%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO016-2 : 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 : n015.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 2.32s 1.49s
% Output : CNFRefutation 2.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 78 ( 78 unt; 0 def)
% Number of atoms : 78 ( 77 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 97 ( 0 sgn 97 !; 0 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',commutativity_of_add) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',commutativity_of_multiply) ).
fof(f3,axiom,
! [X2,X0,X1] : add(multiply(X0,X1),X2) = multiply(add(X0,X2),add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity1) ).
fof(f4,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity2) ).
fof(f5,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity3) ).
fof(f6,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity4) ).
fof(f7,axiom,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_inverse1) ).
fof(f10,axiom,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_inverse1) ).
fof(f13,axiom,
! [X0] : multiply(X0,multiplicative_identity) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id1) ).
fof(f14,axiom,
! [X0] : multiply(multiplicative_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id2) ).
fof(f15,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_id1) ).
fof(f16,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_id2) ).
fof(f17,axiom,
multiply(x,y) = z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_times_y) ).
fof(f18,negated_conjecture,
add(x,z) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sum) ).
fof(f19,plain,
x != add(x,z),
inference(reorient_equations,[],[f18]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X2,X1)) = add(multiply(X0,X2),X1),
inference(cnf_transformation,[],[f3]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X0,X2)) = add(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(cnf_transformation,[],[f5]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(cnf_transformation,[],[f6]) ).
tcf(c_71,plain,
! [X0: $i] : add(X0,inverse(X0)) = multiplicative_identity,
inference(cnf_transformation,[],[f7]) ).
tcf(c_73,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = additive_identity,
inference(cnf_transformation,[],[f10]) ).
tcf(c_75,plain,
! [X0: $i] : multiply(X0,multiplicative_identity) = X0,
inference(cnf_transformation,[],[f13]) ).
tcf(c_76,plain,
! [X0: $i] : multiply(multiplicative_identity,X0) = X0,
inference(cnf_transformation,[],[f14]) ).
tcf(c_77,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(cnf_transformation,[],[f15]) ).
tcf(c_78,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(cnf_transformation,[],[f16]) ).
tcf(c_79,plain,
multiply(x,y) = z,
inference(cnf_transformation,[],[f17]) ).
tcf(c_80,negated_conjecture,
add(x,z) != x,
inference(cnf_transformation,[],[f19]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),inverse(X0)) = multiply(multiplicative_identity,add(X1,inverse(X0))),
inference(superposition,[status(thm)],[c_71,c_67]) ).
tcf(c_245,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = add(multiply(additive_identity,X1),X0),
inference(superposition,[status(thm)],[c_78,c_67]) ).
tcf(c_246,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X1,X2)) = add(multiply(X0,X2),X1),
inference(superposition,[status(thm)],[c_65,c_67]) ).
tcf(c_283,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,X1)) = add(multiply(additive_identity,X1),X0),
inference(superposition,[status(thm)],[c_65,c_245]) ).
tcf(c_286,plain,
! [X0: $i] : add(multiply(additive_identity,additive_identity),X0) = multiply(X0,X0),
inference(superposition,[status(thm)],[c_78,c_245]) ).
tcf(c_294,plain,
! [X0: $i] : multiply(X0,add(multiplicative_identity,X0)) = add(additive_identity,X0),
inference(superposition,[status(thm)],[c_75,c_245]) ).
tcf(c_305,plain,
! [X0: $i] : multiply(X0,add(multiplicative_identity,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_294,c_78]) ).
tcf(c_346,plain,
add(multiplicative_identity,multiplicative_identity) = multiplicative_identity,
inference(superposition,[status(thm)],[c_305,c_76]) ).
tcf(c_543,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = multiply(add(multiplicative_identity,X1),X0),
inference(superposition,[status(thm)],[c_76,c_69]) ).
tcf(c_557,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),X1) = multiply(add(X0,multiplicative_identity),X1),
inference(superposition,[status(thm)],[c_76,c_69]) ).
tcf(c_670,plain,
! [X0: $i] : multiply(x,add(y,X0)) = add(z,multiply(x,X0)),
inference(superposition,[status(thm)],[c_79,c_70]) ).
tcf(c_689,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,inverse(X0))) = add(multiply(X0,X1),additive_identity),
inference(superposition,[status(thm)],[c_73,c_70]) ).
tcf(c_1292,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,X1)) = multiply(X0,add(X1,X0)),
inference(superposition,[status(thm)],[c_283,c_245]) ).
tcf(c_1327,plain,
! [X0: $i,X1: $i] : add(inverse(X0),multiply(X0,X1)) = add(X1,inverse(X0)),
inference(demodulation,[status(thm)],[c_243,c_65,c_76]) ).
