%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG002-1 : 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 : n008.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 12:53:08 PM UTC 2026
% Result : Unsatisfiable 2.19s 1.20s
% Output : CNFRefutation 2.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 57 ( 19 unt; 1 def)
% Number of atoms : 126 ( 1 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 109 ( 54 ~; 55 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 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; 3 con; 0-1 aty)
% Number of variables : 62 ( 0 sgn 62 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(X0,multiplicative_identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f2,axiom,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_abelian) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ product(additive_inverse(X0),additive_inverse(X1),X2)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_of_inverses2) ).
fof(f5,axiom,
! [X2,X0,X1] :
( product(X0,additive_inverse(X1),additive_inverse(X2))
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_to_inverse) ).
fof(f6,axiom,
! [X0] :
( product(X0,X0,additive_identity)
| product(X0,multiplicative_inverse(X0),multiplicative_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_and_identity) ).
fof(f7,axiom,
! [X0] :
( ~ greater_than_0(additive_inverse(X0))
| ~ greater_than_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_greater_than_0) ).
fof(f8,axiom,
! [X0] :
( ~ product(X0,X0,additive_identity)
| ~ greater_than_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greater_than_0_square) ).
fof(f9,axiom,
! [X2,X0,X1] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_product) ).
fof(f10,axiom,
! [X0] :
( greater_than_0(additive_inverse(X0))
| product(X0,X0,additive_identity)
| greater_than_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_and_inverse) ).
fof(f11,axiom,
! [X2,X0,X1] :
( product(X2,X2,additive_identity)
| ~ product(X0,X0,additive_identity)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',square_to_0) ).
fof(f12,axiom,
! [X2,X0,X1] :
( greater_than_0(X2)
| ~ greater_than_0(X1)
| ~ greater_than_0(X0)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_and_greater_than_0) ).
fof(f13,axiom,
greater_than_0(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_greater_than_0) ).
fof(f14,negated_conjecture,
~ greater_than_0(multiplicative_inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_inverse_greater_than_0) ).
tcf(c_63,plain,
! [X0: $i] : product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_64,plain,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
inference(cnf_transformation,[],[f2]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X0,X1,X2)
| ~ product(additive_inverse(X0),additive_inverse(X1),X2) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X0,additive_inverse(X1),additive_inverse(X2))
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_68,plain,
! [X0: $i] :
( product(X0,X0,additive_identity)
| product(X0,multiplicative_inverse(X0),multiplicative_identity) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_69,plain,
! [X0: $i] :
( ~ greater_than_0(X0)
| ~ greater_than_0(additive_inverse(X0)) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_70,plain,
! [X0: $i] :
( ~ greater_than_0(X0)
| ~ product(X0,X0,additive_identity) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_72,plain,
! [X0: $i] :
( greater_than_0(X0)
| greater_than_0(additive_inverse(X0))
| product(X0,X0,additive_identity) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X2,additive_identity)
| ~ product(X0,X0,additive_identity)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater_than_0(X2)
| ~ greater_than_0(X1)
| ~ greater_than_0(X0)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_75,plain,
greater_than_0(a),
inference(cnf_transformation,[],[f13]) ).
tcf(c_76,negated_conjecture,
~ greater_than_0(multiplicative_inverse(a)),
inference(cnf_transformation,[],[f14]) ).
tcf(c_187,definition,
iPr_def_10 = multiplicative_inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_188,negated_conjecture,
~ greater_than_0(iPr_def_10),
inference(demodulation,[status(thm)],[c_76,c_187]) ).
tcf(c_503,plain,
( product(a,iPr_def_10,multiplicative_identity)
| product(a,a,additive_identity) ),
inference(superposition,[status(thm)],[c_187,c_68]) ).
tcf(c_543,plain,
! [X0: $i] :
( greater_than_0(additive_inverse(X0))
| greater_than_0(additive_inverse(additive_inverse(X0)))
| product(X0,X0,additive_identity) ),
inference(superposition,[status(thm)],[c_72,c_66]) ).
