%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP111-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 01:30:55 PM UTC 2026
% Result : Unsatisfiable 0.90s 1.65s
% Output : CNFRefutation 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 59 ( 49 unt; 0 def)
% Number of atoms : 83 ( 82 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 61 ( 37 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 12 ( 2 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 119 ( 0 sgn 119 !; 0 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(inverse(double_divide(inverse(double_divide(X0,inverse(X1))),X2)),double_divide(X0,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,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/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f4,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,[],[f3]) ).
fof(f5,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
| a2 != inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2)))))
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(definition_unfolding,[],[f4,f2,f2,f2,f2,f2,f2,f2,f2,f2,f2]) ).
tcf(c_52,negated_conjecture,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) )
| ( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) )
| ( inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 ) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(inverse(double_divide(X0,inverse(X1))),X2)),double_divide(X0,X2)) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(X0),double_divide(inverse(double_divide(X1,inverse(X0))),double_divide(X1,inverse(X2)))) = X2,
inference(superposition,[status(thm)],[c_53,c_53]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0,inverse(X1))),X2)),inverse(X3))),double_divide(X0,X2))),X1) = X3,
inference(superposition,[status(thm)],[c_53,c_53]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(inverse(double_divide(inverse(double_divide(inverse(X0),inverse(X1))),double_divide(inverse(double_divide(X2,inverse(X0))),double_divide(X2,inverse(X3))))),X3) = X1,
inference(superposition,[status(thm)],[c_114,c_53]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(X0),inverse(X1))),double_divide(inverse(double_divide(X2,inverse(X0))),double_divide(X2,inverse(X3))))),inverse(X4))),X3)),X1) = X4,
inference(superposition,[status(thm)],[c_114,c_115]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(inverse(double_divide(inverse(X0),double_divide(inverse(double_divide(inverse(double_divide(X1,inverse(inverse(X2)))),X3)),double_divide(X1,X3)))),X0) = X2,
inference(superposition,[status(thm)],[c_115,c_115]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i] : double_divide(inverse(double_divide(inverse(X0),inverse(X1))),X0) = X1,
inference(demodulation,[status(thm)],[c_145,c_53]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i] : double_divide(inverse(X0),double_divide(inverse(X1),X1)) = X0,
inference(superposition,[status(thm)],[c_181,c_53]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(X0),inverse(X1))),inverse(X2))),X0)),X1) = X2,
inference(superposition,[status(thm)],[c_181,c_53]) ).
tcf(c_257,plain,
! [X0: $i,X1: $i] : double_divide(inverse(double_divide(inverse(X0),X0)),inverse(X1)) = X1,
inference(superposition,[status(thm)],[c_187,c_181]) ).
tcf(c_283,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(inverse(X0),X1)),double_divide(inverse(double_divide(inverse(X2),X2)),X1)) = X0,
inference(superposition,[status(thm)],[c_257,c_53]) ).
tcf(c_287,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(X0),X0)),inverse(X1))),inverse(X2))),X2) = X1,
inference(superposition,[status(thm)],[c_257,c_53]) ).
tcf(c_295,plain,
! [X0: $i,X1: $i] : double_divide(inverse(double_divide(inverse(X0),inverse(X1))),X1) = X0,
inference(light_normalisation,[status(thm)],[c_287,c_257]) ).
tcf(c_578,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(X0),double_divide(inverse(double_divide(inverse(X1),X1)),X2)) = double_divide(inverse(X2),inverse(X0)),
inference(superposition,[status(thm)],[c_181,c_283]) ).
tcf(c_622,plain,
! [X0: $i,X1: $i] : double_divide(inverse(X0),inverse(double_divide(inverse(X1),X0))) = X1,
inference(demodulation,[status(thm)],[c_283,c_578]) ).
tcf(c_705,plain,
! [X0: $i,X1: $i] : double_divide(inverse(X0),double_divide(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_295,c_53]) ).
tcf(c_712,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(inverse(double_divide(X0,inverse(X1))),X2)),X1) = double_divide(X0,X2),
inference(superposition,[status(thm)],[c_295,c_115]) ).
tcf(c_723,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(X0,inverse(X1))),double_divide(X0,inverse(X2))) = double_divide(inverse(X1),X2),
inference(superposition,[status(thm)],[c_295,c_119]) ).
tcf(c_725,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[c_295,c_257]) ).
tcf(c_799,plain,
! [X0: $i,X1: $i] : double_divide(inverse(X0),double_divide(X1,inverse(X1))) = X0,
inference(superposition,[status(thm)],[c_725,c_187]) ).