tcf(c_1331,plain,
add(inverse(x),z) = add(y,inverse(x)),
inference(superposition,[status(thm)],[c_79,c_1327]) ).
tcf(c_1336,plain,
! [X0: $i] : add(inverse(X0),inverse(X0)) = add(inverse(X0),additive_identity),
inference(superposition,[status(thm)],[c_73,c_1327]) ).
tcf(c_1337,plain,
! [X0: $i] : add(inverse(X0),X0) = add(multiplicative_identity,inverse(X0)),
inference(superposition,[status(thm)],[c_75,c_1327]) ).
tcf(c_1345,plain,
! [X0: $i] : add(add(multiplicative_identity,X0),inverse(X0)) = add(inverse(X0),X0),
inference(superposition,[status(thm)],[c_305,c_1327]) ).
tcf(c_1432,plain,
add(y,inverse(x)) = add(z,inverse(x)),
inference(demodulation,[status(thm)],[c_1331,c_65]) ).
tcf(c_1496,plain,
! [X0: $i] : add(multiplicative_identity,inverse(X0)) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_1337,c_65,c_71]) ).
tcf(c_1519,plain,
! [X0: $i] : add(inverse(X0),inverse(X0)) = inverse(X0),
inference(demodulation,[status(thm)],[c_1336,c_77]) ).
tcf(c_2007,plain,
! [X0: $i,X1: $i] : multiply(X0,add(additive_identity,X1)) = add(multiply(X0,X1),additive_identity),
inference(superposition,[status(thm)],[c_77,c_246]) ).
tcf(c_2196,plain,
! [X0: $i] : multiply(add(multiplicative_identity,multiplicative_identity),X0) = add(X0,X0),
inference(superposition,[status(thm)],[c_76,c_543]) ).
tcf(c_2223,plain,
! [X0: $i] : multiply(add(multiplicative_identity,X0),additive_identity) = multiply(X0,additive_identity),
inference(superposition,[status(thm)],[c_543,c_78]) ).
tcf(c_2230,plain,
! [X0: $i] : multiply(add(multiplicative_identity,X0),inverse(X0)) = add(inverse(X0),inverse(X0)),
inference(superposition,[status(thm)],[c_543,c_1327]) ).
tcf(c_2232,plain,
! [X0: $i] : add(X0,X0) = X0,
inference(light_normalisation,[status(thm)],[c_2196,c_76,c_346]) ).
tcf(c_2233,plain,
! [X0: $i] : multiply(add(multiplicative_identity,X0),inverse(X0)) = inverse(X0),
inference(light_normalisation,[status(thm)],[c_2230,c_1519]) ).
tcf(c_2303,plain,
! [X0: $i,X1: $i] : multiply(add(X0,X1),X0) = add(X0,multiply(X1,X0)),
inference(superposition,[status(thm)],[c_2232,c_68]) ).
tcf(c_2355,plain,
! [X0: $i] : multiply(additive_identity,add(multiplicative_identity,X0)) = multiply(X0,additive_identity),
inference(demodulation,[status(thm)],[c_2223,c_66]) ).
tcf(c_2379,plain,
multiply(additive_identity,additive_identity) = additive_identity,
inference(superposition,[status(thm)],[c_2355,c_305]) ).
tcf(c_2385,plain,
! [X0: $i] : multiply(X0,X0) = add(additive_identity,X0),
inference(demodulation,[status(thm)],[c_286,c_2379]) ).
tcf(c_2386,plain,
! [X0: $i] : multiply(X0,X0) = X0,
inference(light_normalisation,[status(thm)],[c_2385,c_78]) ).
tcf(c_2761,plain,
! [X0: $i] : multiply(inverse(X0),add(multiplicative_identity,X0)) = inverse(X0),
inference(demodulation,[status(thm)],[c_2233,c_66]) ).
tcf(c_2776,plain,
! [X0: $i] : multiply(add(multiplicative_identity,inverse(X0)),add(multiplicative_identity,X0)) = add(add(multiplicative_identity,X0),inverse(X0)),
inference(superposition,[status(thm)],[c_2761,c_543]) ).
tcf(c_2781,plain,
! [X0: $i] : multiply(multiplicative_identity,add(multiplicative_identity,X0)) = add(inverse(X0),X0),
inference(light_normalisation,[status(thm)],[c_2776,c_1345,c_1496]) ).
tcf(c_2829,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,X1)) = multiply(add(X1,multiplicative_identity),X0),
inference(demodulation,[status(thm)],[c_557,c_65,c_66,c_2303]) ).