tcf(c_571,plain,
( product(a,iPr_def_10,multiplicative_identity)
| ~ greater_than_0(a) ),
inference(superposition,[status(thm)],[c_503,c_70]) ).
tcf(c_572,plain,
product(a,iPr_def_10,multiplicative_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_571,c_75]) ).
tcf(c_573,plain,
product(iPr_def_10,a,multiplicative_identity),
inference(superposition,[status(thm)],[c_572,c_71]) ).
tcf(c_632,plain,
! [X0: $i] :
( greater_than_0(additive_inverse(additive_inverse(X0)))
| product(X0,X0,additive_identity)
| greater_than_0(additive_inverse(additive_inverse(additive_inverse(X0)))) ),
inference(superposition,[status(thm)],[c_543,c_66]) ).
tcf(c_635,plain,
! [X0: $i] :
( greater_than_0(additive_inverse(X0))
| greater_than_0(additive_inverse(additive_inverse(X0)))
| ~ greater_than_0(X0) ),
inference(superposition,[status(thm)],[c_543,c_70]) ).
tcf(c_652,plain,
! [X0: $i] :
( ~ greater_than_0(X0)
| greater_than_0(additive_inverse(additive_inverse(X0))) ),
inference(global_subsumption_just,[status(thm)],[c_635,c_69,c_635]) ).
tcf(c_653,plain,
! [X0: $i] :
( greater_than_0(additive_inverse(additive_inverse(X0)))
| ~ greater_than_0(X0) ),
inference(renaming,[status(thm)],[c_652]) ).
tcf(c_671,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater_than_0(additive_inverse(X2))
| ~ greater_than_0(X0)
| ~ greater_than_0(additive_inverse(X1))
| ~ product(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_67,c_74]) ).
tcf(c_711,plain,
( product(multiplicative_identity,multiplicative_identity,additive_identity)
| ~ product(iPr_def_10,iPr_def_10,additive_identity) ),
inference(superposition,[status(thm)],[c_573,c_73]) ).
tcf(c_712,plain,
~ product(iPr_def_10,iPr_def_10,additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_711,c_64]) ).
tcf(c_737,plain,
! [X0: $i] :
( ~ greater_than_0(additive_inverse(X0))
| ~ greater_than_0(additive_inverse(additive_inverse(X0))) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_745,plain,
( greater_than_0(iPr_def_10)
| greater_than_0(additive_inverse(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_72,c_712]) ).
tcf(c_746,plain,
greater_than_0(additive_inverse(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_745,c_188]) ).
tcf(c_1099,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X0,X1,additive_inverse(X2))
| ~ product(additive_inverse(X0),X1,X2) ),
inference(superposition,[status(thm)],[c_67,c_66]) ).
tcf(c_1383,plain,
! [X0: $i] :
( product(X0,X0,additive_identity)
| greater_than_0(additive_inverse(additive_inverse(additive_inverse(X0))))
| greater_than_0(additive_inverse(additive_inverse(additive_inverse(additive_inverse(X0))))) ),
inference(superposition,[status(thm)],[c_632,c_66]) ).
tcf(c_2451,plain,
! [X0: $i] : product(X0,multiplicative_identity,additive_inverse(additive_inverse(X0))),
inference(superposition,[status(thm)],[c_63,c_1099]) ).
tcf(c_2701,plain,
! [X0: $i] : product(X0,multiplicative_identity,additive_inverse(additive_inverse(additive_inverse(additive_inverse(X0))))),
inference(superposition,[status(thm)],[c_2451,c_1099]) ).
tcf(c_2713,plain,
! [X0: $i] :
( ~ greater_than_0(additive_inverse(additive_inverse(X0)))
| ~ greater_than_0(additive_inverse(additive_inverse(additive_inverse(X0)))) ),
inference(instantiation,[status(thm)],[c_737]) ).
