%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO022-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n005.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 01:00:15 PM UTC 2026
% Result : Unsatisfiable 3.63s 1.19s
% Output : CNFRefutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 81 ( 81 unt; 4 def)
% Number of atoms : 193 ( 80 equ)
% Maximal formula atoms : 1 ( 2 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 : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 57 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : multiply(add(X0,X1),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add) ).
fof(f2,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X1,X0),multiply(X2,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add_property) ).
fof(f4,axiom,
! [X0,X1] : add(multiply(X0,X1),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_multiply) ).
fof(f5,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = multiply(add(X1,X0),add(X2,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_multiply_property) ).
fof(f7,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_multiply) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : multiply(add(X0,X1),X1) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(X1,add(X0,X2)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),X1) = X1,
inference(cnf_transformation,[],[f4]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X2,X1)) = add(X1,multiply(X0,X2)),
inference(cnf_transformation,[],[f5]) ).
tcf(c_62,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
inference(cnf_transformation,[],[f7]) ).
tcf(c_87,definition,
iPr_def_10 = multiply(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_88,definition,
iPr_def_11 = multiply(iPr_def_10,c),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_89,definition,
iPr_def_12 = multiply(b,c),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_90,definition,
iPr_def_13 = multiply(a,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_91,negated_conjecture,
iPr_def_11 != iPr_def_13,
inference(demodulation,[status(thm)],[c_62,c_89,c_90,c_87,c_88]) ).
tcf(c_154,plain,
! [X0: $i] : add(X0,X0) = X0,
inference(superposition,[status(thm)],[c_56,c_59]) ).
tcf(c_156,plain,
add(iPr_def_10,b) = b,
inference(superposition,[status(thm)],[c_87,c_59]) ).
tcf(c_157,plain,
add(iPr_def_12,c) = c,
inference(superposition,[status(thm)],[c_89,c_59]) ).
tcf(c_159,plain,
add(iPr_def_13,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_90,c_59]) ).
tcf(c_160,plain,
! [X0: $i] : multiply(X0,X0) = X0,
inference(superposition,[status(thm)],[c_59,c_56]) ).
tcf(c_190,plain,
! [X0: $i] : add(iPr_def_10,multiply(X0,b)) = multiply(b,add(a,X0)),
inference(superposition,[status(thm)],[c_87,c_57]) ).
tcf(c_191,plain,
! [X0: $i] : add(iPr_def_12,multiply(X0,c)) = multiply(c,add(b,X0)),
inference(superposition,[status(thm)],[c_89,c_57]) ).
tcf(c_192,plain,
! [X0: $i] : add(iPr_def_11,multiply(X0,c)) = multiply(c,add(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_88,c_57]) ).
tcf(c_193,plain,
! [X0: $i] : add(iPr_def_13,multiply(X0,iPr_def_12)) = multiply(iPr_def_12,add(a,X0)),
inference(superposition,[status(thm)],[c_90,c_57]) ).
tcf(c_194,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,add(X1,add(X2,X0))) = add(multiply(X1,X0),X0),
inference(superposition,[status(thm)],[c_56,c_57]) ).
tcf(c_196,plain,
! [X0: $i] : add(multiply(X0,b),iPr_def_10) = multiply(b,add(X0,a)),
inference(superposition,[status(thm)],[c_87,c_57]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,add(X1,add(X2,X0))) = X0,
inference(demodulation,[status(thm)],[c_194,c_59]) ).
tcf(c_213,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X1)) = multiply(X1,X0),
inference(superposition,[status(thm)],[c_154,c_57]) ).
tcf(c_214,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(demodulation,[status(thm)],[c_213,c_154]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = X0,
inference(demodulation,[status(thm)],[c_56,c_214]) ).
tcf(c_217,plain,
multiply(iPr_def_12,a) = iPr_def_13,
inference(demodulation,[status(thm)],[c_90,c_214]) ).
tcf(c_233,plain,
add(iPr_def_13,a) = a,
inference(superposition,[status(thm)],[c_217,c_59]) ).
tcf(c_290,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = multiply(X0,add(X1,X0)),
inference(superposition,[status(thm)],[c_154,c_60]) ).
tcf(c_308,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X1)) = add(X1,X0),
inference(superposition,[status(thm)],[c_60,c_160]) ).
tcf(c_309,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(demodulation,[status(thm)],[c_308,c_160]) ).
tcf(c_312,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = X0,
inference(light_normalisation,[status(thm)],[c_290,c_216]) ).
