3)
| ~ sum(X3,X4,X5)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X0,additive_inverse(X1),additive_inverse(X2))
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_116,plain,
sum(b,additive_inverse(c),bS_Ic),
inference(cnf_transformation,[],[f32]) ).
tcf(c_117,plain,
product(a,b,aPb),
inference(cnf_transformation,[],[f33]) ).
tcf(c_118,plain,
product(a,c,aPc),
inference(cnf_transformation,[],[f34]) ).
tcf(c_119,plain,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
inference(cnf_transformation,[],[f35]) ).
tcf(c_120,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
inference(cnf_transformation,[],[f36]) ).
tcf(c_320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(a,bS_Ic,aPb_S_IaPc)
| ~ product(a,X1,X3)
| ~ product(a,X0,X2)
| ~ sum(X2,X3,aPb_S_IaPc)
| ~ sum(X0,X1,bS_Ic) ),
inference(instantiation,[status(thm)],[c_106]) ).
tcf(c_378,plain,
! [X0: $i,X1: $i] :
( product(a,bS_Ic,aPb_S_IaPc)
| ~ product(a,b,X1)
| ~ sum(X1,X0,aPb_S_IaPc)
| ~ sum(b,additive_inverse(c),bS_Ic)
| ~ product(a,additive_inverse(c),X0) ),
inference(instantiation,[status(thm)],[c_320]) ).
tcf(c_501,plain,
! [X0: $i] :
( product(a,bS_Ic,aPb_S_IaPc)
| ~ product(a,b,aPb)
| ~ sum(aPb,X0,aPb_S_IaPc)
| ~ sum(b,additive_inverse(c),bS_Ic)
| ~ product(a,additive_inverse(c),X0) ),
inference(instantiation,[status(thm)],[c_378]) ).
tcf(c_1182,plain,
! [X0: $i] :
( product(a,additive_inverse(c),additive_inverse(X0))
| ~ product(a,c,X0) ),
inference(instantiation,[status(thm)],[c_113]) ).
tcf(c_1215,plain,
( product(a,bS_Ic,aPb_S_IaPc)
| ~ product(a,b,aPb)
| ~ sum(aPb,additive_inverse(aPc),aPb_S_IaPc)
| ~ sum(b,additive_inverse(c),bS_Ic)
| ~ product(a,additive_inverse(c),additive_inverse(aPc)) ),
inference(instantiation,[status(thm)],[c_501]) ).
tcf(c_6294,plain,
( product(a,additive_inverse(c),additive_inverse(aPc))
| ~ product(a,c,aPc) ),
inference(instantiation,[status(thm)],[c_1182]) ).
tcf(c_6295,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_6294,c_1215,c_116,c_119,c_120,c_117,c_118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 07:42:33 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 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...
% 3.62/1.18 % SZS status Started for theBenchmark.p
% 3.62/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 3.62/1.18
% 3.62/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.62/1.18
% 3.62/1.18 % ------ iProver source info
% 3.62/1.18
% 3.62/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.62/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.62/1.18 % git: non_committed_changes: false
% 3.62/1.18
% 3.62/1.18 % ------ Parsing...% successful
% 3.62/1.18
% 3.62/1.18
% 3.62/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.62/1.18
% 3.62/1.18 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.62/1.18
% 3.62/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.62/1.18 % ------ Proving...
% 3.62/1.18 % ------ Problem Properties
% 3.62/1.18
% 3.62/1.18 %
% 3.62/1.18 % clauses 36
% 3.62/1.18 % conjectures 1
% 3.62/1.18 % EPR 24
% 3.62/1.18 % Horn 36
% 3.62/1.18 % unary 13
% 3.62/1.18 % binary 7
% 3.62/1.18 % lits 87
% 3.62/1.18 % lits eq 0
% 3.62/1.18 % fd_pure 0
% 3.62/1.18 % fd_pseudo 0
% 3.62/1.18 % fd_cond 0
% 3.62/1.18 % fd_pseudo_cond 0
% 3.62/1.18 % AC symbols 0
% 3.62/1.18
% 3.62/1.18 % ------ Schedule dynamic 5 is on
% 3.62/1.18
% 3.62/1.18 % ------ no equalities: superposition off
% 3.62/1.18
% 3.62/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.62/1.18
% 3.62/1.18
% 3.62/1.18 % ------
% 3.62/1.18 % Current options:
% 3.62/1.18 % ------
% 3.62/1.18
% 3.62/1.18
% 3.62/1.18 %
% 3.62/1.18
% 3.62/1.18 % ------ Proving...
% 3.62/1.18 %
% 3.62/1.18
% 3.62/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 3.62/1.18
% 3.62/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.62/1.18
% 3.62/1.18
%------------------------------------------------------------------------------