%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO012-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n007.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 01:00:12 PM UTC 2026
% Result : Unsatisfiable 2.11s 1.29s
% Output : CNFRefutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 51 unt; 0 def)
% Number of atoms : 51 ( 50 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 72 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',commutativity_of_add) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',commutativity_of_multiply) ).
fof(f3,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',distributivity1) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',distributivity2) ).
fof(f5,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',additive_id1) ).
fof(f6,axiom,
! [X0] : multiply(X0,multiplicative_identity) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_id1) ).
fof(f7,axiom,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',additive_inverse1) ).
fof(f8,plain,
! [X0] : multiplicative_identity = add(X0,inverse(X0)),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_inverse1) ).
fof(f10,plain,
! [X0] : additive_identity = multiply(X0,inverse(X0)),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
inverse(inverse(x)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_is_an_involution) ).
fof(f12,plain,
x != inverse(inverse(x)),
inference(reorient_equations,[],[f11]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X0,X2)) = add(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f3]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_62,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(cnf_transformation,[],[f5]) ).
tcf(c_63,plain,
! [X0: $i] : multiply(X0,multiplicative_identity) = X0,
inference(cnf_transformation,[],[f6]) ).
tcf(c_64,plain,
! [X0: $i] : add(X0,inverse(X0)) = multiplicative_identity,
inference(cnf_transformation,[],[f8]) ).
tcf(c_65,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = additive_identity,
inference(cnf_transformation,[],[f10]) ).
tcf(c_66,negated_conjecture,
inverse(inverse(x)) != x,
inference(cnf_transformation,[],[f12]) ).
tcf(c_147,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(superposition,[status(thm)],[c_62,c_58]) ).
tcf(c_159,plain,
! [X0: $i] : multiply(multiplicative_identity,X0) = X0,
inference(superposition,[status(thm)],[c_63,c_59]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,X1)) = add(X0,multiply(additive_identity,X1)),
inference(superposition,[status(thm)],[c_62,c_60]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i] : add(X0,multiply(inverse(X0),X1)) = multiply(multiplicative_identity,add(X0,X1)),
inference(superposition,[status(thm)],[c_64,c_60]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = multiply(X0,add(multiplicative_identity,X1)),
inference(superposition,[status(thm)],[c_63,c_61]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i] : multiply(X0,add(inverse(X0),X1)) = add(additive_identity,multiply(X0,X1)),
inference(superposition,[status(thm)],[c_65,c_61]) ).
tcf(c_219,plain,
! [X0: $i,X1: $i] : add(X0,multiply(multiplicative_identity,X1)) = multiply(multiplicative_identity,add(X0,X1)),
inference(superposition,[status(thm)],[c_159,c_61]) ).
tcf(c_439,plain,
! [X0: $i,X1: $i] : add(X0,multiply(inverse(X0),X1)) = add(X0,multiply(multiplicative_identity,X1)),
inference(light_normalisation,[status(thm)],[c_169,c_219]) ).
tcf(c_440,plain,
! [X0: $i,X1: $i] : add(X0,multiply(inverse(X0),X1)) = add(X0,X1),
inference(demodulation,[status(thm)],[c_439,c_159]) ).
tcf(c_444,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,inverse(X0))) = add(X0,X1),
inference(superposition,[status(thm)],[c_59,c_440]) ).
tcf(c_446,plain,
! [X0: $i] : add(X0,inverse(X0)) = add(X0,multiplicative_identity),
inference(superposition,[status(thm)],[c_63,c_440]) ).
tcf(c_447,plain,
! [X0: $i] : add(X0,inverse(inverse(X0))) = add(X0,additive_identity),
inference(superposition,[status(thm)],[c_65,c_440]) ).
tcf(c_461,plain,
! [X0: $i] : add(X0,multiplicative_identity) = multiplicative_identity,
inference(light_normalisation,[status(thm)],[c_446,c_64]) ).
tcf(c_463,plain,
! [X0: $i] : add(X0,inverse(inverse(X0))) = X0,
inference(light_normalisation,[status(thm)],[c_447,c_62]) ).
tcf(c_483,plain,
! [X0: $i] : add(multiplicative_identity,X0) = multiplicative_identity,
inference(superposition,[status(thm)],[c_461,c_58]) ).