tcf(c_314,plain,
add(iPr_def_12,iPr_def_13) = iPr_def_12,
inference(demodulation,[status(thm)],[c_159,c_309]) ).
tcf(c_487,plain,
multiply(iPr_def_13,iPr_def_12) = iPr_def_13,
inference(superposition,[status(thm)],[c_314,c_216]) ).
tcf(c_493,plain,
multiply(iPr_def_12,iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_487,c_214]) ).
tcf(c_533,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,X1)) = X0,
inference(superposition,[status(thm)],[c_309,c_216]) ).
tcf(c_583,plain,
add(a,iPr_def_10) = a,
inference(superposition,[status(thm)],[c_87,c_312]) ).
tcf(c_584,plain,
add(b,iPr_def_12) = b,
inference(superposition,[status(thm)],[c_89,c_312]) ).
tcf(c_585,plain,
add(iPr_def_10,iPr_def_11) = iPr_def_10,
inference(superposition,[status(thm)],[c_88,c_312]) ).
tcf(c_600,plain,
add(iPr_def_12,b) = b,
inference(demodulation,[status(thm)],[c_584,c_309]) ).
tcf(c_601,plain,
add(iPr_def_10,a) = a,
inference(demodulation,[status(thm)],[c_583,c_309]) ).
tcf(c_738,plain,
! [X0: $i] : add(b,multiply(iPr_def_12,X0)) = multiply(b,add(X0,b)),
inference(superposition,[status(thm)],[c_600,c_60]) ).
tcf(c_743,plain,
! [X0: $i] : add(b,multiply(iPr_def_12,X0)) = b,
inference(demodulation,[status(thm)],[c_738,c_216]) ).
tcf(c_755,plain,
! [X0: $i] : add(a,multiply(X0,iPr_def_10)) = multiply(add(X0,a),a),
inference(superposition,[status(thm)],[c_601,c_60]) ).
tcf(c_756,plain,
! [X0: $i] : add(a,multiply(X0,iPr_def_10)) = a,
inference(demodulation,[status(thm)],[c_755,c_214,c_216]) ).
tcf(c_966,plain,
multiply(b,add(a,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_190,c_312]) ).
tcf(c_967,plain,
multiply(b,add(iPr_def_10,a)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_966,c_309]) ).
tcf(c_968,plain,
multiply(b,a) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_967,c_601]) ).
tcf(c_1054,plain,
multiply(iPr_def_12,c) = iPr_def_12,
inference(superposition,[status(thm)],[c_157,c_533]) ).
tcf(c_1136,plain,
! [X0: $i] : add(iPr_def_12,multiply(X0,c)) = multiply(c,add(iPr_def_12,X0)),
inference(superposition,[status(thm)],[c_1054,c_57]) ).
tcf(c_1199,plain,
! [X0: $i] : multiply(c,add(b,X0)) = multiply(c,add(iPr_def_12,X0)),
inference(light_normalisation,[status(thm)],[c_191,c_1136]) ).
tcf(c_1204,plain,
multiply(c,add(iPr_def_12,b)) = multiply(c,b),
inference(superposition,[status(thm)],[c_154,c_1199]) ).
tcf(c_1215,plain,
multiply(c,add(iPr_def_12,b)) = multiply(b,c),
inference(demodulation,[status(thm)],[c_1204,c_214]) ).
tcf(c_1216,plain,
multiply(c,b) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_1215,c_89,c_600]) ).
tcf(c_1777,plain,
multiply(b,c) = iPr_def_12,
inference(superposition,[status(thm)],[c_1216,c_214]) ).
tcf(c_1806,plain,
multiply(c,add(iPr_def_10,b)) = add(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_1777,c_192]) ).
tcf(c_1819,plain,
multiply(c,add(iPr_def_10,iPr_def_11)) = iPr_def_11,
inference(superposition,[status(thm)],[c_192,c_312]) ).
tcf(c_1820,plain,
multiply(c,iPr_def_10) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_1819,c_585]) ).
tcf(c_1828,plain,
add(iPr_def_11,iPr_def_12) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_1806,c_156,c_1216]) ).
tcf(c_1857,plain,
multiply(iPr_def_11,iPr_def_12) = iPr_def_11,
inference(superposition,[status(thm)],[c_1828,c_533]) ).
tcf(c_1983,plain,
add(b,iPr_def_13) = b,
inference(superposition,[status(thm)],[c_493,c_743]) ).
tcf(c_1993,plain,
add(iPr_def_13,b) = b,
inference(demodulation,[status(thm)],[c_1983,c_309]) ).
