%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP768-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n019.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 01:35:22 PM UTC 2026
% Result : Unsatisfiable 3.03s 1.65s
% Output : CNFRefutation 3.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 22
% Syntax : Number of formulae : 82 ( 82 unt; 10 def)
% Number of atoms : 207 ( 81 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 12 ( 10 usr; 11 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 75 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : product(X0,difference(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
fof(f4,axiom,
! [X0,X1] : difference(X0,product(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
fof(f5,axiom,
! [X0,X1] : quotient(product(X0,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
fof(f6,axiom,
! [X0,X1] : product(quotient(X0,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
fof(f7,axiom,
! [X2,X0,X1] : difference(X0,product(product(X0,X1),X2)) = quotient(product(X1,product(X2,X0)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
fof(f9,axiom,
! [X0] : i(X0) = difference(X0,one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
fof(f10,axiom,
! [X0] : j(X0) = quotient(one,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
fof(f11,axiom,
! [X0] : product(i(X0),X0) = product(X0,j(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
fof(f12,axiom,
! [X0] : eta(X0) = product(i(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
fof(f13,plain,
! [X0] : product(i(X0),X0) = eta(X0),
inference(reorient_equations,[],[f12]) ).
fof(f17,axiom,
! [X2,X0,X1] : product(eta(X0),product(X1,X2)) = product(product(eta(X0),X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos16) ).
fof(f20,axiom,
! [X0,X1] : t(X0,X1) = quotient(product(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos19) ).
fof(f21,negated_conjecture,
t(eta(x0),product(x1,x2)) != product(t(eta(x0),x1),t(eta(x0),x2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f22,plain,
! [X0] : eta(X0) = product(difference(X0,one),X0),
inference(definition_unfolding,[],[f13,f9]) ).
fof(f23,plain,
! [X0] : product(difference(X0,one),X0) = product(X0,quotient(one,X0)),
inference(definition_unfolding,[],[f11,f9,f10]) ).
fof(f27,plain,
! [X2,X0,X1] : product(product(difference(X0,one),X0),product(X1,X2)) = product(product(product(difference(X0,one),X0),X1),X2),
inference(definition_unfolding,[],[f17,f22,f22]) ).
fof(f30,plain,
quotient(product(product(difference(x0,one),x0),product(x1,x2)),product(difference(x0,one),x0)) != product(quotient(product(product(difference(x0,one),x0),x1),product(difference(x0,one),x0)),quotient(product(product(difference(x0,one),x0),x2),product(difference(x0,one),x0))),
inference(definition_unfolding,[],[f21,f20,f22,f20,f22,f20,f22]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] : product(X0,difference(X0,X1)) = X1,
inference(cnf_transformation,[],[f3]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] : difference(X0,product(X0,X1)) = X1,
inference(cnf_transformation,[],[f4]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] : quotient(product(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f5]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] : product(quotient(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f6]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,product(product(X0,X1),X2)) = quotient(product(X1,product(X2,X0)),X0),
inference(cnf_transformation,[],[f7]) ).
tcf(c_77,plain,
! [X0: $i] : product(difference(X0,one),X0) = product(X0,quotient(one,X0)),
inference(cnf_transformation,[],[f23]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] : product(product(product(difference(X0,one),X0),X1),X2) = product(product(difference(X0,one),X0),product(X1,X2)),
inference(cnf_transformation,[],[f27]) ).
tcf(c_84,negated_conjecture,
product(quotient(product(product(difference(x0,one),x0),x1),product(difference(x0,one),x0)),quotient(product(product(difference(x0,one),x0),x2),product(difference(x0,one),x0))) != quotient(product(product(difference(x0,one),x0),product(x1,x2)),product(difference(x0,one),x0)),
inference(cnf_transformation,[],[f30]) ).
tcf(c_136,definition,
iPr_def_10 = difference(x0,one),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_137,definition,
iPr_def_11 = product(iPr_def_10,x0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_138,definition,
iPr_def_12 = product(iPr_def_11,x1),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_139,definition,
iPr_def_13 = quotient(iPr_def_12,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_140,definition,
iPr_def_14 = product(iPr_def_11,x2),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_141,definition,
iPr_def_15 = quotient(iPr_def_14,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_142,definition,
iPr_def_16 = product(iPr_def_13,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_143,definition,
iPr_def_17 = product(x1,x2),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_144,definition,
iPr_def_18 = product(iPr_def_11,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_145,definition,
iPr_def_19 = quotient(iPr_def_18,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_146,negated_conjecture,
iPr_def_16 != iPr_def_19,
inference(demodulation,[status(thm)],[c_84,c_143,c_144,c_145,c_140,c_141,c_136,c_137,c_138,c_139,c_142]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i,X2: $i] : product(product(product(difference(X0,one),X0),X1),X2) = product(product(difference(X0,one),X0),product(X1,X2)),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_153,plain,
! [X0: $i] : product(difference(X0,one),X0) = product(X0,quotient(one,X0)),
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,product(product(X0,X1),X2)) = quotient(product(X1,product(X2,X0)),X0),
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] : product(quotient(X0,X1),X1) = X0,
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i] : quotient(product(X0,X1),X1) = X0,
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i] : difference(X0,product(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i] : product(X0,difference(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_253,plain,
! [X0: $i,X1: $i,X2: $i] : product(product(product(X0,quotient(one,X0)),X1),X2) = product(product(X0,quotient(one,X0)),product(X1,X2)),
inference(demodulation,[status(thm)],[c_149,c_153]) ).
