%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n015.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 02:38:08 PM UTC 2026
% Result : Unsatisfiable 3.76s 1.20s
% Output : CNFRefutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 69 ( 57 unt; 0 def)
% Number of atoms : 221 ( 62 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 76 ( 40 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 118 ( 0 sgn 118 !; 0 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
fof(f2,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).
fof(f9,axiom,
! [X2,X0,X1] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity2) ).
fof(f15,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity4) ).
fof(f18,axiom,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
fof(f19,axiom,
product(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_inverse_times_b_inverse) ).
fof(f20,negated_conjecture,
c != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
tcf(c_69,plain,
! [X0: $i] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_70,plain,
! [X0: $i] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_74,plain,
! [X0: $i] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[],[f6]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X2,X5,X4)
| ~ sum(X1,X5,X3)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_86,plain,
product(a,b,c),
inference(cnf_transformation,[],[f18]) ).
tcf(c_87,plain,
product(additive_inverse(a),additive_inverse(b),d),
inference(cnf_transformation,[],[f19]) ).
tcf(c_88,negated_conjecture,
c != d,
inference(cnf_transformation,[],[f20]) ).
tcf(c_96,plain,
multiply(a,b) = c,
inference(well_definedness,[status(thm)],[c_86]) ).
tcf(c_97,plain,
multiply(additive_inverse(a),additive_inverse(b)) = d,
inference(well_definedness,[status(thm)],[c_87]) ).
tcf(c_98,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_69]) ).
tcf(c_99,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(well_definedness,[status(thm)],[c_70]) ).
tcf(c_103,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(well_definedness,[status(thm)],[c_74]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( add(X2,X5) = X4 )
| ( add(X1,X5) != X3 )
| ( add(X0,X3) != X4 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_76]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( add(X1,X0) = X2 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_77]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X0,X5) = X6 )
| ( add(X2,X4) != X6 )
| ( add(X1,X3) != X5 )
| ( multiply(X0,X3) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_81]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X5,X1) = X6 )
| ( add(X2,X4) != X6 )
| ( add(X0,X3) != X5 )
| ( multiply(X3,X1) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_83]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(unflattening,[status(thm)],[c_108]) ).
tcf(c_245,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_106]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(unflattening,[status(thm)],[c_120]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_116]) ).
tcf(c_287,negated_conjecture,
c != d,
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_341,plain,
! [X0: $i,X1: $i,X2: $i] : add(X0,add(X1,X2)) = add(X1,add(X0,X2)),
inference(superposition,[status(thm)],[c_245,c_239]) ).
tcf(c_359,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = add(additive_identity,X1),
inference(superposition,[status(thm)],[c_103,c_245]) ).
tcf(c_361,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(add(X0,X1)))) = additive_identity,
inference(superposition,[status(thm)],[c_245,c_103]) ).
tcf(c_363,plain,
! [X0: $i,X1: $i] : add(multiply(additive_identity,X0),multiply(X1,X0)) = multiply(X1,X0),
inference(superposition,[status(thm)],[c_98,c_247]) ).
tcf(c_365,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(additive_inverse(X0),X1)) = multiply(additive_identity,X1),
inference(superposition,[status(thm)],[c_103,c_247]) ).
tcf(c_372,plain,
! [X0: $i,X1: $i] : add(multiply(X0,additive_identity),multiply(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_98,c_249]) ).
tcf(c_374,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(X0,additive_inverse(X1))) = multiply(X0,additive_identity),
inference(superposition,[status(thm)],[c_103,c_249]) ).
tcf(c_389,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_359,c_98]) ).
tcf(c_394,plain,
! [X0: $i] : additive_inverse(additive_inverse(X0)) = add(X0,additive_identity),
inference(superposition,[status(thm)],[c_103,c_389]) ).
tcf(c_395,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(superposition,[status(thm)],[c_239,c_389]) ).
tcf(c_406,plain,
! [X0: $i] : additive_inverse(additive_inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_394,c_99]) ).
tcf(c_458,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(additive_inverse(X1),X0))) = add(X1,additive_identity),
inference(superposition,[status(thm)],[c_361,c_389]) ).
tcf(c_520,plain,
add(multiply(additive_identity,b),c) = c,
inference(superposition,[status(thm)],[c_96,c_363]) ).
tcf(c_535,plain,
add(c,multiply(additive_identity,b)) = c,
inference(theory_normalisation,[status(thm)],[c_520,c_245,c_239]) ).
tcf(c_581,plain,
add(multiply(additive_inverse(a),additive_identity),d) = d,
inference(superposition,[status(thm)],[c_97,c_372]) ).
tcf(c_596,plain,
add(d,multiply(additive_inverse(a),additive_identity)) = d,
inference(theory_normalisation,[status(thm)],[c_581,c_245,c_239]) ).
tcf(c_639,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(additive_inverse(X1),X0))) = X1,
inference(demodulation,[status(thm)],[c_458,c_99]) ).
tcf(c_653,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(X1,X0))) = additive_inverse(X1),
inference(superposition,[status(thm)],[c_406,c_639]) ).