tcf(c_805,plain,
! [X0: $i,X1: $i] : double_divide(inverse(double_divide(X0,inverse(X0))),inverse(X1)) = X1,
inference(superposition,[status(thm)],[c_725,c_257]) ).
tcf(c_807,plain,
! [X0: $i,X1: $i] : double_divide(inverse(double_divide(X0,inverse(X1))),inverse(X0)) = X1,
inference(superposition,[status(thm)],[c_725,c_181]) ).
tcf(c_880,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(superposition,[status(thm)],[c_725,c_705]) ).
tcf(c_887,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X1,inverse(X1))) = inverse(X0),
inference(superposition,[status(thm)],[c_725,c_799]) ).
tcf(c_978,plain,
! [X0: $i,X1: $i] : inverse(double_divide(inverse(X0),X1)) = double_divide(inverse(X1),X0),
inference(superposition,[status(thm)],[c_622,c_880]) ).
tcf(c_983,plain,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) )
| ( inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(inverse(a3),double_divide(c3,b3)) )
| ( inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 ) ),
inference(demodulation,[status(thm)],[c_52,c_978]) ).
tcf(c_1150,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(inverse(X0),double_divide(double_divide(X1,X0),inverse(X2))),X1) = X2,
inference(demodulation,[status(thm)],[c_189,c_725,c_978]) ).
tcf(c_1153,plain,
! [X0: $i,X1: $i] : double_divide(inverse(inverse(X0)),X1) = double_divide(X1,X0),
inference(superposition,[status(thm)],[c_887,c_1150]) ).
tcf(c_1175,plain,
! [X0: $i,X1: $i] : double_divide(X0,X1) = double_divide(X1,X0),
inference(light_normalisation,[status(thm)],[c_1153,c_725]) ).
tcf(c_1181,plain,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) )
| ( inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != double_divide(inverse(a3),double_divide(c3,b3)) )
| ( inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 ) ),
inference(demodulation,[status(thm)],[c_983,c_1175]) ).
tcf(c_1229,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,inverse(X0)),X1) = inverse(X1),
inference(superposition,[status(thm)],[c_1175,c_887]) ).
tcf(c_1307,plain,
( ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) )
| ( inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != double_divide(inverse(a3),double_divide(c3,b3)) )
| ( inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 ) ),
inference(ground_joinability,[status(thm)],[c_1181,c_1175]) ).
tcf(c_1308,plain,
( ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) )
| ( inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != double_divide(inverse(a3),double_divide(b3,c3)) )
| ( inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 ) ),
inference(demodulation,[status(thm)],[c_1307,c_1175]) ).
tcf(c_1333,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,inverse(X0))) = inverse(double_divide(X1,inverse(X1))),
inference(superposition,[status(thm)],[c_1229,c_887]) ).
tcf(c_1337,plain,
( ( inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != double_divide(inverse(a3),double_divide(b3,c3)) )
| ( inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1308,c_1333]) ).
tcf(c_1599,plain,
! [X0: $i,X1: $i] : double_divide(X0,inverse(double_divide(X1,inverse(X1)))) = inverse(X0),
inference(superposition,[status(thm)],[c_805,c_887]) ).
tcf(c_1601,plain,
( ( inverse(inverse(a2)) != a2 )
| ( inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != double_divide(inverse(a3),double_divide(b3,c3)) ) ),
inference(demodulation,[status(thm)],[c_1337,c_1599]) ).
tcf(c_1602,plain,
inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != double_divide(inverse(a3),double_divide(b3,c3)),
inference(ground_joinability,[status(thm)],[c_1601,c_725]) ).
tcf(c_1608,plain,
! [X0: $i,X1: $i] : double_divide(inverse(X0),inverse(double_divide(X0,inverse(X1)))) = X1,
inference(demodulation,[status(thm)],[c_807,c_1175]) ).
tcf(c_1619,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,inverse(X1))) = double_divide(inverse(X0),X1),
inference(superposition,[status(thm)],[c_1608,c_880]) ).
tcf(c_1622,plain,
double_divide(inverse(a3),double_divide(b3,c3)) != double_divide(inverse(c3),double_divide(a3,b3)),
inference(demodulation,[status(thm)],[c_1602,c_1619]) ).
tcf(c_1970,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(X0,double_divide(inverse(X1),X2))) = double_divide(inverse(X0),double_divide(inverse(X2),X1)),
inference(superposition,[status(thm)],[c_978,c_1619]) ).
tcf(c_1971,plain,
! [X0: $i,X1: $i] : double_divide(inverse(X0),inverse(X1)) = inverse(double_divide(X0,X1)),
inference(superposition,[status(thm)],[c_725,c_1619]) ).
