%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP430-1 : TPTP v9.3.1. Released v2.6.0.
% 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 01:34:04 PM UTC 2026
% Result : Unsatisfiable 7.54s 2.06s
% Output : CNFRefutation 7.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 2
% Syntax : Number of formulae : 52 ( 52 unt; 0 def)
% Number of atoms : 52 ( 51 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 157 ( 0 sgn 157 !; 0 ?; 153 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] : multiply(X0,inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))),X0)))) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))),X0)))) = X3,
inference(cnf_transformation,[],[f1]) ).
tcf(c_52,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(cnf_transformation,[],[f2]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : multiply(X0,inverse(multiply(inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))),X4))),multiply(multiply(multiply(X5,inverse(X5)),inverse(X3)),X0)))) = X4,
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(X0,inverse(multiply(multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X3))),multiply(X4,inverse(X4))),multiply(X2,X0)))) = X3,
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : multiply(inverse(multiply(X0,multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X0))),multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,X5)))))),inverse(multiply(X5,X2))) = X4,
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : multiply(X0,inverse(multiply(inverse(multiply(multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X3))),multiply(X4,inverse(X4))),multiply(X2,X5))),multiply(multiply(multiply(X6,inverse(X6)),inverse(X3)),X0)))) = X5,
inference(superposition,[status(thm)],[c_95,c_51]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : multiply(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,X2))),multiply(X3,inverse(X3))) = multiply(X4,inverse(multiply(multiply(X1,multiply(X5,inverse(X5))),multiply(X2,X4)))),
inference(superposition,[status(thm)],[c_95,c_51]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,multiply(X2,inverse(multiply(multiply(X3,multiply(X4,inverse(X4))),multiply(X1,X2))))))) = X3,
inference(superposition,[status(thm)],[c_107,c_51]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(X0,inverse(multiply(multiply(X1,inverse(multiply(multiply(X2,multiply(X3,inverse(X3))),multiply(X4,X1)))),multiply(X2,X0)))) = X4,
inference(superposition,[status(thm)],[c_107,c_95]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,multiply(X2,multiply(X3,inverse(X3)))))) = multiply(X4,inverse(multiply(X1,multiply(X2,X4)))),
inference(superposition,[status(thm)],[c_51,c_148]) ).
tcf(c_287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,X2))) = multiply(multiply(X3,inverse(X3)),inverse(multiply(X1,X2))),
inference(superposition,[status(thm)],[c_95,c_143]) ).
tcf(c_383,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,inverse(X0)),inverse(X1)) = multiply(multiply(X2,inverse(X2)),inverse(X1)),
inference(superposition,[status(thm)],[c_143,c_287]) ).
tcf(c_509,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(X0),inverse(multiply(inverse(X1),multiply(multiply(X2,inverse(X2)),inverse(X0))))) = X1,
inference(superposition,[status(thm)],[c_383,c_51]) ).
tcf(c_872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,inverse(multiply(X1,multiply(X2,X0)))) = multiply(X3,inverse(multiply(X1,multiply(X2,X3)))),
inference(superposition,[status(thm)],[c_202,c_202]) ).
tcf(c_1098,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(multiply(inverse(X1),multiply(multiply(X2,inverse(X2)),X0)))) = X1,
inference(superposition,[status(thm)],[c_872,c_509]) ).
tcf(c_1210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,inverse(multiply(multiply(multiply(X1,inverse(X1)),multiply(X2,inverse(X2))),multiply(X3,X0)))) = inverse(X3),
inference(superposition,[status(thm)],[c_1098,c_51]) ).
tcf(c_1291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,multiply(multiply(X2,inverse(X2)),multiply(X3,inverse(X3))))))) = X1,
inference(superposition,[status(thm)],[c_1210,c_51]) ).
tcf(c_1307,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,inverse(X1)))) = multiply(X2,inverse(X2)),
inference(superposition,[status(thm)],[c_1210,c_143]) ).