tcf(c_576,plain,
! [X0: $i] : add(X0,X0) = add(X0,additive_identity),
inference(superposition,[status(thm)],[c_65,c_444]) ).
tcf(c_588,plain,
! [X0: $i] : add(X0,X0) = X0,
inference(light_normalisation,[status(thm)],[c_576,c_62]) ).
tcf(c_601,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = multiply(X0,add(X0,X1)),
inference(superposition,[status(thm)],[c_588,c_60]) ).
tcf(c_683,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_189,c_63,c_483]) ).
tcf(c_707,plain,
! [X0: $i] : multiply(additive_identity,X0) = additive_identity,
inference(superposition,[status(thm)],[c_683,c_147]) ).
tcf(c_714,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,X1)) = add(X0,additive_identity),
inference(demodulation,[status(thm)],[c_168,c_707]) ).
tcf(c_715,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,X1)) = X0,
inference(light_normalisation,[status(thm)],[c_714,c_62,c_601]) ).
tcf(c_917,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_58,c_715]) ).
tcf(c_982,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),X0) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_463,c_917]) ).
tcf(c_1033,plain,
! [X0: $i,X1: $i] : multiply(X0,add(inverse(X0),X1)) = multiply(X0,X1),
inference(demodulation,[status(thm)],[c_190,c_147]) ).
tcf(c_1040,plain,
! [X0: $i] : multiply(X0,inverse(inverse(X0))) = multiply(X0,multiplicative_identity),
inference(superposition,[status(thm)],[c_64,c_1033]) ).
tcf(c_1065,plain,
! [X0: $i] : multiply(X0,inverse(inverse(X0))) = X0,
inference(light_normalisation,[status(thm)],[c_1040,c_63]) ).
tcf(c_1855,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_982,c_59,c_1065]) ).
tcf(c_1856,plain,
x != x,
inference(demodulation,[status(thm)],[c_66,c_1855]) ).
tcf(c_1862,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_1856]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO012-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 06:28:54 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.41 Running UEQ theorem proving
% 0.15/0.41 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
% 0.15/0.42
% 0.15/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.42
% 0.15/0.42 % Detected problem language: tptp
% 0.15/0.43 % Proving...
% 2.11/1.29 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.11/1.29 % SZS status Started for theBenchmark.p
% 2.11/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.11/1.29
% 2.11/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.11/1.29
% 2.11/1.29 % ------ iProver source info
% 2.11/1.29
% 2.11/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.11/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.11/1.29 % git: non_committed_changes: false
% 2.11/1.29
% 2.11/1.29 % ------ Parsing...% successful
% 2.11/1.29
% 2.11/1.29
% 2.11/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.11/1.29
% 2.11/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.11/1.29
% 2.11/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.11/1.29
% 2.11/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.11/1.29 % ------ Proving...
% 2.11/1.29 % ------ Problem Properties
% 2.11/1.29
% 2.11/1.29 %
% 2.11/1.29 % clauses 9
% 2.11/1.29 % conjectures 1
% 2.11/1.29 % EPR 0
% 2.11/1.29 % Horn 9
% 2.11/1.29 % unary 9
% 2.11/1.29 % binary 0
% 2.11/1.29 % lits 9
% 2.11/1.29 % lits eq 9
% 2.11/1.29 % fd_pure 0
% 2.11/1.29 % fd_pseudo 0
% 2.11/1.29 % fd_cond 0
% 2.11/1.29 % fd_pseudo_cond 0
% 2.11/1.29 % AC symbols 0
% 2.11/1.29
% 2.11/1.29 % ------ Input Options Time Limit: Unbounded
% 2.11/1.29
% 2.11/1.29
% 2.11/1.29 % ------
% 2.11/1.29 % Current options:
% 2.11/1.29 % ------
% 2.11/1.29
% 2.11/1.29
% 2.11/1.29 %
% 2.11/1.29
% 2.11/1.29 % ------ Proving...
% 2.11/1.29 %
% 2.11/1.29
% 2.11/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.11/1.29
% 2.11/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.11/1.29
% 2.11/1.29
%------------------------------------------------------------------------------