tcf(c_1979,plain,
! [X0: $i,X1: $i] : inverse(double_divide(inverse(X0),X1)) = double_divide(X0,inverse(X1)),
inference(superposition,[status(thm)],[c_1619,c_725]) ).
tcf(c_2029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(inverse(double_divide(X0,X1))),double_divide(inverse(double_divide(X2,inverse(X0))),double_divide(X2,inverse(X3))))),inverse(X4))),X3)),X1) = X4,
inference(light_normalisation,[status(thm)],[c_136,c_1971]) ).
tcf(c_2030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(X0,inverse(double_divide(X1,double_divide(X2,double_divide(double_divide(inverse(X3),X1),double_divide(X3,X0)))))) = X2,
inference(demodulation,[status(thm)],[c_2029,c_725,c_723,c_1175,c_1970,c_1979]) ).
tcf(c_2037,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,inverse(double_divide(X1,double_divide(X2,X0)))) = double_divide(inverse(X2),X1),
inference(superposition,[status(thm)],[c_880,c_2030]) ).
tcf(c_2328,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(double_divide(inverse(X0),X1),X2)),X1) = double_divide(X0,X2),
inference(light_normalisation,[status(thm)],[c_712,c_1619]) ).
tcf(c_2329,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,inverse(double_divide(double_divide(inverse(X1),X0),X2))) = double_divide(X1,X2),
inference(demodulation,[status(thm)],[c_2328,c_1175]) ).
tcf(c_2352,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,inverse(double_divide(double_divide(X1,X0),X2))) = double_divide(inverse(X1),X2),
inference(superposition,[status(thm)],[c_725,c_2329]) ).
tcf(c_4810,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(X0),double_divide(X1,X2)) = double_divide(inverse(X1),double_divide(X0,X2)),
inference(superposition,[status(thm)],[c_2352,c_2037]) ).
tcf(c_4813,plain,
double_divide(inverse(a3),double_divide(b3,c3)) != double_divide(inverse(a3),double_divide(c3,b3)),
inference(demodulation,[status(thm)],[c_1622,c_4810]) ).
tcf(c_4814,plain,
$false,
inference(ground_joinability,[status(thm)],[c_4813,c_1175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP111-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n007.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 13:31:38 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 0.90/1.65 % SZS status Started for theBenchmark.p
% 0.90/1.65 % SZS status Unsatisfiable for theBenchmark.p
% 0.90/1.65
% 0.90/1.65 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.90/1.65
% 0.90/1.65 % ------ iProver source info
% 0.90/1.65
% 0.90/1.65 % git: date: 2026-07-19 20:42:38 +0200
% 0.90/1.65 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.90/1.65 % git: non_committed_changes: false
% 0.90/1.65
% 0.90/1.65 % ------ Parsing...% successful
% 0.90/1.65
% 0.90/1.65
% 0.90/1.65 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.90/1.65
% 0.90/1.65 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.90/1.65
% 0.90/1.65 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.90/1.65
% 0.90/1.65 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 0.90/1.65 % ------ Proving...
% 0.90/1.65 % ------ Problem Properties
% 0.90/1.65
% 0.90/1.65 %
% 0.90/1.65 % clauses 2
% 0.90/1.65 % conjectures 1
% 0.90/1.65 % EPR 0
% 0.90/1.65 % Horn 2
% 0.90/1.65 % unary 1
% 0.90/1.65 % binary 0
% 0.90/1.65 % lits 5
% 0.90/1.65 % lits eq 5
% 0.90/1.65 % fd_pure 0
% 0.90/1.65 % fd_pseudo 0
% 0.90/1.65 % fd_cond 0
% 0.90/1.65 % fd_pseudo_cond 0
% 0.90/1.65 % AC symbols 0
% 0.90/1.65
% 0.90/1.65 % ------ Schedule dynamic 5 is on
% 0.90/1.65
% 0.90/1.65 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.90/1.65
% 0.90/1.65
% 0.90/1.65 % ------
% 0.90/1.65 % Current options:
% 0.90/1.65 % ------
% 0.90/1.65
% 0.90/1.65
% 0.90/1.65 %
% 0.90/1.65
% 0.90/1.65 % ------ Proving...
% 0.90/1.65 %
% 0.90/1.65
% 0.90/1.65 % SZS status Unsatisfiable for theBenchmark.p
% 0.90/1.65
% 0.90/1.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.90/1.65
% 0.90/1.65
%------------------------------------------------------------------------------