tcf(c_265,plain,
product(iPr_def_13,iPr_def_11) = iPr_def_12,
inference(superposition,[status(thm)],[c_139,c_156]) ).
tcf(c_266,plain,
product(iPr_def_15,iPr_def_11) = iPr_def_14,
inference(superposition,[status(thm)],[c_141,c_156]) ).
tcf(c_267,plain,
product(iPr_def_19,iPr_def_11) = iPr_def_18,
inference(superposition,[status(thm)],[c_145,c_156]) ).
tcf(c_279,plain,
! [X0: $i,X1: $i] : difference(quotient(X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_156,c_158]) ).
tcf(c_280,plain,
difference(x1,iPr_def_17) = x2,
inference(superposition,[status(thm)],[c_143,c_158]) ).
tcf(c_282,plain,
difference(iPr_def_11,iPr_def_12) = x1,
inference(superposition,[status(thm)],[c_138,c_158]) ).
tcf(c_284,plain,
difference(iPr_def_13,iPr_def_16) = iPr_def_15,
inference(superposition,[status(thm)],[c_142,c_158]) ).
tcf(c_285,plain,
difference(iPr_def_11,iPr_def_18) = iPr_def_17,
inference(superposition,[status(thm)],[c_144,c_158]) ).
tcf(c_289,plain,
! [X0: $i,X1: $i] : quotient(X0,difference(X1,X0)) = X1,
inference(superposition,[status(thm)],[c_159,c_157]) ).
tcf(c_291,plain,
product(x0,quotient(one,x0)) = product(iPr_def_10,x0),
inference(superposition,[status(thm)],[c_136,c_153]) ).
tcf(c_310,plain,
! [X0: $i] : difference(x2,product(product(x2,X0),iPr_def_11)) = quotient(product(X0,iPr_def_14),x2),
inference(superposition,[status(thm)],[c_140,c_155]) ).
tcf(c_557,plain,
product(x0,quotient(one,x0)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_291,c_137]) ).
tcf(c_714,plain,
! [X0: $i] : difference(iPr_def_11,product(product(iPr_def_11,X0),iPr_def_13)) = quotient(product(X0,iPr_def_12),iPr_def_11),
inference(superposition,[status(thm)],[c_265,c_155]) ).
tcf(c_872,plain,
! [X0: $i] : difference(iPr_def_11,product(product(iPr_def_11,X0),iPr_def_15)) = quotient(product(X0,iPr_def_14),iPr_def_11),
inference(superposition,[status(thm)],[c_266,c_155]) ).
tcf(c_876,plain,
quotient(iPr_def_18,iPr_def_11) = iPr_def_19,
inference(superposition,[status(thm)],[c_267,c_157]) ).
tcf(c_906,plain,
product(x1,x2) = iPr_def_17,
inference(superposition,[status(thm)],[c_280,c_159]) ).
tcf(c_908,plain,
product(iPr_def_11,x1) = iPr_def_12,
inference(superposition,[status(thm)],[c_282,c_159]) ).
tcf(c_910,plain,
product(iPr_def_13,iPr_def_15) = iPr_def_16,
inference(superposition,[status(thm)],[c_284,c_159]) ).
tcf(c_911,plain,
product(iPr_def_11,iPr_def_17) = iPr_def_18,
inference(superposition,[status(thm)],[c_285,c_159]) ).
tcf(c_960,plain,
! [X0: $i,X1: $i] : product(product(iPr_def_11,X0),X1) = product(iPr_def_11,product(X0,X1)),
inference(superposition,[status(thm)],[c_557,c_253]) ).
tcf(c_1180,plain,
! [X0: $i] : difference(iPr_def_11,product(iPr_def_11,product(X0,iPr_def_15))) = quotient(product(X0,iPr_def_14),iPr_def_11),
inference(demodulation,[status(thm)],[c_872,c_960]) ).
tcf(c_1181,plain,
! [X0: $i] : quotient(product(X0,iPr_def_14),iPr_def_11) = product(X0,iPr_def_15),
inference(demodulation,[status(thm)],[c_1180,c_158]) ).
tcf(c_1182,plain,
! [X0: $i] : difference(iPr_def_11,product(iPr_def_11,product(X0,iPr_def_13))) = quotient(product(X0,iPr_def_12),iPr_def_11),
inference(demodulation,[status(thm)],[c_714,c_960]) ).
