%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO012-1 : 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 : n017.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 4.04s 1.33s
% Output : CNFRefutation 4.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 37 unt; 2 def)
% Number of atoms : 140 ( 37 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 41 ( 23 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 62 ( 0 sgn 62 !; 0 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X2,X0,X1] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',commutativity_of_addition) ).
fof(f4,axiom,
! [X2,X0,X1] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',commutativity_of_multiplication) ).
fof(f5,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
fof(f7,axiom,
! [X0] : product(multiplicative_identity,X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_identity1) ).
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/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity4) ).
fof(f18,axiom,
! [X0] : sum(X0,inverse(X0),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_inverse2) ).
fof(f20,axiom,
! [X0] : product(X0,inverse(X0),additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse2) ).
fof(f23,negated_conjecture,
inverse(inverse(x)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_is_an_involution) ).
fof(f24,plain,
x != inverse(inverse(x)),
inference(reorient_equations,[],[f23]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_76,plain,
! [X0: $i] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_78,plain,
! [X0: $i] : product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[],[f7]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X2,X6,X5)
| ~ product(X1,X6,X4)
| ~ product(X0,X6,X3)
| ~ sum(X3,X4,X5)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_89,plain,
! [X0: $i] : sum(X0,inverse(X0),multiplicative_identity),
inference(cnf_transformation,[],[f18]) ).
tcf(c_91,plain,
! [X0: $i] : product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[],[f20]) ).
tcf(c_94,negated_conjecture,
inverse(inverse(x)) != x,
inference(cnf_transformation,[],[f24]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( add(X1,X0) = X2 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_74]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X1,X0) = X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_75]) ).
tcf(c_112,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_76]) ).
tcf(c_114,plain,
! [X0: $i] : multiply(multiplicative_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_78]) ).
tcf(c_122,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_83]) ).
tcf(c_133,plain,
! [X0: $i] : add(X0,inverse(X0)) = multiplicative_identity,
inference(well_definedness,[status(thm)],[c_89]) ).
tcf(c_135,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = additive_identity,
inference(well_definedness,[status(thm)],[c_91]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(unflattening,[status(thm)],[c_110]) ).
tcf(c_275,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(unflattening,[status(thm)],[c_108]) ).
tcf(c_283,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(unflattening,[status(thm)],[c_122]) ).
tcf(c_327,definition,
iPr_def_10 = inverse(x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_328,definition,
iPr_def_11 = inverse(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_329,negated_conjecture,
iPr_def_11 != x,
inference(demodulation,[status(thm)],[c_94,c_327,c_328]) ).
tcf(c_392,plain,
add(x,iPr_def_10) = multiplicative_identity,
inference(superposition,[status(thm)],[c_327,c_133]) ).
tcf(c_393,plain,
add(iPr_def_10,iPr_def_11) = multiplicative_identity,
inference(superposition,[status(thm)],[c_328,c_133]) ).
tcf(c_396,plain,
multiply(x,iPr_def_10) = additive_identity,
inference(superposition,[status(thm)],[c_327,c_135]) ).
tcf(c_397,plain,
multiply(iPr_def_10,iPr_def_11) = additive_identity,
inference(superposition,[status(thm)],[c_328,c_135]) ).
tcf(c_399,plain,
add(iPr_def_10,x) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_392,c_275]) ).
tcf(c_400,plain,
multiply(iPr_def_10,x) = additive_identity,
inference(demodulation,[status(thm)],[c_396,c_273]) ).
tcf(c_625,plain,
! [X0: $i] : add(multiply(iPr_def_10,X0),multiply(iPr_def_11,X0)) = multiply(multiplicative_identity,X0),
inference(superposition,[status(thm)],[c_393,c_283]) ).
tcf(c_626,plain,
! [X0: $i] : add(multiply(iPr_def_10,X0),multiply(x,X0)) = multiply(multiplicative_identity,X0),
inference(superposition,[status(thm)],[c_399,c_283]) ).
tcf(c_656,plain,
! [X0: $i] : add(multiply(iPr_def_10,X0),multiply(x,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_626,c_114]) ).
tcf(c_657,plain,
! [X0: $i] : add(multiply(iPr_def_10,X0),multiply(iPr_def_11,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_625,c_114]) ).
tcf(c_796,plain,
add(additive_identity,multiply(x,iPr_def_11)) = iPr_def_11,
inference(superposition,[status(thm)],[c_397,c_656]) ).
tcf(c_811,plain,
multiply(iPr_def_11,x) = iPr_def_11,
inference(demodulation,[status(thm)],[c_796,c_112,c_273]) ).
tcf(c_859,plain,
add(multiply(iPr_def_10,x),iPr_def_11) = x,
inference(superposition,[status(thm)],[c_811,c_657]) ).
tcf(c_862,plain,
add(additive_identity,iPr_def_11) = x,
inference(light_normalisation,[status(thm)],[c_859,c_400]) ).
tcf(c_872,plain,
add(additive_identity,iPr_def_11) != iPr_def_11,
inference(demodulation,[status(thm)],[c_329,c_862]) ).
tcf(c_873,plain,
$false,
inference(ground_joinability,[status(thm)],[c_872,c_112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO012-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n017.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 06:24:47 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 4.04/1.33 % SZS status Started for theBenchmark.p
% 4.04/1.33 % SZS status Unsatisfiable for theBenchmark.p
% 4.04/1.33
% 4.04/1.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.04/1.33
% 4.04/1.33 % ------ iProver source info
% 4.04/1.33
% 4.04/1.33 % git: date: 2026-07-19 20:42:38 +0200
% 4.04/1.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.04/1.33 % git: non_committed_changes: false
% 4.04/1.33
% 4.04/1.33 % ------ Parsing...% successful
% 4.04/1.33
% 4.04/1.33
% 4.04/1.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.04/1.33
% 4.04/1.33 % ------ 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 %
% 4.04/1.33
% 4.04/1.33 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 4.04/1.33 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.04/1.33
% 4.04/1.33 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.04/1.33 % ------ Proving...
% 4.04/1.33 % ------ Problem Properties
% 4.04/1.33
% 4.04/1.33 %
% 4.04/1.33 % clauses 15
% 4.04/1.33 % conjectures 1
% 4.04/1.33 % EPR 1
% 4.04/1.33 % Horn 15
% 4.04/1.33 % unary 15
% 4.04/1.33 % binary 0
% 4.04/1.33 % lits 15
% 4.04/1.33 % lits eq 15
% 4.04/1.33 % fd_pure 0
% 4.04/1.33 % fd_pseudo 0
% 4.04/1.33 % fd_cond 0
% 4.04/1.33 % fd_pseudo_cond 0
% 4.04/1.33 % AC symbols 0
% 4.04/1.33
% 4.04/1.33 % ------ Schedule UEQ
% 4.04/1.33
% 4.04/1.33 % ------ Option_UEQ Time Limit: 10.
% 4.04/1.33
% 4.04/1.33
% 4.04/1.33 % ------
% 4.04/1.33 % Current options:
% 4.04/1.33 % ------
% 4.04/1.33
% 4.04/1.33
% 4.04/1.33 %
% 4.04/1.33
% 4.04/1.33 % ------ Proving...
% 4.04/1.33 %
% 4.04/1.33
% 4.04/1.33 % SZS status Unsatisfiable for theBenchmark.p
% 4.04/1.33
% 4.04/1.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.04/1.33
% 4.04/1.33
%------------------------------------------------------------------------------