%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP094-1 : 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 : n001.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 2.03s 1.29s
% Output : CNFRefutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 70 ( 61 unt; 13 def)
% Number of atoms : 187 ( 91 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 : 5 ( 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 : 39 ( 0 sgn 39 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(divide(identity,divide(X0,X1)),divide(divide(X1,X2),X0)) = X2,
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(X0,X1)),divide(divide(X1,X2),X0)) = X2,
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,identity),divide(divide(X0,X1),X0)) = X1,
inference(superposition,[status(thm)],[c_55,c_54]) ).
tcf(c_157,plain,
! [X0: $i] : divide(divide(identity,iPr_def_21),divide(divide(a4,X0),identity)) = X0,
inference(superposition,[status(thm)],[c_90,c_54]) ).
tcf(c_160,plain,
! [X0: $i] : divide(divide(identity,iPr_def_14),divide(divide(iPr_def_12,X0),b3)) = X0,
inference(superposition,[status(thm)],[c_83,c_54]) ).
tcf(c_186,plain,
! [X0: $i] : divide(iPr_def_15,divide(divide(iPr_def_12,X0),b3)) = X0,
inference(light_normalisation,[status(thm)],[c_160,c_84]) ).
tcf(c_250,plain,
divide(iPr_def_15,divide(identity,b3)) = iPr_def_12,
inference(superposition,[status(thm)],[c_55,c_186]) ).
tcf(c_253,plain,
divide(iPr_def_15,iPr_def_10) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_250,c_79]) ).
tcf(c_365,plain,
! [X0: $i,X1: $i] : divide(identity,divide(divide(X0,X1),X0)) = X1,
inference(demodulation,[status(thm)],[c_152,c_55]) ).
tcf(c_367,plain,
! [X0: $i] : divide(identity,divide(identity,X0)) = X0,
inference(superposition,[status(thm)],[c_55,c_365]) ).
tcf(c_372,plain,
divide(identity,divide(iPr_def_21,identity)) = a4,
inference(superposition,[status(thm)],[c_90,c_365]) ).
tcf(c_377,plain,
divide(identity,divide(iPr_def_16,a3)) = iPr_def_15,
inference(superposition,[status(thm)],[c_85,c_365]) ).
tcf(c_500,plain,
divide(identity,iPr_def_17) = a2,
inference(superposition,[status(thm)],[c_86,c_367]) ).
tcf(c_503,plain,
divide(identity,iPr_def_19) = b4,
inference(superposition,[status(thm)],[c_88,c_367]) ).
tcf(c_504,plain,
divide(identity,iPr_def_21) = a4,
inference(superposition,[status(thm)],[c_90,c_367]) ).
tcf(c_505,plain,
divide(identity,iPr_def_15) = iPr_def_14,
inference(superposition,[status(thm)],[c_84,c_367]) ).
tcf(c_508,plain,
! [X0: $i,X1: $i] : divide(X0,divide(divide(X0,X1),identity)) = X1,
inference(superposition,[status(thm)],[c_367,c_54]) ).
tcf(c_510,plain,
a2 = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_500,c_87]) ).
tcf(c_515,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_510]) ).
tcf(c_516,plain,
( ( iPr_def_20 != iPr_def_22 )
| ( iPr_def_13 != iPr_def_16 ) ),
inference(equality_resolution_simp,[status(thm)],[c_515]) ).
tcf(c_577,plain,
! [X0: $i] : divide(divide(identity,iPr_def_14),divide(divide(iPr_def_15,X0),identity)) = X0,
inference(superposition,[status(thm)],[c_505,c_54]) ).
tcf(c_580,plain,
! [X0: $i] : divide(iPr_def_15,divide(divide(iPr_def_15,X0),identity)) = X0,
inference(light_normalisation,[status(thm)],[c_577,c_84]) ).
tcf(c_706,plain,
! [X0: $i] : divide(a4,divide(divide(identity,X0),iPr_def_21)) = X0,
inference(superposition,[status(thm)],[c_372,c_54]) ).
tcf(c_787,plain,
! [X0: $i] : divide(iPr_def_15,divide(divide(a3,X0),iPr_def_16)) = X0,
inference(superposition,[status(thm)],[c_377,c_54]) ).
tcf(c_950,plain,
! [X0: $i] : divide(X0,divide(identity,identity)) = X0,
inference(superposition,[status(thm)],[c_55,c_508]) ).
tcf(c_999,plain,
! [X0: $i,X1: $i] : divide(divide(X0,X1),identity) = divide(X0,divide(X1,identity)),
inference(superposition,[status(thm)],[c_508,c_508]) ).
tcf(c_1002,plain,
! [X0: $i,X1: $i,X2: $i] : divide(divide(identity,divide(X0,X1)),divide(X2,X0)) = divide(divide(X1,X2),identity),
inference(superposition,[status(thm)],[c_508,c_54]) ).
