%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP093-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 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 01:30:43 PM UTC 2026
% Result : Unsatisfiable 2.16s 1.19s
% Output : CNFRefutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 81 ( 72 unt; 13 def)
% Number of atoms : 218 ( 102 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 54 ( 32 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 43 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(divide(identity,divide(divide(divide(X0,X1),X2),X0)),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = divide(X0,divide(identity,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0] : inverse(X0) = divide(identity,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f4,axiom,
! [X0] : identity = divide(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f6,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != multiply(multiply(inverse(b2),b2),a2)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,plain,
( divide(a4,divide(identity,b4)) != divide(b4,divide(identity,a4))
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| a2 != divide(divide(divide(identity,b2),divide(identity,b2)),divide(identity,a2))
| divide(divide(identity,a1),divide(identity,a1)) != divide(divide(identity,b1),divide(identity,b1)) ),
inference(definition_unfolding,[],[f6,f2,f3,f2,f3,f2,f2,f3,f2,f2,f2,f2,f2,f2]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] : divide(divide(identity,divide(divide(divide(X0,X1),X2),X0)),X2) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_55,plain,
! [X0: $i] : divide(X0,X0) = identity,
inference(cnf_transformation,[],[f4]) ).
tcf(c_56,negated_conjecture,
( ( divide(a4,divide(identity,b4)) != divide(b4,divide(identity,a4)) )
| ( divide(divide(identity,a1),divide(identity,a1)) != divide(divide(identity,b1),divide(identity,b1)) )
| ( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) )
| ( divide(divide(divide(identity,b2),divide(identity,b2)),divide(identity,a2)) != a2 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_71,plain,
( ( identity != identity )
| ( divide(a4,divide(identity,b4)) != divide(b4,divide(identity,a4)) )
| ( divide(identity,divide(identity,a2)) != a2 )
| ( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ) ),
inference(demodulation,[status(thm)],[c_56,c_55]) ).
tcf(c_72,plain,
( ( divide(a4,divide(identity,b4)) != divide(b4,divide(identity,a4)) )
| ( divide(identity,divide(identity,a2)) != a2 )
| ( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ) ),
inference(equality_resolution_simp,[status(thm)],[c_71]) ).
tcf(c_79,definition,
iPr_def_10 = divide(identity,b3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_80,definition,
iPr_def_11 = divide(a3,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_81,definition,
iPr_def_12 = divide(identity,c3),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_82,definition,
iPr_def_13 = divide(iPr_def_11,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_83,definition,
iPr_def_14 = divide(b3,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_84,definition,
iPr_def_15 = divide(identity,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_85,definition,
iPr_def_16 = divide(a3,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_86,definition,
iPr_def_17 = divide(identity,a2),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_87,definition,
iPr_def_18 = divide(identity,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_88,definition,
iPr_def_19 = divide(identity,b4),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_89,definition,
iPr_def_20 = divide(a4,iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_90,definition,
iPr_def_21 = divide(identity,a4),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_91,definition,
iPr_def_22 = divide(b4,iPr_def_21),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_92,plain,
( ( iPr_def_20 != iPr_def_22 )
| ( iPr_def_18 != a2 )
| ( iPr_def_13 != iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_72,c_90,c_91,c_88,c_89,c_86,c_87,c_83,c_84,c_85,c_81,c_79,c_80,c_82]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] : divide(divide(identity,divide(identity,X0)),divide(X0,X1)) = X1,
inference(superposition,[status(thm)],[c_55,c_54]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i] : divide(divide(identity,divide(divide(identity,X0),X1)),X0) = X1,
inference(superposition,[status(thm)],[c_55,c_54]) ).
tcf(c_160,plain,
! [X0: $i] : divide(divide(identity,divide(divide(iPr_def_11,X0),a3)),X0) = iPr_def_10,
inference(superposition,[status(thm)],[c_80,c_54]) ).
tcf(c_162,plain,
! [X0: $i] : divide(divide(identity,divide(divide(iPr_def_14,X0),b3)),X0) = iPr_def_12,
inference(superposition,[status(thm)],[c_83,c_54]) ).
tcf(c_163,plain,
! [X0: $i] : divide(divide(identity,divide(divide(iPr_def_15,X0),identity)),X0) = iPr_def_14,
inference(superposition,[status(thm)],[c_84,c_54]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i,X2: $i] : divide(divide(divide(X0,X1),X2),X0) = divide(divide(identity,divide(X1,identity)),X2),
inference(superposition,[status(thm)],[c_54,c_54]) ).
tcf(c_190,plain,
! [X0: $i] : divide(identity,divide(identity,X0)) = X0,
inference(superposition,[status(thm)],[c_55,c_152]) ).
tcf(c_219,plain,
! [X0: $i,X1: $i] : divide(X0,divide(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_152,c_190]) ).
tcf(c_265,plain,
! [X0: $i] : divide(X0,identity) = X0,
inference(superposition,[status(thm)],[c_55,c_219]) ).
