%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG041-1 : 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 : n009.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 02:38:17 PM UTC 2026
% Result : Unsatisfiable 1.42s 1.39s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 28 unt; 1 def)
% Number of atoms : 87 ( 34 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 34 ( 19 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 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 : 5 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 35 ( 0 sgn 35 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_multiplication2) ).
fof(f18,axiom,
! [X0] : product(additive_identity,X0,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity1) ).
fof(f20,axiom,
! [X0] : product(X0,multiplicative_identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_multiplicative_identity) ).
fof(f22,axiom,
! [X0] :
( X0 = additive_identity
| product(X0,h(X0),multiplicative_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause41) ).
fof(f23,plain,
! [X0] :
( additive_identity = X0
| product(X0,h(X0),multiplicative_identity) ),
inference(reorient_equations,[],[f22]) ).
fof(f26,negated_conjecture,
product(a,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
fof(f27,negated_conjecture,
a != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_additive_identity) ).
fof(f28,plain,
additive_identity != a,
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
b != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_is_additive_identity) ).
fof(f30,plain,
additive_identity != b,
inference(reorient_equations,[],[f29]) ).
tcf(c_85,plain,
! [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,[],[f11]) ).
tcf(c_92,plain,
! [X0: $i] : product(additive_identity,X0,additive_identity),
inference(cnf_transformation,[],[f18]) ).
tcf(c_94,plain,
! [X0: $i] : product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[],[f20]) ).
tcf(c_96,plain,
! [X0: $i] :
( product(X0,h(X0),multiplicative_identity)
| ( X0 = additive_identity ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_98,negated_conjecture,
product(a,b,additive_identity),
inference(cnf_transformation,[],[f26]) ).
tcf(c_99,negated_conjecture,
additive_identity != a,
inference(cnf_transformation,[],[f28]) ).
tcf(c_100,negated_conjecture,
additive_identity != b,
inference(cnf_transformation,[],[f30]) ).
tcf(c_113,plain,
! [X0: $i] : multiply(additive_identity,X0) = additive_identity,
inference(well_definedness,[status(thm)],[c_92]) ).
tcf(c_115,plain,
! [X0: $i] : multiply(X0,multiplicative_identity) = X0,
inference(well_definedness,[status(thm)],[c_94]) ).
tcf(c_117,plain,
! [X0: $i] :
( ( X0 = additive_identity )
| ( multiply(X0,h(X0)) = multiplicative_identity ) ),
inference(well_definedness,[status(thm)],[c_96]) ).
tcf(c_119,plain,
multiply(a,b) = additive_identity,
inference(well_definedness,[status(thm)],[c_98]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( multiply(X2,X5) = X4 )
| ( multiply(X1,X5) != X3 )
| ( multiply(X0,X3) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_85]) ).
tcf(c_292,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(unflattening,[status(thm)],[c_134]) ).
tcf(c_356,definition,
iPr_def_10 = multiply(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_357,plain,
iPr_def_10 = additive_identity,
inference(demodulation,[status(thm)],[c_119,c_356]) ).
tcf(c_358,negated_conjecture,
additive_identity != b,
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_359,negated_conjecture,
additive_identity != a,
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_428,plain,
b != iPr_def_10,
inference(light_normalisation,[status(thm)],[c_358,c_357]) ).
tcf(c_429,plain,
a != iPr_def_10,
inference(light_normalisation,[status(thm)],[c_359,c_357]) ).
tcf(c_430,plain,
! [X0: $i] : multiply(iPr_def_10,X0) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_113,c_357]) ).
tcf(c_433,plain,
! [X0: $i] :
( ( X0 = iPr_def_10 )
| ( multiply(X0,h(X0)) = multiplicative_identity ) ),
inference(light_normalisation,[status(thm)],[c_117,c_357]) ).
tcf(c_479,plain,
! [X0: $i] : multiply(a,multiply(b,X0)) = multiply(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_356,c_292]) ).
tcf(c_485,plain,
! [X0: $i] : multiply(a,multiply(b,X0)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_479,c_430]) ).
tcf(c_502,plain,
( ( b = iPr_def_10 )
| ( multiply(a,multiplicative_identity) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_433,c_485]) ).
tcf(c_505,plain,
multiply(a,multiplicative_identity) = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_502,c_428]) ).
tcf(c_507,plain,
a = iPr_def_10,
inference(demodulation,[status(thm)],[c_505,c_115]) ).
tcf(c_508,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_507,c_429]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG041-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.19/0.43 % Computer : n009.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Thu Sep 24 07:56:14 UTC 2026
% 0.19/0.43 % CPUTime :
% 0.19/0.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.19/0.49 Running first-order theorem proving
% 0.19/0.49 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
% 0.25/0.50
% 0.25/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.25/0.50
% 0.25/0.50 % Detected problem language: tptp
% 0.25/0.52 % Proving...
% 1.42/1.39 % SZS status Started for theBenchmark.p
% 1.42/1.39 % SZS status Unsatisfiable for theBenchmark.p
% 1.42/1.39
% 1.42/1.39 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.42/1.39
% 1.42/1.39 % ------ iProver source info
% 1.42/1.39
% 1.42/1.39 % git: date: 2026-07-19 20:42:38 +0200
% 1.42/1.39 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.42/1.39 % git: non_committed_changes: false
% 1.42/1.39
% 1.42/1.39 % ------ Parsing...% successful
% 1.42/1.39
% 1.42/1.39
% 1.42/1.39 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.42/1.39
% 1.42/1.39 % ------ 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 %
% 1.42/1.39
% 1.42/1.39 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.42/1.39
% 1.42/1.39 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.42/1.39 % ------ Proving...
% 1.42/1.39 % ------ Problem Properties
% 1.42/1.39
% 1.42/1.39 %
% 1.42/1.39 % clauses 18
% 1.42/1.39 % conjectures 2
% 1.42/1.39 % EPR 3
% 1.42/1.39 % Horn 16
% 1.42/1.39 % unary 16
% 1.42/1.39 % binary 2
% 1.42/1.39 % lits 20
% 1.42/1.39 % lits eq 20
% 1.42/1.39 % fd_pure 0
% 1.42/1.39 % fd_pseudo 0
% 1.42/1.39 % fd_cond 2
% 1.42/1.39 % fd_pseudo_cond 0
% 1.42/1.39 % AC symbols 1
% 1.42/1.39
% 1.42/1.39 % ------ Schedule dynamic 5 is on
% 1.42/1.39
% 1.42/1.39 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.42/1.39
% 1.42/1.39
% 1.42/1.39 % ------
% 1.42/1.39 % Current options:
% 1.42/1.39 % ------
% 1.42/1.39
% 1.42/1.39
% 1.42/1.39 %
% 1.42/1.39
% 1.42/1.39 % ------ Proving...
% 1.42/1.39 %
% 1.42/1.39
% 1.42/1.39 % SZS status Unsatisfiable for theBenchmark.p
% 1.42/1.39
% 1.42/1.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.42/1.39
% 1.42/1.39
%------------------------------------------------------------------------------