tcf(c_3171,plain,
multiply(x,add(y,inverse(x))) = add(z,additive_identity),
inference(superposition,[status(thm)],[c_73,c_670]) ).
tcf(c_3173,plain,
multiply(x,add(y,x)) = add(z,x),
inference(superposition,[status(thm)],[c_2386,c_670]) ).
tcf(c_3193,plain,
multiply(x,add(z,inverse(x))) = add(z,additive_identity),
inference(light_normalisation,[status(thm)],[c_3171,c_1432]) ).
tcf(c_3240,plain,
multiply(x,z) = z,
inference(demodulation,[status(thm)],[c_3193,c_77,c_78,c_689,c_2007]) ).
tcf(c_3242,plain,
! [X0: $i] : multiply(x,add(z,X0)) = add(z,multiply(x,X0)),
inference(superposition,[status(thm)],[c_3240,c_70]) ).
tcf(c_3248,plain,
! [X0: $i] : multiply(x,add(y,X0)) = multiply(x,add(z,X0)),
inference(demodulation,[status(thm)],[c_670,c_3242]) ).
tcf(c_3274,plain,
multiply(x,add(x,z)) = add(x,z),
inference(demodulation,[status(thm)],[c_3173,c_65,c_1292,c_3248]) ).
tcf(c_3296,plain,
! [X0: $i] : add(multiplicative_identity,X0) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_2781,c_65,c_71,c_76]) ).
tcf(c_3321,plain,
! [X0: $i] : add(X0,multiplicative_identity) = multiplicative_identity,
inference(superposition,[status(thm)],[c_3296,c_65]) ).
tcf(c_3342,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,X1)) = multiply(multiplicative_identity,X0),
inference(demodulation,[status(thm)],[c_2829,c_3321]) ).
tcf(c_3343,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,X1)) = X0,
inference(light_normalisation,[status(thm)],[c_3342,c_76]) ).
tcf(c_3345,plain,
add(x,z) = x,
inference(demodulation,[status(thm)],[c_3274,c_3343]) ).
tcf(c_3351,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3345,c_80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO016-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.58 % Computer : n015.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Fri Sep 25 06:36:43 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.62 Running UEQ theorem proving
% 0.10/0.62 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.63
% 0.10/0.63 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.63
% 0.10/0.63 % Detected problem language: tptp
% 0.14/0.64 % Proving...
% 2.32/1.49 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.32/1.49 % SZS status Started for theBenchmark.p
% 2.32/1.49 % SZS status Unsatisfiable for theBenchmark.p
% 2.32/1.49
% 2.32/1.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.32/1.49
% 2.32/1.49 % ------ iProver source info
% 2.32/1.49
% 2.32/1.49 % git: date: 2026-07-19 20:42:38 +0200
% 2.32/1.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.32/1.49 % git: non_committed_changes: false
% 2.32/1.49
% 2.32/1.49 % ------ Parsing...% successful
% 2.32/1.49
% 2.32/1.49
% 2.32/1.49 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.32/1.49
% 2.32/1.49 % ------ Preprocessing... sup_sim: 4 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 %
% 2.32/1.49
% 2.32/1.49 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.32/1.49
% 2.32/1.49 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.32/1.49 % ------ Proving...
% 2.32/1.49 % ------ Problem Properties
% 2.32/1.49
% 2.32/1.49 %
% 2.32/1.49 % clauses 14
% 2.32/1.49 % conjectures 1
% 2.32/1.49 % EPR 0
% 2.32/1.49 % Horn 14
% 2.32/1.49 % unary 14
% 2.32/1.49 % binary 0
% 2.32/1.49 % lits 14
% 2.32/1.49 % lits eq 14
% 2.32/1.49 % fd_pure 0
% 2.32/1.49 % fd_pseudo 0
% 2.32/1.49 % fd_cond 0
% 2.32/1.49 % fd_pseudo_cond 0
% 2.32/1.49 % AC symbols 0
% 2.32/1.49
% 2.32/1.49 % ------ Input Options Time Limit: Unbounded
% 2.32/1.49
% 2.32/1.49
% 2.32/1.49 % ------
% 2.32/1.49 % Current options:
% 2.32/1.49 % ------
% 2.32/1.49
% 2.32/1.49
% 2.32/1.49 %
% 2.32/1.49
% 2.32/1.49 % ------ Proving...
% 2.32/1.49 %
% 2.32/1.49
% 2.32/1.49 % SZS status Unsatisfiable for theBenchmark.p
% 2.32/1.49
% 2.32/1.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.32/1.49
% 2.32/1.49
%------------------------------------------------------------------------------