tcf(c_266,plain,
divide(identity,iPr_def_17) = a2,
inference(superposition,[status(thm)],[c_86,c_219]) ).
tcf(c_267,plain,
divide(identity,iPr_def_10) = b3,
inference(superposition,[status(thm)],[c_79,c_219]) ).
tcf(c_268,plain,
divide(identity,iPr_def_12) = c3,
inference(superposition,[status(thm)],[c_81,c_219]) ).
tcf(c_269,plain,
divide(identity,iPr_def_19) = b4,
inference(superposition,[status(thm)],[c_88,c_219]) ).
tcf(c_270,plain,
divide(identity,iPr_def_21) = a4,
inference(superposition,[status(thm)],[c_90,c_219]) ).
tcf(c_272,plain,
divide(iPr_def_11,iPr_def_13) = iPr_def_12,
inference(superposition,[status(thm)],[c_82,c_219]) ).
tcf(c_274,plain,
divide(identity,iPr_def_15) = iPr_def_14,
inference(superposition,[status(thm)],[c_84,c_219]) ).
tcf(c_277,plain,
divide(a4,iPr_def_20) = iPr_def_19,
inference(superposition,[status(thm)],[c_89,c_219]) ).
tcf(c_278,plain,
divide(b4,iPr_def_22) = iPr_def_21,
inference(superposition,[status(thm)],[c_91,c_219]) ).
tcf(c_285,plain,
a2 = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_266,c_87]) ).
tcf(c_292,plain,
( ( iPr_def_20 != iPr_def_22 )
| ( iPr_def_18 != iPr_def_18 )
| ( iPr_def_13 != iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_92,c_285]) ).
tcf(c_293,plain,
( ( iPr_def_20 != iPr_def_22 )
| ( iPr_def_13 != iPr_def_16 ) ),
inference(equality_resolution_simp,[status(thm)],[c_292]) ).
tcf(c_324,plain,
! [X0: $i,X1: $i] : divide(divide(identity,X0),X1) = divide(divide(identity,X1),X0),
inference(superposition,[status(thm)],[c_219,c_154]) ).
tcf(c_332,plain,
! [X0: $i,X1: $i] : divide(divide(identity,divide(X0,X1)),divide(identity,X0)) = X1,
inference(superposition,[status(thm)],[c_219,c_154]) ).
tcf(c_380,plain,
divide(identity,b3) = iPr_def_10,
inference(superposition,[status(thm)],[c_267,c_219]) ).
tcf(c_388,plain,
divide(identity,b4) = iPr_def_19,
inference(superposition,[status(thm)],[c_269,c_219]) ).
tcf(c_405,plain,
divide(iPr_def_11,iPr_def_12) = iPr_def_13,
inference(superposition,[status(thm)],[c_272,c_219]) ).
tcf(c_407,plain,
divide(identity,iPr_def_14) = iPr_def_15,
inference(superposition,[status(thm)],[c_274,c_219]) ).
tcf(c_410,plain,
divide(a4,iPr_def_19) = iPr_def_20,
inference(superposition,[status(thm)],[c_277,c_219]) ).
tcf(c_411,plain,
divide(b4,iPr_def_21) = iPr_def_22,
inference(superposition,[status(thm)],[c_278,c_219]) ).
tcf(c_874,plain,
! [X0: $i] : divide(divide(identity,X0),divide(divide(iPr_def_11,X0),a3)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_160,c_324]) ).
tcf(c_897,plain,
divide(divide(identity,iPr_def_12),divide(iPr_def_13,a3)) = iPr_def_10,
inference(superposition,[status(thm)],[c_405,c_874]) ).
tcf(c_903,plain,
divide(c3,divide(iPr_def_13,a3)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_897,c_268]) ).
tcf(c_1033,plain,
! [X0: $i] : divide(divide(identity,X0),divide(divide(iPr_def_14,X0),b3)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_162,c_324]) ).
tcf(c_1055,plain,
divide(divide(identity,iPr_def_14),divide(identity,b3)) = iPr_def_12,
inference(superposition,[status(thm)],[c_55,c_1033]) ).
tcf(c_1063,plain,
divide(iPr_def_15,iPr_def_10) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_1055,c_380,c_407]) ).
tcf(c_1091,plain,
! [X0: $i] : divide(divide(identity,X0),divide(iPr_def_15,X0)) = iPr_def_14,
inference(demodulation,[status(thm)],[c_163,c_265,c_324]) ).
tcf(c_1392,plain,
divide(iPr_def_15,iPr_def_12) = iPr_def_10,
inference(superposition,[status(thm)],[c_1063,c_219]) ).
tcf(c_1408,plain,
divide(divide(identity,iPr_def_12),iPr_def_10) = iPr_def_14,
inference(superposition,[status(thm)],[c_1392,c_1091]) ).