tcf(c_2846,plain,
! [X0: $i] :
( greater_than_0(additive_inverse(additive_inverse(additive_inverse(additive_inverse(X0)))))
| ~ greater_than_0(multiplicative_identity)
| ~ greater_than_0(X0) ),
inference(superposition,[status(thm)],[c_2701,c_74]) ).
tcf(c_3254,plain,
! [X0: $i] :
( greater_than_0(additive_inverse(additive_inverse(additive_inverse(additive_inverse(X0)))))
| ~ greater_than_0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_2846,c_70,c_653,c_1383,c_2713]) ).
tcf(c_3261,plain,
! [X0: $i] :
( ~ greater_than_0(X0)
| ~ greater_than_0(additive_inverse(additive_inverse(additive_inverse(X0)))) ),
inference(superposition,[status(thm)],[c_3254,c_69]) ).
tcf(c_3402,plain,
! [X0: $i] :
( greater_than_0(additive_inverse(X0))
| ~ greater_than_0(X0)
| ~ greater_than_0(additive_inverse(multiplicative_identity)) ),
inference(superposition,[status(thm)],[c_63,c_671]) ).
tcf(c_3414,plain,
( greater_than_0(additive_inverse(multiplicative_identity))
| ~ greater_than_0(a)
| ~ greater_than_0(additive_inverse(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_572,c_671]) ).
tcf(c_3448,plain,
greater_than_0(additive_inverse(multiplicative_identity)),
inference(forward_subsumption_resolution,[status(thm)],[c_3414,c_75,c_746]) ).
tcf(c_3449,plain,
! [X0: $i] :
( greater_than_0(additive_inverse(X0))
| ~ greater_than_0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3402,c_3448]) ).
tcf(c_3565,plain,
! [X0: $i] : ~ greater_than_0(X0),
inference(global_subsumption_just,[status(thm)],[c_3261,c_69,c_3449]) ).
tcf(c_3568,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_75,c_3565]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n008.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 04:30:54 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.41 Running first-order theorem proving
% 0.16/0.41 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
% 0.16/0.42
% 0.16/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.42
% 0.16/0.42 % Detected problem language: tptp
% 0.16/0.43 % Proving...
% 2.19/1.20 % SZS status Started for theBenchmark.p
% 2.19/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 2.19/1.20
% 2.19/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.19/1.20
% 2.19/1.20 % ------ iProver source info
% 2.19/1.20
% 2.19/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 2.19/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.19/1.20 % git: non_committed_changes: false
% 2.19/1.20
% 2.19/1.20 % ------ Parsing...% successful
% 2.19/1.20
% 2.19/1.20
% 2.19/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.19/1.20
% 2.19/1.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.19/1.20
% 2.19/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.19/1.20
% 2.19/1.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.19/1.20 % ------ Proving...
% 2.19/1.20 % ------ Problem Properties
% 2.19/1.20
% 2.19/1.20 %
% 2.19/1.20 % clauses 15
% 2.19/1.20 % conjectures 1
% 2.19/1.20 % EPR 8
% 2.19/1.20 % Horn 13
% 2.19/1.20 % unary 5
% 2.19/1.20 % binary 7
% 2.19/1.20 % lits 29
% 2.19/1.20 % lits eq 1
% 2.19/1.20 % fd_pure 0
% 2.19/1.20 % fd_pseudo 0
% 2.19/1.20 % fd_cond 0
% 2.19/1.20 % fd_pseudo_cond 0
% 2.19/1.20 % AC symbols 0
% 2.19/1.20
% 2.19/1.20 % ------ Schedule dynamic 5 is on
% 2.19/1.20
% 2.19/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.19/1.20
% 2.19/1.20
% 2.19/1.20 % ------
% 2.19/1.20 % Current options:
% 2.19/1.20 % ------
% 2.19/1.20
% 2.19/1.20
% 2.19/1.20 %
% 2.19/1.20
% 2.19/1.20 % ------ Proving...
% 2.19/1.20 %
% 2.19/1.20
% 2.19/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 2.19/1.20
% 2.19/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.19/1.20
% 2.19/1.20
%------------------------------------------------------------------------------