tcf(c_730,plain,
add(multiply(additive_identity,b),additive_inverse(c)) = additive_inverse(c),
inference(superposition,[status(thm)],[c_535,c_653]) ).
tcf(c_733,plain,
add(multiply(additive_inverse(a),additive_identity),additive_inverse(d)) = additive_inverse(d),
inference(superposition,[status(thm)],[c_596,c_653]) ).
tcf(c_818,plain,
add(c,additive_inverse(c)) = multiply(additive_identity,b),
inference(superposition,[status(thm)],[c_730,c_395]) ).
tcf(c_931,plain,
multiply(additive_identity,b) = additive_identity,
inference(demodulation,[status(thm)],[c_818,c_103]) ).
tcf(c_1058,plain,
multiply(additive_inverse(a),additive_identity) = add(d,additive_inverse(d)),
inference(superposition,[status(thm)],[c_733,c_395]) ).
tcf(c_1063,plain,
multiply(additive_inverse(a),additive_identity) = additive_identity,
inference(demodulation,[status(thm)],[c_1058,c_103]) ).
tcf(c_1149,plain,
add(c,multiply(additive_inverse(a),b)) = multiply(additive_identity,b),
inference(superposition,[status(thm)],[c_96,c_365]) ).
tcf(c_1185,plain,
add(c,multiply(additive_inverse(a),b)) = additive_identity,
inference(light_normalisation,[status(thm)],[c_1149,c_931]) ).
tcf(c_1227,plain,
add(multiply(additive_inverse(a),b),d) = multiply(additive_inverse(a),additive_identity),
inference(superposition,[status(thm)],[c_97,c_374]) ).
tcf(c_1248,plain,
add(d,multiply(additive_inverse(a),b)) = multiply(additive_inverse(a),additive_identity),
inference(theory_normalisation,[status(thm)],[c_1227,c_245,c_239]) ).
tcf(c_1249,plain,
add(d,multiply(additive_inverse(a),b)) = additive_identity,
inference(light_normalisation,[status(thm)],[c_1248,c_1063]) ).
tcf(c_1269,plain,
! [X0: $i] : add(c,add(X0,multiply(additive_inverse(a),b))) = add(X0,additive_identity),
inference(superposition,[status(thm)],[c_1185,c_341]) ).
tcf(c_1271,plain,
! [X0: $i] : add(c,add(X0,multiply(additive_inverse(a),b))) = X0,
inference(light_normalisation,[status(thm)],[c_1269,c_99]) ).
tcf(c_1368,plain,
add(c,additive_identity) = d,
inference(superposition,[status(thm)],[c_1249,c_1271]) ).
tcf(c_1378,plain,
add(additive_identity,c) = d,
inference(theory_normalisation,[status(thm)],[c_1368,c_245,c_239]) ).
tcf(c_1389,plain,
add(additive_identity,c) != c,
inference(demodulation,[status(thm)],[c_287,c_1378]) ).
tcf(c_1390,plain,
$false,
inference(ground_joinability,[status(thm)],[c_1389,c_98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n015.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 : Thu Sep 24 07:44:10 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 first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 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...
% 3.76/1.20 % SZS status Started for theBenchmark.p
% 3.76/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 3.76/1.20
% 3.76/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.76/1.20
% 3.76/1.20 % ------ iProver source info
% 3.76/1.20
% 3.76/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 3.76/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.76/1.20 % git: non_committed_changes: false
% 3.76/1.20
% 3.76/1.20 % ------ Parsing...% successful
% 3.76/1.20
% 3.76/1.20
% 3.76/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.76/1.20
% 3.76/1.20 % ------ Preprocessing... sup_sim: 15 sf_s rm: 0 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.76/1.20
% 3.76/1.20 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.76/1.20 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.76/1.20
% 3.76/1.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.76/1.20 % ------ Proving...
% 3.76/1.20 % ------ Problem Properties
% 3.76/1.20
% 3.76/1.20 %
% 3.76/1.20 % clauses 11
% 3.76/1.20 % conjectures 1
% 3.76/1.20 % EPR 1
% 3.76/1.20 % Horn 11
% 3.76/1.20 % unary 11
% 3.76/1.20 % binary 0
% 3.76/1.20 % lits 11
% 3.76/1.20 % lits eq 11
% 3.76/1.20 % fd_pure 0
% 3.76/1.20 % fd_pseudo 0
% 3.76/1.20 % fd_cond 0
% 3.76/1.20 % fd_pseudo_cond 0
% 3.76/1.20 % AC symbols 1
% 3.76/1.20
% 3.76/1.20 % ------ Schedule UEQ
% 3.76/1.20
% 3.76/1.20 % ------ Option_UEQ Time Limit: 10.
% 3.76/1.20
% 3.76/1.20
% 3.76/1.20 % ------
% 3.76/1.20 % Current options:
% 3.76/1.20 % ------
% 3.76/1.20
% 3.76/1.20
% 3.76/1.20 %
% 3.76/1.20
% 3.76/1.20 % ------ Proving...
% 3.76/1.20 %
% 3.76/1.20
% 3.76/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 3.76/1.20
% 3.76/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.76/1.20
% 3.76/1.20
%------------------------------------------------------------------------------