tcf(c_1409,plain,
divide(c3,iPr_def_10) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_1408,c_268]) ).
tcf(c_1504,plain,
! [X0: $i,X1: $i,X2: $i] : divide(divide(divide(X0,X1),X2),X0) = divide(divide(identity,X1),X2),
inference(demodulation,[status(thm)],[c_169,c_265]) ).
tcf(c_1506,plain,
! [X0: $i,X1: $i] : divide(divide(identity,X0),divide(X1,X0)) = divide(identity,X1),
inference(superposition,[status(thm)],[c_55,c_1504]) ).
tcf(c_1557,plain,
! [X0: $i,X1: $i,X2: $i] : divide(divide(identity,divide(X0,X1)),X2) = divide(divide(X1,X2),X0),
inference(superposition,[status(thm)],[c_219,c_1504]) ).
tcf(c_2039,plain,
divide(divide(identity,iPr_def_21),iPr_def_22) = divide(identity,b4),
inference(superposition,[status(thm)],[c_411,c_1506]) ).
tcf(c_2130,plain,
divide(a4,iPr_def_22) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_2039,c_270,c_388]) ).
tcf(c_3173,plain,
divide(a4,iPr_def_19) = iPr_def_22,
inference(superposition,[status(thm)],[c_2130,c_219]) ).
tcf(c_3174,plain,
iPr_def_20 = iPr_def_22,
inference(light_normalisation,[status(thm)],[c_3173,c_410]) ).
tcf(c_3175,plain,
iPr_def_13 != iPr_def_16,
inference(backward_subsumption_resolution,[status(thm)],[c_293,c_3174]) ).
tcf(c_3250,plain,
divide(c3,iPr_def_10) = divide(iPr_def_13,a3),
inference(superposition,[status(thm)],[c_903,c_219]) ).
tcf(c_3251,plain,
divide(iPr_def_13,a3) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_3250,c_1409]) ).
tcf(c_3256,plain,
divide(iPr_def_13,iPr_def_14) = a3,
inference(superposition,[status(thm)],[c_3251,c_219]) ).
tcf(c_3370,plain,
! [X0: $i,X1: $i] : divide(divide(X0,divide(identity,X1)),X1) = X0,
inference(demodulation,[status(thm)],[c_332,c_1557]) ).
tcf(c_3398,plain,
! [X0: $i] : divide(divide(X0,iPr_def_14),iPr_def_15) = X0,
inference(superposition,[status(thm)],[c_274,c_3370]) ).
tcf(c_4293,plain,
divide(a3,iPr_def_15) = iPr_def_13,
inference(superposition,[status(thm)],[c_3256,c_3398]) ).
tcf(c_4305,plain,
iPr_def_13 = iPr_def_16,
inference(demodulation,[status(thm)],[c_85,c_4293]) ).
tcf(c_4306,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4305,c_3175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP093-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 13:28:37 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 2.16/1.19 % SZS status Started for theBenchmark.p
% 2.16/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 2.16/1.19
% 2.16/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.16/1.19
% 2.16/1.19 % ------ iProver source info
% 2.16/1.19
% 2.16/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 2.16/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.16/1.19 % git: non_committed_changes: false
% 2.16/1.19
% 2.16/1.19 % ------ Parsing...% successful
% 2.16/1.19
% 2.16/1.19
% 2.16/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.16/1.19
% 2.16/1.19 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.16/1.19
% 2.16/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.16/1.19
% 2.16/1.19 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.16/1.19 % ------ Proving...
% 2.16/1.19 % ------ Problem Properties
% 2.16/1.19
% 2.16/1.19 %
% 2.16/1.19 % clauses 16
% 2.16/1.19 % conjectures 0
% 2.16/1.19 % EPR 1
% 2.16/1.19 % Horn 16
% 2.16/1.19 % unary 15
% 2.16/1.19 % binary 0
% 2.16/1.19 % lits 18
% 2.16/1.19 % lits eq 18
% 2.16/1.20 % fd_pure 0
% 2.16/1.20 % fd_pseudo 0
% 2.16/1.20 % fd_cond 0
% 2.16/1.20 % fd_pseudo_cond 0
% 2.16/1.20 % AC symbols 0
% 2.16/1.20
% 2.16/1.20 % ------ Schedule dynamic 5 is on
% 2.16/1.20
% 2.16/1.20 % ------ no conjectures: strip conj schedule
% 2.16/1.20
% 2.16/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.16/1.20
% 2.16/1.20
% 2.16/1.20 % ------
% 2.16/1.20 % Current options:
% 2.16/1.20 % ------
% 2.16/1.20
% 2.16/1.20
% 2.16/1.20 %
% 2.16/1.20
% 2.16/1.20 % ------ Proving...
% 2.16/1.20 %
% 2.16/1.20
% 2.16/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 2.16/1.20
% 2.16/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.16/1.20
% 2.16/1.20
%------------------------------------------------------------------------------