tcf(c_1488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(multiply(X2,inverse(X2)),X0))),X3)) = X3,
inference(superposition,[status(thm)],[c_93,c_1098]) ).
tcf(c_1761,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(superposition,[status(thm)],[c_1307,c_1307]) ).
tcf(c_1968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(X0),inverse(multiply(X1,multiply(X2,inverse(X2))))) = multiply(X3,inverse(multiply(X1,multiply(X0,X3)))),
inference(superposition,[status(thm)],[c_1761,c_872]) ).
tcf(c_2081,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(X0))),multiply(multiply(X1,inverse(X1)),X2)) = X2,
inference(superposition,[status(thm)],[c_1307,c_1488]) ).
tcf(c_4927,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(X0,inverse(multiply(X1,multiply(multiply(X2,inverse(X2)),X0))))) = X1,
inference(superposition,[status(thm)],[c_872,c_1291]) ).
tcf(c_4929,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,inverse(X0)),multiply(X1,inverse(X1))) = inverse(inverse(multiply(X2,inverse(X2)))),
inference(superposition,[status(thm)],[c_1210,c_1291]) ).
tcf(c_7138,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(X0),inverse(inverse(multiply(X1,inverse(X1)))))),inverse(multiply(inverse(X2),X0))) = X2,
inference(superposition,[status(thm)],[c_4929,c_96]) ).
tcf(c_7157,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(multiply(inverse(inverse(multiply(X1,inverse(X1)))),multiply(X2,X0)))) = inverse(X2),
inference(superposition,[status(thm)],[c_4929,c_1210]) ).
tcf(c_7165,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,inverse(X0)),inverse(multiply(inverse(X1),inverse(inverse(multiply(X2,inverse(X2))))))) = X1,
inference(superposition,[status(thm)],[c_4929,c_1098]) ).
tcf(c_8052,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(X0),inverse(multiply(inverse(inverse(multiply(X1,inverse(X1)))),multiply(X2,inverse(X2))))) = inverse(X0),
inference(superposition,[status(thm)],[c_7157,c_1968]) ).
tcf(c_10202,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(multiply(inverse(inverse(multiply(X1,inverse(X1)))),multiply(X2,inverse(X2))))) = X0,
inference(superposition,[status(thm)],[c_4927,c_8052]) ).
tcf(c_10463,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(inverse(multiply(X0,inverse(X0)))),multiply(X1,inverse(X1))) = multiply(X2,inverse(X2)),
inference(superposition,[status(thm)],[c_10202,c_1761]) ).
tcf(c_10927,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(X1,inverse(X1)))) = X0,
inference(superposition,[status(thm)],[c_10463,c_10202]) ).
tcf(c_11327,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(inverse(inverse(X0))),inverse(inverse(multiply(X1,inverse(X1)))))) = X0,
inference(superposition,[status(thm)],[c_10927,c_7138]) ).
tcf(c_12733,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,inverse(X0)),X1) = inverse(inverse(X1)),
inference(superposition,[status(thm)],[c_11327,c_7165]) ).
tcf(c_12735,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(inverse(X1),inverse(inverse(X0))))) = X1,
inference(superposition,[status(thm)],[c_11327,c_7138]) ).
tcf(c_12747,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,inverse(X0))),inverse(inverse(X1))) = X1,
inference(demodulation,[status(thm)],[c_2081,c_12733]) ).
tcf(c_13210,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(inverse(multiply(X0,inverse(X0))))),X1) = inverse(inverse(X1)),
inference(superposition,[status(thm)],[c_12733,c_12733]) ).
tcf(c_13221,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(inverse(inverse(inverse(multiply(X1,inverse(X1))))))) = X0,
inference(superposition,[status(thm)],[c_12733,c_10927]) ).
tcf(c_13770,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(multiply(X0,inverse(X0)))),inverse(inverse(X1))) = X1,
inference(superposition,[status(thm)],[c_13221,c_12735]) ).
