%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 02:38:06 PM UTC 2026
% Result : Unsatisfiable 3.34s 1.27s
% Output : CNFRefutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 25 unt; 1 def)
% Number of atoms : 101 ( 25 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 47 ( 26 ~; 21 |; 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 : 7 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 62 ( 0 sgn 62 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
fof(f2,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).
fof(f13,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/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity2) ).
fof(f18,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_times_0_is_0) ).
tcf(c_67,plain,
! [X0: $i] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_68,plain,
! [X0: $i] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_72,plain,
! [X0: $i] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[],[f6]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X2,X5,X4)
| ~ sum(X1,X5,X3)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_84,negated_conjecture,
~ product(a,additive_identity,additive_identity),
inference(cnf_transformation,[],[f18]) ).
tcf(c_92,plain,
multiply(a,additive_identity) != additive_identity,
inference(well_definedness,[status(thm)],[c_84]) ).
tcf(c_93,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_67]) ).
tcf(c_94,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(well_definedness,[status(thm)],[c_68]) ).
tcf(c_98,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(well_definedness,[status(thm)],[c_72]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( add(X2,X5) = X4 )
| ( add(X1,X5) != X3 )
| ( add(X0,X3) != X4 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_74]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X0,X5) = X6 )
| ( add(X2,X4) != X6 )
| ( add(X1,X3) != X5 )
| ( multiply(X0,X3) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_79]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_101]) ).
tcf(c_240,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_111]) ).
tcf(c_272,definition,
iPr_def_10 = multiply(a,additive_identity),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_273,plain,
iPr_def_10 != additive_identity,
inference(demodulation,[status(thm)],[c_92,c_272]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = add(additive_identity,X1),
inference(superposition,[status(thm)],[c_98,c_236]) ).
tcf(c_351,plain,
! [X0: $i,X1: $i] : add(multiply(X0,additive_identity),multiply(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_93,c_240]) ).
tcf(c_364,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_338,c_93]) ).
tcf(c_540,plain,
add(iPr_def_10,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_272,c_351]) ).
tcf(c_556,plain,
! [X0: $i] : add(iPr_def_10,add(iPr_def_10,X0)) = add(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_540,c_236]) ).
tcf(c_589,plain,
! [X0: $i] : add(iPr_def_10,X0) = X0,
inference(superposition,[status(thm)],[c_364,c_556]) ).
tcf(c_614,plain,
additive_identity = iPr_def_10,
inference(superposition,[status(thm)],[c_589,c_94]) ).
tcf(c_640,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_273,c_614]) ).
tcf(c_641,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_640]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.36 % Computer : n005.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Thu Sep 24 07:40:02 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 3.34/1.27 % SZS status Started for theBenchmark.p
% 3.34/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 3.34/1.27
% 3.34/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.34/1.27
% 3.34/1.27 % ------ iProver source info
% 3.34/1.27
% 3.34/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.34/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.34/1.27 % git: non_committed_changes: false
% 3.34/1.27
% 3.34/1.27 % ------ Parsing...% successful
% 3.34/1.27
% 3.34/1.27
% 3.34/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.34/1.27
% 3.34/1.27 % ------ Preprocessing... sup_sim: 15 sf_s rm: 0 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.34/1.27
% 3.34/1.27 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.34/1.27 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.34/1.27
% 3.34/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.34/1.27 % ------ Proving...
% 3.34/1.27 % ------ Problem Properties
% 3.34/1.27
% 3.34/1.27 %
% 3.34/1.27 % clauses 10
% 3.34/1.27 % conjectures 0
% 3.34/1.27 % EPR 1
% 3.34/1.27 % Horn 10
% 3.34/1.27 % unary 10
% 3.34/1.27 % binary 0
% 3.34/1.27 % lits 10
% 3.34/1.27 % lits eq 10
% 3.34/1.27 % fd_pure 0
% 3.34/1.27 % fd_pseudo 0
% 3.34/1.27 % fd_cond 0
% 3.34/1.27 % fd_pseudo_cond 0
% 3.34/1.27 % AC symbols 1
% 3.34/1.27
% 3.34/1.27 % ------ Schedule UEQ
% 3.34/1.27
% 3.34/1.27 % ------ Option_UEQ Time Limit: 10.
% 3.34/1.27
% 3.34/1.27
% 3.34/1.27 % ------
% 3.34/1.27 % Current options:
% 3.34/1.27 % ------
% 3.34/1.27
% 3.34/1.27
% 3.34/1.27 %
% 3.34/1.27
% 3.34/1.27 % ------ Proving...
% 3.34/1.27 %
% 3.34/1.27
% 3.34/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 3.34/1.27
% 3.34/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.34/1.27
% 3.34/1.27
%------------------------------------------------------------------------------