tcf(c_1183,plain,
! [X0: $i] : quotient(product(X0,iPr_def_12),iPr_def_11) = product(X0,iPr_def_13),
inference(demodulation,[status(thm)],[c_1182,c_158]) ).
tcf(c_1816,plain,
! [X0: $i] : difference(product(X0,iPr_def_15),product(X0,iPr_def_14)) = iPr_def_11,
inference(superposition,[status(thm)],[c_1181,c_279]) ).
tcf(c_1825,plain,
! [X0: $i] : product(product(X0,iPr_def_13),iPr_def_11) = product(X0,iPr_def_12),
inference(superposition,[status(thm)],[c_1183,c_156]) ).
tcf(c_1834,plain,
! [X0: $i] : product(iPr_def_11,product(x1,X0)) = product(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_908,c_960]) ).
tcf(c_2202,plain,
difference(x2,product(x2,iPr_def_12)) = quotient(product(iPr_def_13,iPr_def_14),x2),
inference(superposition,[status(thm)],[c_1825,c_310]) ).
tcf(c_2239,plain,
difference(iPr_def_16,product(iPr_def_13,iPr_def_14)) = iPr_def_11,
inference(superposition,[status(thm)],[c_910,c_1816]) ).
tcf(c_2273,plain,
product(iPr_def_11,iPr_def_17) = product(iPr_def_12,x2),
inference(superposition,[status(thm)],[c_906,c_1834]) ).
tcf(c_2320,plain,
product(iPr_def_12,x2) = iPr_def_18,
inference(demodulation,[status(thm)],[c_2273,c_911]) ).
tcf(c_2325,plain,
quotient(product(iPr_def_13,iPr_def_14),x2) = iPr_def_12,
inference(demodulation,[status(thm)],[c_2202,c_158]) ).
tcf(c_2842,plain,
quotient(product(iPr_def_13,iPr_def_14),iPr_def_11) = iPr_def_16,
inference(superposition,[status(thm)],[c_2239,c_289]) ).
tcf(c_2970,plain,
product(iPr_def_12,x2) = product(iPr_def_13,iPr_def_14),
inference(superposition,[status(thm)],[c_2325,c_156]) ).
tcf(c_3014,plain,
product(iPr_def_13,iPr_def_14) = iPr_def_18,
inference(demodulation,[status(thm)],[c_2970,c_2320]) ).
tcf(c_3015,plain,
quotient(iPr_def_18,iPr_def_11) = iPr_def_16,
inference(demodulation,[status(thm)],[c_2842,c_3014]) ).
tcf(c_3016,plain,
iPr_def_16 = iPr_def_19,
inference(demodulation,[status(thm)],[c_3015,c_876]) ).
tcf(c_3017,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3016,c_146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP768-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 16:00:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running UEQ theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.03/1.65 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 3.03/1.65 % SZS status Started for theBenchmark.p
% 3.03/1.65 % SZS status Unsatisfiable for theBenchmark.p
% 3.03/1.65
% 3.03/1.65 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.03/1.65
% 3.03/1.65 % ------ iProver source info
% 3.03/1.65
% 3.03/1.65 % git: date: 2026-07-19 20:42:38 +0200
% 3.03/1.65 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.03/1.65 % git: non_committed_changes: false
% 3.03/1.65
% 3.03/1.65 % ------ Parsing...% successful
% 3.03/1.65
% 3.03/1.65
% 3.03/1.65 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.03/1.65
% 3.03/1.65 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.03/1.65
% 3.03/1.65 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.03/1.65
% 3.03/1.65 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.03/1.65 % ------ Proving...
% 3.03/1.65 % ------ Problem Properties
% 3.03/1.65
% 3.03/1.65 %
% 3.03/1.65 % clauses 26
% 3.03/1.65 % conjectures 1
% 3.03/1.65 % EPR 1
% 3.03/1.65 % Horn 26
% 3.03/1.65 % unary 26
% 3.03/1.65 % binary 0
% 3.03/1.65 % lits 26
% 3.03/1.65 % lits eq 26
% 3.03/1.65 % fd_pure 0
% 3.03/1.65 % fd_pseudo 0
% 3.03/1.65 % fd_cond 0
% 3.03/1.65 % fd_pseudo_cond 0
% 3.03/1.65 % AC symbols 0
% 3.03/1.65
% 3.03/1.65 % ------ Input Options Time Limit: Unbounded
% 3.03/1.65
% 3.03/1.65
% 3.03/1.65 % ------
% 3.03/1.65 % Current options:
% 3.03/1.65 % ------
% 3.03/1.65
% 3.03/1.65
% 3.03/1.65 %
% 3.03/1.65
% 3.03/1.65 % ------ Proving...
% 3.03/1.65 %
% 3.03/1.65
% 3.03/1.65 % SZS status Unsatisfiable for theBenchmark.p
% 3.03/1.65
% 3.03/1.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.03/1.65
% 3.03/1.65
%------------------------------------------------------------------------------