tcf(c_14030,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,inverse(X0))),X1) = inverse(inverse(X1)),
inference(superposition,[status(thm)],[c_13770,c_12733]) ).
tcf(c_14070,plain,
! [X0: $i] : inverse(inverse(inverse(inverse(X0)))) = X0,
inference(demodulation,[status(thm)],[c_12747,c_14030]) ).
tcf(c_14072,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(X1))) = X0,
inference(demodulation,[status(thm)],[c_13221,c_14070]) ).
tcf(c_14074,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(multiply(X1,multiply(X2,X0)))) = multiply(inverse(X2),inverse(X1)),
inference(demodulation,[status(thm)],[c_1968,c_14072]) ).
tcf(c_14197,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(inverse(inverse(X1))),X1)) = X0,
inference(superposition,[status(thm)],[c_14070,c_14072]) ).
tcf(c_15655,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(inverse(multiply(inverse(inverse(inverse(multiply(X1,X0)))),multiply(X1,X2))))) = X2,
inference(demodulation,[status(thm)],[c_106,c_12733,c_14070,c_14072,c_14074]) ).
tcf(c_16590,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),inverse(inverse(inverse(inverse(multiply(X0,X1)))))) = X1,
inference(superposition,[status(thm)],[c_13210,c_15655]) ).
tcf(c_16625,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_16590,c_14070]) ).
tcf(c_16670,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_16625,c_16625]) ).
tcf(c_16689,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X1),X1)) = X0,
inference(demodulation,[status(thm)],[c_14197,c_16670]) ).
tcf(c_16782,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[c_16689,c_16625]) ).
tcf(c_16786,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_52,c_16782]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP430-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n005.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 14:43:49 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running UEQ theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 7.54/2.06 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 7.54/2.06 % SZS status Started for theBenchmark.p
% 7.54/2.06 % SZS status Unsatisfiable for theBenchmark.p
% 7.54/2.06
% 7.54/2.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.54/2.06
% 7.54/2.06 % ------ iProver source info
% 7.54/2.06
% 7.54/2.06 % git: date: 2026-07-19 20:42:38 +0200
% 7.54/2.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.54/2.06 % git: non_committed_changes: false
% 7.54/2.06
% 7.54/2.06 % ------ Parsing...% successful
% 7.54/2.06
% 7.54/2.06
% 7.54/2.06 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.54/2.06
% 7.54/2.06 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 7.54/2.06
% 7.54/2.06 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.54/2.06
% 7.54/2.06 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 7.54/2.06 % ------ Proving...
% 7.54/2.06 % ------ Problem Properties
% 7.54/2.06
% 7.54/2.06 %
% 7.54/2.06 % clauses 2
% 7.54/2.06 % conjectures 1
% 7.54/2.06 % EPR 0
% 7.54/2.06 % Horn 2
% 7.54/2.06 % unary 2
% 7.54/2.06 % binary 0
% 7.54/2.06 % lits 2
% 7.54/2.06 % lits eq 2
% 7.54/2.06 % fd_pure 0
% 7.54/2.06 % fd_pseudo 0
% 7.54/2.06 % fd_cond 0
% 7.54/2.06 % fd_pseudo_cond 0
% 7.54/2.06 % AC symbols 0
% 7.54/2.06
% 7.54/2.06 % ------ Input Options Time Limit: Unbounded
% 7.54/2.06
% 7.54/2.06
% 7.54/2.06 % ------
% 7.54/2.06 % Current options:
% 7.54/2.06 % ------
% 7.54/2.06
% 7.54/2.06
% 7.54/2.06 %
% 7.54/2.06
% 7.54/2.06 % ------ Proving...
% 7.54/2.06 %
% 7.54/2.06
% 7.54/2.06 % SZS status Unsatisfiable for theBenchmark.p
% 7.54/2.06
% 7.54/2.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.54/2.06
% 7.54/2.06
%------------------------------------------------------------------------------