tcf(c_1009,plain,
! [X0: $i,X1: $i] : divide(divide(X0,divide(X0,X1)),identity) = X1,
inference(demodulation,[status(thm)],[c_54,c_1002]) ).
tcf(c_1097,plain,
! [X0: $i] : divide(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_950,c_55]) ).
tcf(c_1106,plain,
! [X0: $i] : divide(a4,divide(divide(a4,X0),identity)) = X0,
inference(light_normalisation,[status(thm)],[c_157,c_504]) ).
tcf(c_1107,plain,
! [X0: $i] : divide(a4,divide(a4,X0)) = X0,
inference(demodulation,[status(thm)],[c_1106,c_999,c_1097]) ).
tcf(c_1109,plain,
divide(a4,iPr_def_20) = iPr_def_19,
inference(superposition,[status(thm)],[c_89,c_1107]) ).
tcf(c_1111,plain,
divide(a4,iPr_def_19) = iPr_def_20,
inference(superposition,[status(thm)],[c_1109,c_1107]) ).
tcf(c_1161,plain,
! [X0: $i] : divide(iPr_def_15,divide(iPr_def_15,X0)) = X0,
inference(demodulation,[status(thm)],[c_580,c_999,c_1097]) ).
tcf(c_1334,plain,
divide(a4,divide(b4,iPr_def_21)) = iPr_def_19,
inference(superposition,[status(thm)],[c_503,c_706]) ).
tcf(c_1346,plain,
divide(a4,iPr_def_22) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_1334,c_91]) ).
tcf(c_1409,plain,
divide(a4,iPr_def_19) = iPr_def_22,
inference(superposition,[status(thm)],[c_1346,c_1107]) ).
tcf(c_1410,plain,
iPr_def_20 = iPr_def_22,
inference(light_normalisation,[status(thm)],[c_1409,c_1111]) ).
tcf(c_1411,plain,
iPr_def_13 != iPr_def_16,
inference(backward_subsumption_resolution,[status(thm)],[c_516,c_1410]) ).
tcf(c_1502,plain,
divide(iPr_def_15,divide(iPr_def_11,iPr_def_16)) = iPr_def_10,
inference(superposition,[status(thm)],[c_80,c_787]) ).
tcf(c_1511,plain,
divide(iPr_def_11,iPr_def_16) = divide(iPr_def_15,iPr_def_10),
inference(superposition,[status(thm)],[c_1502,c_1161]) ).
tcf(c_1512,plain,
divide(iPr_def_11,iPr_def_16) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_1511,c_253]) ).
tcf(c_1576,plain,
! [X0: $i,X1: $i] : divide(X0,divide(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1009,c_999,c_1097]) ).
tcf(c_1652,plain,
divide(iPr_def_11,iPr_def_12) = iPr_def_16,
inference(superposition,[status(thm)],[c_1512,c_1576]) ).
tcf(c_1654,plain,
iPr_def_13 = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_1652,c_82]) ).
tcf(c_1655,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1654,c_1411]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP094-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 13:36:35 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 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...
% 2.03/1.29 % SZS status Started for theBenchmark.p
% 2.03/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.03/1.29
% 2.03/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.03/1.29
% 2.03/1.29 % ------ iProver source info
% 2.03/1.29
% 2.03/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.03/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.03/1.29 % git: non_committed_changes: false
% 2.03/1.29
% 2.03/1.29 % ------ Parsing...% successful
% 2.03/1.29
% 2.03/1.29
% 2.03/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.03/1.29
% 2.03/1.29 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.03/1.29
% 2.03/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.03/1.29
% 2.03/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.03/1.29 % ------ Proving...
% 2.03/1.29 % ------ Problem Properties
% 2.03/1.29
% 2.03/1.29 %
% 2.03/1.29 % clauses 16
% 2.03/1.29 % conjectures 0
% 2.03/1.29 % EPR 1
% 2.03/1.29 % Horn 16
% 2.03/1.29 % unary 15
% 2.03/1.29 % binary 0
% 2.03/1.29 % lits 18
% 2.03/1.29 % lits eq 18
% 2.03/1.29 % fd_pure 0
% 2.03/1.29 % fd_pseudo 0
% 2.03/1.29 % fd_cond 0
% 2.03/1.29 % fd_pseudo_cond 0
% 2.03/1.29 % AC symbols 0
% 2.03/1.29
% 2.03/1.29 % ------ Schedule dynamic 5 is on
% 2.03/1.29
% 2.03/1.29 % ------ no conjectures: strip conj schedule
% 2.03/1.29
% 2.03/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.03/1.29
% 2.03/1.29
% 2.03/1.29 % ------
% 2.03/1.29 % Current options:
% 2.03/1.29 % ------
% 2.03/1.29
% 2.03/1.29
% 2.03/1.29 %
% 2.03/1.29
% 2.03/1.29 % ------ Proving...
% 2.03/1.29 %
% 2.03/1.29
% 2.03/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.03/1.29
% 2.03/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.03/1.29
% 2.03/1.29
%------------------------------------------------------------------------------