%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO016-1 : 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 : 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 01:00:14 PM UTC 2026
% Result : Unsatisfiable 3.94s 16.20s
% Output : CNFRefutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 42 unt; 1 def)
% Number of atoms : 180 ( 44 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 83 ( 44 ~; 39 |; 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 : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 117 ( 0 sgn 117 !; 0 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X2,X0,X1] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',commutativity_of_addition) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity2) ).
fof(f7,axiom,
! [X0] : product(multiplicative_identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_identity1) ).
fof(f8,axiom,
! [X0] : product(X0,multiplicative_identity,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_identity2) ).
fof(f10,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/Axioms/BOO002-0.ax',distributivity2) ).
fof(f12,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity4) ).
fof(f14,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( sum(X0,X5,X6)
| ~ product(X2,X4,X6)
| ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity6) ).
fof(f18,axiom,
! [X0] : sum(X0,inverse(X0),multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_inverse2) ).
fof(f20,axiom,
! [X0] : product(X0,inverse(X0),additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse2) ).
fof(f23,axiom,
product(x,y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_times_y) ).
fof(f24,negated_conjecture,
~ sum(x,z,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sum) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_78,plain,
! [X0: $i] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_79,plain,
! [X0: $i] : product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[],[f7]) ).
tcf(c_80,plain,
! [X0: $i] : product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[],[f8]) ).
tcf(c_82,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,[],[f10]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sum(X6,X2,X5)
| ~ sum(X6,X1,X4)
| ~ sum(X6,X0,X3)
| ~ product(X3,X4,X5)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_90,plain,
! [X0: $i] : sum(X0,inverse(X0),multiplicative_identity),
inference(cnf_transformation,[],[f18]) ).
tcf(c_92,plain,
! [X0: $i] : product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[],[f20]) ).
tcf(c_95,plain,
product(x,y,z),
inference(cnf_transformation,[],[f23]) ).
tcf(c_96,negated_conjecture,
~ sum(x,z,x),
inference(cnf_transformation,[],[f24]) ).
tcf(c_108,plain,
multiply(x,y) = z,
inference(well_definedness,[status(thm)],[c_95]) ).
tcf(c_109,plain,
add(x,z) != x,
inference(well_definedness,[status(thm)],[c_96]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( add(X1,X0) = X2 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_75]) ).
tcf(c_117,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(well_definedness,[status(thm)],[c_78]) ).
tcf(c_118,plain,
! [X0: $i] : multiply(multiplicative_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_79]) ).
tcf(c_119,plain,
! [X0: $i] : multiply(X0,multiplicative_identity) = X0,
inference(well_definedness,[status(thm)],[c_80]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X6,X2) = X5 )
| ( multiply(X6,X1) != X4 )
| ( multiply(X6,X0) != X3 )
| ( add(X3,X4) != X5 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_82]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X2,X6) = X5 )
| ( multiply(X1,X6) != X4 )
| ( multiply(X0,X6) != X3 )
| ( add(X3,X4) != X5 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_84]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( add(X0,X5) = X6 )
| ( multiply(X2,X4) != X6 )
| ( multiply(X1,X3) != X5 )
| ( add(X0,X3) != X4 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_86]) ).
tcf(c_137,plain,
! [X0: $i] : add(X0,inverse(X0)) = multiplicative_identity,
inference(well_definedness,[status(thm)],[c_90]) ).
tcf(c_139,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = additive_identity,
inference(well_definedness,[status(thm)],[c_92]) ).
tcf(c_281,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(unflattening,[status(thm)],[c_112]) ).
tcf(c_287,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X0,X2)) = add(X0,multiply(X1,X2)),
inference(unflattening,[status(thm)],[c_130]) ).
tcf(c_289,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(unflattening,[status(thm)],[c_126]) ).
tcf(c_291,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_122]) ).
tcf(c_333,definition,
iPr_def_10 = add(x,z),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_334,plain,
iPr_def_10 != x,
inference(demodulation,[status(thm)],[c_109,c_333]) ).
tcf(c_443,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(multiply(X0,X0),multiply(X0,X1)),add(multiply(X2,X0),multiply(X2,X1))) = add(X0,multiply(X2,X1)),
inference(demodulation,[status(thm)],[c_287,c_289,c_291]) ).
tcf(c_710,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(X0,inverse(X1))) = multiply(X0,multiplicative_identity),
inference(superposition,[status(thm)],[c_137,c_291]) ).
tcf(c_747,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(X0,inverse(X1))) = X0,
inference(light_normalisation,[status(thm)],[c_710,c_119]) ).