tcf(c_2015,plain,
multiply(iPr_def_12,add(a,iPr_def_11)) = add(iPr_def_13,iPr_def_11),
inference(superposition,[status(thm)],[c_1857,c_193]) ).
tcf(c_2026,plain,
multiply(iPr_def_12,add(iPr_def_11,a)) = add(iPr_def_11,iPr_def_13),
inference(demodulation,[status(thm)],[c_2015,c_309]) ).
tcf(c_2079,plain,
multiply(iPr_def_13,b) = iPr_def_13,
inference(superposition,[status(thm)],[c_1993,c_533]) ).
tcf(c_2099,plain,
add(a,iPr_def_11) = a,
inference(superposition,[status(thm)],[c_1820,c_756]) ).
tcf(c_2108,plain,
add(iPr_def_11,a) = a,
inference(demodulation,[status(thm)],[c_2099,c_309]) ).
tcf(c_2605,plain,
multiply(b,add(iPr_def_13,a)) = add(iPr_def_13,iPr_def_10),
inference(superposition,[status(thm)],[c_2079,c_196]) ).
tcf(c_2613,plain,
multiply(b,add(iPr_def_13,a)) = add(iPr_def_10,iPr_def_13),
inference(demodulation,[status(thm)],[c_2605,c_309]) ).
tcf(c_2614,plain,
add(iPr_def_10,iPr_def_13) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_2613,c_233,c_968]) ).
tcf(c_2822,plain,
! [X0: $i] : multiply(iPr_def_13,add(X0,iPr_def_12)) = iPr_def_13,
inference(superposition,[status(thm)],[c_314,c_201]) ).
tcf(c_2971,plain,
! [X0: $i] : multiply(iPr_def_13,add(iPr_def_12,X0)) = iPr_def_13,
inference(superposition,[status(thm)],[c_309,c_2822]) ).
tcf(c_3073,plain,
multiply(iPr_def_13,c) = iPr_def_13,
inference(superposition,[status(thm)],[c_157,c_2971]) ).
tcf(c_3201,plain,
multiply(c,add(iPr_def_10,iPr_def_13)) = add(iPr_def_11,iPr_def_13),
inference(superposition,[status(thm)],[c_3073,c_192]) ).
tcf(c_3205,plain,
add(iPr_def_11,iPr_def_13) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_3201,c_1820,c_2614]) ).
tcf(c_4574,plain,
iPr_def_11 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_2026,c_217,c_2108,c_3205]) ).
tcf(c_4575,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4574,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO022-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n005.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Fri Sep 25 06:34:33 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.40 Running UEQ theorem proving
% 0.12/0.40 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 3.63/1.19 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 3.63/1.19 % SZS status Started for theBenchmark.p
% 3.63/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 3.63/1.19
% 3.63/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.63/1.19
% 3.63/1.19 % ------ iProver source info
% 3.63/1.19
% 3.63/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.63/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.63/1.19 % git: non_committed_changes: false
% 3.63/1.19
% 3.63/1.19 % ------ Parsing...% successful
% 3.63/1.19
% 3.63/1.19
% 3.63/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.63/1.19
% 3.63/1.19 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.63/1.19
% 3.63/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.63/1.19
% 3.63/1.19 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.63/1.19 % ------ Proving...
% 3.63/1.19 % ------ Problem Properties
% 3.63/1.19
% 3.63/1.19 %
% 3.63/1.19 % clauses 11
% 3.63/1.19 % conjectures 1
% 3.63/1.19 % EPR 1
% 3.63/1.19 % Horn 11
% 3.63/1.19 % unary 11
% 3.63/1.19 % binary 0
% 3.63/1.19 % lits 11
% 3.63/1.19 % lits eq 11
% 3.63/1.19 % fd_pure 0
% 3.63/1.19 % fd_pseudo 0
% 3.63/1.19 % fd_cond 0
% 3.63/1.19 % fd_pseudo_cond 0
% 3.63/1.19 % AC symbols 0
% 3.63/1.19
% 3.63/1.19 % ------ Input Options Time Limit: Unbounded
% 3.63/1.19
% 3.63/1.19
% 3.63/1.19 % ------
% 3.63/1.19 % Current options:
% 3.63/1.19 % ------
% 3.63/1.19
% 3.63/1.19
% 3.63/1.19 %
% 3.63/1.19
% 3.63/1.19 % ------ Proving...
% 3.63/1.19 %
% 3.63/1.19
% 3.63/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 3.63/1.19
% 3.63/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.63/1.19
% 3.63/1.19
%------------------------------------------------------------------------------