tcf(c_809,plain,
! [X0: $i] : add(X0,multiply(multiplicative_identity,inverse(X0))) = multiplicative_identity,
inference(superposition,[status(thm)],[c_118,c_747]) ).
tcf(c_820,plain,
! [X0: $i] : add(multiply(X0,X0),additive_identity) = X0,
inference(superposition,[status(thm)],[c_139,c_747]) ).
tcf(c_830,plain,
! [X0: $i,X1: $i] : add(add(multiply(X0,X0),multiply(X0,inverse(X0))),X1) = add(X0,multiply(X1,inverse(X0))),
inference(superposition,[status(thm)],[c_747,c_443]) ).
tcf(c_837,plain,
! [X0: $i,X1: $i] : add(add(multiply(X0,X0),additive_identity),X1) = add(X0,multiply(X1,inverse(X0))),
inference(light_normalisation,[status(thm)],[c_830,c_139]) ).
tcf(c_840,plain,
! [X0: $i] : multiply(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_820,c_117]) ).
tcf(c_908,plain,
! [X0: $i] : add(multiplicative_identity,X0) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_809,c_117,c_281,c_837,c_840]) ).
tcf(c_913,plain,
! [X0: $i,X1: $i] : add(multiply(X0,multiplicative_identity),multiply(X0,X1)) = multiply(X0,multiplicative_identity),
inference(superposition,[status(thm)],[c_908,c_291]) ).
tcf(c_916,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = X0,
inference(light_normalisation,[status(thm)],[c_913,c_119]) ).
tcf(c_980,plain,
add(x,z) = x,
inference(superposition,[status(thm)],[c_108,c_916]) ).
tcf(c_994,plain,
x = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_980,c_333]) ).
tcf(c_1000,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_334,c_994]) ).
tcf(c_1001,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_1000]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/15.29 % CPULimit : 300
% 0.09/15.29 % WCLimit : 300
% 0.09/15.29 % DateTime : Fri Sep 25 06:33:37 UTC 2026
% 0.09/15.29 % CPUTime :
% 0.09/15.29 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.20/15.33 Running first-order theorem proving
% 0.20/15.33 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
% 0.20/15.34
% 0.20/15.34 % ======== iProver multi-core TPTP/SMT =========
% 0.20/15.34
% 0.20/15.34 % Detected problem language: tptp
% 0.20/15.35 % Proving...
% 3.94/16.20 % SZS status Started for theBenchmark.p
% 3.94/16.20 % SZS status Unsatisfiable for theBenchmark.p
% 3.94/16.20
% 3.94/16.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.94/16.20
% 3.94/16.20 % ------ iProver source info
% 3.94/16.20
% 3.94/16.20 % git: date: 2026-07-19 20:42:38 +0200
% 3.94/16.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.94/16.20 % git: non_committed_changes: false
% 3.94/16.20
% 3.94/16.20 % ------ Parsing...% successful
% 3.94/16.20
% 3.94/16.20
% 3.94/16.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.94/16.20
% 3.94/16.20 % ------ Preprocessing... sup_sim: 18 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 %
% 3.94/16.20
% 3.94/16.20 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.94/16.20 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.94/16.20
% 3.94/16.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.94/16.20 % ------ Proving...
% 3.94/16.20 % ------ Problem Properties
% 3.94/16.20
% 3.94/16.20 %
% 3.94/16.20 % clauses 15
% 3.94/16.20 % conjectures 0
% 3.94/16.20 % EPR 1
% 3.94/16.20 % Horn 15
% 3.94/16.20 % unary 15
% 3.94/16.20 % binary 0
% 3.94/16.20 % lits 15
% 3.94/16.20 % lits eq 15
% 3.94/16.20 % fd_pure 0
% 3.94/16.20 % fd_pseudo 0
% 3.94/16.20 % fd_cond 0
% 3.94/16.20 % fd_pseudo_cond 0
% 3.94/16.20 % AC symbols 0
% 3.94/16.20
% 3.94/16.20 % ------ Schedule UEQ
% 3.94/16.20
% 3.94/16.20 % ------ Option_UEQ Time Limit: 10.
% 3.94/16.20
% 3.94/16.20
% 3.94/16.20 % ------
% 3.94/16.20 % Current options:
% 3.94/16.20 % ------
% 3.94/16.20
% 3.94/16.20
% 3.94/16.20 %
% 3.94/16.20
% 3.94/16.20 % ------ Proving...
% 3.94/16.20 %
% 3.94/16.20
% 3.94/16.20 % SZS status Unsatisfiable for theBenchmark.p
% 3.94/16.20
% 3.94/16.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.94/16.20
% 3.94/16.20
%------------------------------------------------------------------------------